The spectral and temporal variability of the isolated X-ray pulsar RX J0720.4-3125 = Untersuchung der spektralen und zeitlichen Variabilität des isolierten Röntgenpulsars RX J0720.4-3125 [[Elektronische Ressource]] / Markus Matthias Hohle. Gutachter: Ralph Neuhäuser ; Joachim Trümper ; Fred Walter
136 Pages
English

The spectral and temporal variability of the isolated X-ray pulsar RX J0720.4-3125 = Untersuchung der spektralen und zeitlichen Variabilität des isolierten Röntgenpulsars RX J0720.4-3125 [[Elektronische Ressource]] / Markus Matthias Hohle. Gutachter: Ralph Neuhäuser ; Joachim Trümper ; Fred Walter

Downloading requires you to have access to the YouScribe library
Learn all about the services we offer

Description

The spectral and temporal variabilityof the isolated X-ray pulsarRX J0720.4-3125Untersuchung der spektralen und zeitlichenVariabilitat des isolierten R ontgenpulsarsRX J0720.4-3125A thesis submitted for the degree ofdoctor rerum naturalium (Dr. rer. nat.)th2010 September 29presented to the council of the Physikalisch-Astronomische Fakultat derFriedrich-Schiller-Universitat JenaDipl. Phys. Markus Matthias Hohlethborn on November 12 1982 in P o neck, Thuringia, GermanyMax-Planck-Institut fur extraterrestrische Physik, Garching, GermanyAstrophysikalisches Institut und Universitatssternwarte derFriedrich-Schiller-Universitat, Jena, Germany1. Reviewer: Prof. Dr. Ralph Neuhauser2. Reviewer: Prof. Dr. Joachim Trump er (Co-referent)3. Reviewer: Prof. Dr. (USA) Fred WalterDay of the defense: January, 27th 2011Signature from head of PhD committee:AbstractThe radio-quiet thermally emitting X-ray pulsar RX J0720.4 3125 belongs toa group of seven isolated neutron stars (often referred to as the \Magni centSeven"). They share similar properties such as pure thermal radiation (blackbody emission with broad absorption features in some cases), long pulse peri-13ods (3 12 s) and high magnetic eld strengths ( B 10 Gauss) on theirsurfaces. These neutron stars are nearby ( 500 pc) and up to a few millionyears old (i.e. relatively young and still hot), thus, most of them have beenidenti ed with dim ( 25 28 mag) blue optical counterparts.RX J0720.

Subjects

Informations

Published by
Published 01 January 2011
Reads 35
Language English
Document size 3 MB

TheofsptheectralandisolatedtempX-raoyralvapulsarriability
J0720.4-3125RX

VaUntersuchungriabilit¨atdesderspisoliertenektralenR¨undontgenpulsazeitlichenrs
J0720.4-3125RX

Athesissubmittedforthedegreeof
doctorrerumnaturalium(Dr.rer.nat.)
th29erSeptemb2010

presentedtothecouncilofthePhysikalisch-AstronomischeFakulta¨tder
Jenaat¨riedrich-Schiller-UniversitF

Dipl.Phys.MarkusMatthiasHohle

bornonNovember12th1982inP¨oßneck,Thuringia,Germany

Max-Planck-Institutf¨urextraterrestrischePhysik,Garching,Germany
AstrophysikalischesInstitutundUniversit¨atssternwarteder
Friedrich-Schiller-Universit¨at,Jena,Germany

1.Reviewer:Prof.Dr.RalphNeuh¨auser

2.Reviewer:Prof.Dr.JoachimTr¨umper(Co-referent)

3.Reviewer:Prof.Dr.(USA)FredWalter

yDa

of

the

defense:

ryJanua,

27th

2011

Signature

from

head

of

PhD

committee:

Abstract

Theradio-quietthermallyemittingX-raypulsarRXJ0720.4−3125belongsto
agroupofsevenisolatedneutronstars(oftenreferredtoasthe“Magnificent
Seven”).Theysharesimilarpropertiessuchaspurethermalradiation(black
bodyemissionwithbroadabsorptionfeaturesinsomecases),longpulseperi-
ods(3−12s)andhighmagneticfieldstrengths(B≈1013Gauss)ontheir
surfaces.Theseneutronstarsarenearby(≤500pc)anduptoafewmillion
yearsold(i.e.relativelyyoungandstillhot),thus,mostofthemhavebeen
identifiedwithdim(25−28mag)blueopticalcounterparts.
RXJ0720.4−3125isuniqueamongthe“MagnificentSeven”asitshowslong
termvariationsinitsspectralproperties(temperature,sizeoftheemittingarea
andequivalentwidthofthebroadabsorptionfeature)andirregularitiesinthe
pulseperiodontimescalesofyears.
Themaintwotheoriesputforwardtoexplainthebehaviourof
RXJ0720.4−3125areeitherfreeprecessionoraglitch−asuddeneventlike
astarquakeoranimpactofamassiveobject,thatreleasedmuchenergyina
time.rtshoInthiswork,mostrecentdatafromnewobservationswithXMM-Newtonand
Chandraaswellasalreadyexistingarchivaldataareanalysed(altogethernow
coveringatimespanofalmosttwentyyears).Whilethespectralchanges
clearlydonotfollowasinusoidalvariationifthenewobservationsareincluded,
thephaseresidualsseemtofollowaperiodicbehaviour.Anupdatedphase
coherenttimingsolutionwasperformedanditwasshownthatforsuchinvesti-
gationsarestrictiontothehardenergybandat400−1000eVismostsuitable
toachievebestagreementbetweenthephaseresidualsderivedfromdifferent
X-rayinstruments.Basedonthenewdata,differenttheoriestoexplainthe
behaviourofRXJ0720.4−3125aremodeled,reviewedanddiscussed,aswell
asphysicalconsequencesoftheconclusionsarepresented.
Themodeloffreeprecessionexplainswellthetimingbehaviourof
RXJ0720.4−3125,butdoesnotsufficientlyreproducethespectralvaria-
tions.However,sinceprecessionexplainsthevariablephaseshiftbetweenhard
(400−1000eV)andsoft(120−400eV)photons,itisstillfavoured;but,now

i

withalongtermperiodof≈14yrs(not7yrsaspreviouslysuspected).The
longtermprecessionperiodwouldcorrespondtoanellipticityof≈2×10−8
fortheneutronstar.
Afterco-addingallXMM-NewtonRGSandChandraHRC-S/LETGdata,three
narrowabsorptionfeatures(amongthem,twowereunknownbefore)arede-
tectedinthespectraofRXJ0720.4−3125.Theseabsorptionfeatureslikely
originatefromhighlyionisedandneutraloxygen.

Derradioleise,thermischstrahlendeR¨ontgenpulsarRXJ0720.4−3125geh¨ort
zueinerGruppevonsiebenisoliertenNeutronensternen(oftalsdie“Glorrei-
chenSieben”bezeichnet),welchesehr¨ahnlicheEigenschaftenaufweisen.Dies
sindreinethermischeStrahlung(Schwarzk¨orperstrahlung,ineinigenF¨allenmit
Absorptionslinien),langePulsperioden(3−12s)undhoheMagnetfelddichten
(B≈1013Gauss)aufihrenOberfl¨achen.DieseNeutronensternesindsehrnah
(≤500pc)undh¨ochstenswenigeJahrmillionenalt(alsorelativjungunddes-
halbnochheiß).Daherwurdeneinigeauchalsleuchtschwache(25−28mag)
identifiziert.QuellenoptischeblaueUnterden“GlorreichenSieben”istRXJ0720.4−3125einzigartig,daseinespek-
tralenEigenschaften(Temperatur,Gr¨oßederemittierendenFl¨acheundTiefe
derbreitenAbsorptionslinie)sowiediePulsperiodeinZeitr¨aumenvonJahren
riieren.vaDiebeidenhaupts¨achlichdiskutiertenTheorien,welchedasVerhaltenvon
RXJ0720.4−3125erkl¨arenk¨onnten,sindfreiePr¨azessionodereinsogenannter
Glitch−einpl¨otzlichesEreignis,wiez.B.einSternbebenoderderEinschlag
einesmassereichenObjektes,welcherinkurzerZeitvielEnergiefreisetzte.
IndieserArbeitwerdenj¨ungsteDatenvonneuestenBeobachtungenmitXMM-
NewtonundChandrazusammenmitschonexistierendenArchivdaten(ins-
gesamteineZeitspannevonfastzwanzigJahren)ausgewertetundunter-
sucht.W¨arenddiespektralenVer¨anderungendeutlichkeinersinusf¨ormigen
Ver¨anderungmehrfolgen,wennmandieneuenBeobachtungenhinzuzieht,
scheinendiePhasenresidueneinemperiodischenVerhaltenzuunterliegen.Eine
aktualisiertephasenkoherenteZeitl¨osungwurdeerhaltenundzeigte,daßeine
BegrenzungaufdasharteEnergieband(400−1000eV)amgeeignetstenist,
umdievonverschiedenenR¨ontgendetektorenerhaltenenPhasenresiduenin
¨Ubereinstimmungzubringen.VondenneuenDatenausgehend,werdenver-
schiedeneTheorien,welchedasVerhaltenvonRXJ0720.4−3125erkl¨aren,mod-
elliertunddiskutiert,sowiederenG¨ultigkeitneubewertetunddiedarausfol-

ii

gendenphysikalischenKonsequenzener¨ortert.

DasModellderfreienPr¨azessionkannzwanglosdaszeitlicheVerhaltenvon

RXJ0720.4−3125erkl¨aren,reproduziertjedochdiespektralenVer¨anderungen

nichtzufriedenstellend.DaallerdingsfreiePr¨azessiondievariablePhasen-

verschiebungzwischenhartem(400−1000eV)undweichem(120−400eV)

Banderkl¨arenkann,istsieimmernochfavorisiert,abernunmiteinerLangzeit-

periodevonetwa14Jahren(stattsiebenJahren,wiezuvorvermutet).Die

Langzeitpr¨azessionsperiodew¨urdeeinerElliptizit¨atdesNeutronensternsvon
≈2×10−8entsprechen.

DurchdasAufaddierenallerXMM-NewtonRGSundderChandraHRC-

S/LETGDatenkonntendreischmaleAbsorptionslinien(darunterzweibisher

unbekannte)indenSpektrenvonRXJ0720.4−3125detektiertwerden.Diese

stammenrptionslinienAbso

Sauerstoff.tralem

sehr

ahrscheinlichw

iii

von

hochionisiertem

und

neu-

iv

Thesis

•Thelongtermspectralchanges(temperature,sizeoftheemittingareaandequivalent
widthoftheabsorptionfeature)oftheyoungisolatedX-raypulsarRXJ0720.4−3125
donotfollowasinusoidaltrend.

•IntheX-rayspectraofRXJ0720.4−3125,inparticularintheChandraHRC-S/LETG
spectra,absorptionfeaturesweredetected.Mostlikely,theabsorptionlinesare
causedbyhighlyionisedoxygen(OVII/OVIorredshiftedOVIIIat0.57keV,red-
shiftedOVII/OVIat0.48keV)andneutraloxygenat0.53keV(likelycausedbythe
interstellarmedium).Thepresuminglyredshiftedlinesyieldagravitationalredshift
ofgr=1.17.

•Thephaseresidualsderivedfromtheobservationsperformedwithdifferentinstru-
mentsareonlycomparableiftheanalysisisrestrictedtoaparticularenergyband.
Thebestagreementisachievedforthehardenergybandof0.4−1.0keV.This
restrictiontothehardenergybandaccountsbestforthedifferentsensitivitiesofthe
instruments.riousva

•Theupdatedtimingsolutionforthehard(0.4−1.0keV)andthesoftenergy(0.12−
0.4keV)bandleadtolargevaluesforthephaseresidualsifthesimplemodelwith
applied.iswnspin-doconstant

•Thephaseresidualsarereducedifaglitcheventisaddedtothesimpletimingsolution.
However,theglitchsolutionfrompreviousauthorshastobemodified.

•ThephaseresidualsalsoreduceifitisassumedthatRXJ0720.4−3125isafree
precessingneutronstarwithalongtermperiodof14years.Freeprecessionalso
explainsthevariablephasedifferencebetweenthehardandthesoftenergyband.

v

vi

ur¨F

meine

lieb

e

vii

kleine

Leonie.

Acknogementsedlw

Thisworkhasbenefitedfromthesupportandinvolvementofmanypeopleinvarious
regards,thusIamdeeplyindebtedtothem.

SincerethanksaregiventoFrankHaberlforsuggestingandmentoringthisthesis,
aswellasforthepleasantcollaborationinthepastthreeyears.Ihavelearnedplenty
ofimportantthingsinthistime.Theintroductioninthenewsubjectwassimplified
sinceheprovidedmehissoftwarefortheXMM-Newtondatareduction.
IammuchobligedtoRalphNeuh¨auser,whosignificantlysupportedmyscientific
career.Iliketothankhimforhisopennessandawarenessalsoregardingprivate
requests.Thelatteralsohelpedmetoovercomeahardstrokeinmyfamily.
DuringmyvisitsinGarchingIalwaysfeltwelcomed,thusIwouldliketothankthe
X-raygroupforthepleasanttime.
IliketothankBirgitBollerandMonikaM¨ullerforthesupporttoovercomediverse
administrativethingsandIthankMarionLamprechtforthecheerfulaccommodation
duringmystaysattheMPE.ThankstoHaraldBaumgartnerandJ¨urgenWeiprecht
whocaredforthecomputationalsupportattheMPEinGarchingandtheAIUin
.ectivelyrespJena,Inthepastfouryears,sinceIamattheAIUinJena,itwasapleasuretoworkwith
manycolleagues,someevenbecamefriends.Iwouldliketothankthemforthegreat
time.DuringmyworkonneutronstarsIlearnedalotfromsharingknowledgeandideas
withotherscientists.InthisregardIwouldliketoacknowledgemyco-authors
RobertoTurollaformanyfruitfuldiscussionsandideas,JaccoVinkinparticular
forhissupportregardingtomyfirstXMM-Newtonproposal,SilviaZane,Mariano
M´endezandCordeVries.InthisregardmysincerethanksaregiventoSergeiPopov.
IliketothankTheodorPribullaforfittingthephaseresidualswithorbitalmotion
causedbyacompanionwithhiscodeandthanksaregiventoBettinaPosseltforthe
fruitfulcollaborationregardingtheSpitzerandHubbleproposals.
IwouldliketothankThomasEisenbeißforthecollaborationregardingtheV-band
magnitudeofRXJ0720.4−3125andValeriHambaryanforusefulreferencesforperiod
rithms.algodetectionThanksaregiventotherefereesforcarefulreadingandreviewingofmythesis.

viii

IwouldliketothankaswellAndreasBauswein,RolandDiehl,WalburgaFranken-
huizen,HovikGrigorian,ThomasJanka,OlegKargaltsev,EwaldM¨uller,George
Pavlov,ArmenSedrakian,MartenvanKerkwijkandFredWalter.
IalsoliketothanktheMax-Plancksociety,inparticularG¨untherHasinger,for
thefinancialsupportofmywork,andtheDeutscheForschungsgesellschaft(DFG)
throughtheSonderforschungsbereichf¨urGravitationswellenastronomieSFB/TR-7.
ThanksaregiventoDavidBlaschkewhoinvitedmetovarioussummerandwinter
schools,whereIgotacquaintedwithmanyimportantthingsandplacesandwho
broughtmeincontactwithimportantpeople.Theseschoolsarefinanciallysupported
throughtheHelmholtzsocietyandCompStarviatheEuropeanScienceFoundation
(ESF).IdeeplythankmyparentsAngelaandMatthias,mysisterIsabelandmygreatlove
NinafortheirloveandsupportIexperienced,inparticularduringthehardesttimes
Ihad.Withoutyou,Iwouldnothaveachievedalotofthings.

DieseArbeithatinmehrfacherHinsichtvonderUnterst¨utzungundMitwirkungvieler
Menschenprofitiert,denenichzuDankverpflichtetbin.

MeinherzlicherDankgiltFrankHaberlf¨urdieBereitstellungdesThemasunddie
BetreuungmeinerDoktorarbeitsowief¨urdievertrauensvolleZusammenarbeitinden
zur¨uckliegendendreiJahren.VieleshabeichindieserZeitgelernt.DerEinstiegindas
neueThemawurdemirdurchdieBereitstellungseinerQuelltextezurVerarbeitung
derXMM-NewtonDatenenormerleichtert.
Ichm¨ochtemichaufrichtigbeiRalphNeuh¨auserbedanken,dermeinewis-
senschaftlicheLaufbahnvonBeginnaninvielf¨altigerWeiseunterst¨utzthat.Dazu
z¨ahleichauchseineOffenheitundSensibilit¨atgegen¨uberpers¨onlichenBelangen.
Letztereshalfaucheinenschwerenfamili¨arenSchicksalsschlagzu¨uberstehen.
BeimeinenBesucheninGarchinghabeichmichstetssehrwillkommengef¨uhlt.Da-
herm¨ochteichmichf¨urdieangenehmeArbeitsatmosph¨arebeiderR¨ontgengruppe
desMPEinGarchingbedanken.
IchbedankemichbeiBirgitBollerundMonikaM¨ullerf¨urdieHilfebeiderBew¨alti-
gungmannigfaltigerorganisatorischerDingeundbeiMarionLamprechtf¨urdieher-
zlicheUmsorgungwa¨hrendmeinerBesucheamMPE.DankgiltauchHaraldBaum-
gartnerundJ¨urgenWeiprechtf¨urdieBetreuungderRechentechnikamMPEin
Garchingbzw.amAIUinJena.
W¨ahrendmeinervierJahreamAIUinJenasindmirvieleKollegenansHerzgewach-
senundeinigezuFreundengeworden.Ihnenseif¨urdiesch¨oneZeitundguteZusam-
gedankt.eitrbmena

ix

ImLaufemeinerArbeit¨uberNeutronensternekonnteichvielvonderBereitschaft
WissenundIdeenzuteilenundauszutauschenlernen.DabeiseimeinenCo-Autoren
RobertoTurollaf¨urvieleanregendeDiskussionenundIdeen,JaccoVinkinsbeson-
deref¨urdieHilfebeimeinemerstenXMM-NewtonAntrag,SilviaZane,Mariano
M´endezundCordeVriesgedankt.IndiesemZusammenhangm¨ochteichmich
auchganzbesondersbeiSergeiPopovbedanken.IchbedankemichbeiTheodor
Pribullaf¨urdasFittenderPhasenresiduenmitderOrbitbewegungverursachtdurch
einenBegleitermitseinemProgrammundDankgeb¨uhrtauchBettinaPosseltf¨urdie
fruchtbareZusammenarbeithinsichtlichderSpitzer-undHubbleantr¨age.Ichm¨ochte
michbeiThomasEisenbeißf¨urdieZusammenarbeit¨uberdieV-Band-Magnitudevon
RXJ0720.4−3125undbeiValeriHambaryanf¨urwichtigeHinweisebez¨uglichAlgo-
rithmenzurPeriodendetektionbedanken.
AllenGutachternseif¨urdassorgf¨altigeLesenundbewertenmeinerArbeitgedankt.
DesWeiterenm¨ochteichmeineDankbarkeitgegen¨uberAndreasBauswein,Roland
Diehl,WalburgaFrankenhuizen,HovikGrigorian,ThomasJanka,OlegKargaltsev,
EwaldM¨uller,GeorgePavlov,ArmenSedrakian,MartenvanKerkwijkundFred
WalterzumAusdruckbringen.
MeinDankgiltderMax-Planck-Gesellschaft,hierbeiinsbesondereGu¨ntherHasinger,
f¨urdieFinanzierungmeinerArbeit,undderDeutschenForschungsgesellschaft(DFG)
durchdenSonderforschungsbereichf¨urGravitationswellenastronomieSFB/TR-7.
IchbedankemichbeiDavidBlaschkef¨urdieEinladungenzuverschiedenenSommer-
undWinterschulen,aufdenenichvielgelernt,gesehenundwichtigeKontakte
gekn¨upfthabe.DieseSchulenwurdenvonderHelmholtz-GesellschaftundCompStar
¨uberdieEuropeanScienceFoundation(ESF)erm¨oglicht.
IchbedankemichvonganzemHerzenbeimeinenElternAngelaundMatthias,meiner
SchwesterIsabelundmeinergroßenLiebeNinaf¨urihreLiebeundUnterst¨utzung,
dieichvorallemauchindenschwerstenZeitenerfahrendurfte.Ohneeuchh¨atte
ichvielesnichterreichenk¨onnen.

x

Contents

FiguresofList

TofListables

UnitsofList

ductionIntro11.1Thediversityofneutronstars........................
1.2Observablepropertiesofneutronstars....................
1.2.1Agesandmagneticfields......................
1.2.2Radiiandtemperatures.......................
1.2.3Composition,structureandtheirconstraintsfromobservations..
1.3Abriefoverviewonthe“MagnificentSeven”................
1.4RXJ0720.4−3125..............................
1.4.1Spectralandtemporalvariations..................
1.4.2Interpretingthespectralandtemporalvariations..........

reductiondataandData22.1ROSAT....................................
2.2XMM-Newton................................
2.2.1EPIC-pn...............................
2.2.2EPIC-MOS1andEPIC-MOS2....................
2.2.3RGS1andRGS2...........................
2.2.4ReductionofXMM-Newtondata..................
2.3Chandra...................................
2.3.1HRC-S/LETG............................
2.3.2ACIS-CC...............................
2.3.3ReductionofChandradata.....................

xi

xv

xvii

xix

1133457101012

1717182021212225252627

CONTENTS

3

4

5

6

timingrPulsa3.1Phasecoherenttiming............................
3.2Algorithmsforperioddetections.......................
23.2.1Ztest................................
n3.2.2Cashstatisticsandmaximumlikelihood...............
3.2.3Stringlength.............................
3.3Whythehardband?.............................

Results4.1Spectralproperties..............................
4.1.1EPIC-pn...............................
4.1.2EPIC-MOSandRGS.........................
4.1.3ChandraHRC-S/LETG.......................
4.2Timing....................................
4.2.1Individualperiods,lightcurvesandphasedetermination......
4.2.2Timingsolutions...........................

Discussion5.1Updatedinterpretationofthespectralandtemporalvariationsof
RXJ0720.4−3125..............................
5.1.1Precession..............................
5.1.2Theglitchhypothesis........................
5.1.3Tkachenkowaves..........................
5.1.4Circumstellarand/orfallbackdisk..................
5.1.5Orbitalmotion............................
5.2Phaseresolvedspectroscopy.........................

Modellingafreeprecessingneutronstar
6.1Themodel..................................
6.1.1Thegeometryoftheproblem....................
6.1.2Physicalinput............................
6.1.2.1Lightbendingandlightemission.............
6.1.2.2Temperaturedistributions.................
6.1.2.3Freeprecession......................
6.1.3Testofthecodeandevaluationofdifferentemissiongeometries..
6.2Procedureandfitresults...........................
6.2.1Fittingthephaseresiduals......................
6.2.2Fittingthetemperaturevariations..................

xii

29030331313233

3737373942464649

5757575961636567

7172727272747476778385

rySumma7

okoutloandConclusions8

References

CONTENTS

87

89

91

ATimeofarrivals(TOAs)ofthefinaltimingsolutionandindividualPeriods97

103PhDduringPublicationsBB.1Scientificpapers...............................103
B.2AcceptedproposalsforobservationslistedintheADS...........105
B.3ConferencecontributionsandproceedingslistedintheADS........105

107alksTCC.1Scientifictalks................................107
C.2Publictalks..................................108

DTeachingandsupervising

vitaeCurriculumE

xiii

109

111

CONTENTS

xiv

FiguresofList

1.11.21.31.41.51.6

2.12.22.32.42.52.62.7

3.13.23.33.4

4.14.24.34.44.54.6

˙TheP−Pdiagram..............................
SetofdifferentEquationsofStateintheradius-massdiagram.......
Thephaseshiftbetweenthetotalfluxandthehardnessratioof
RXJ0720.4−3125...............................
Variationofblackbodytemperature,equivalentwidthandradiusof
RXJ0720.4−3125...............................
TheXMM-NewtonspectraofRXJ0720.4−3125withthelowestandhighest
measuredtemperatures............................
PhaseresidualsofRXJ0720.4−3125.....................

EPIC-pndetector...............................
EPIC-MOSdetector.............................
TheRGS2spectrumofRXJ0720.4−3125..................
RGS1spatialandenergydispersionplot...................
ZerothorderofRXJ0720.4−3125fromHRC-S/LETG...........
FirstordersofRXJ0720.4−3125fromHRC-S/LETG............
ImageofRXJ0720.4−3125fromACIS-CC.................

2812131415

20212223232526

PeriodogramfromtheXMM-Newtonobservationrevolution1454.....33
StringlengthperiodogramfromtheXMM-Newtonobservationrevolution145434
Phaseresidualsofthehardband......................35
Phaseresidualsofthesoftband.......................35

LongtermvariationsoftheEPIC-pnspectraofRXJ0720.4−3125.....40
AllXMM-NewtonEPIC-pnspectraofRXJ0720.4−3125..........41
Theco-addedRGS1spectrumofRXJ0720.4−3125.............42
ThetemperatureevolutionofRXJ0720.4−3125includingthemostrecent
XMM-NewtonandChandraobservations...................44
TheChandraHRC-S/LETGspectraofRXJ0720.4−3125..........45
Theco-addedHRC-S/LETGspectrumofRXJ0720.4−3125........46

xv

FIGURESOFLIST

4.7Thefitresidualsfromtheco-addedHRC-S/LETGspectra..........47
44.8Individualperiodsfromobservationswithmorethan10photons(hardband).50
˙4.9Evolutionoff,periodandphaseresidualsduringtheiterativeprocessap-
proachingthefinaltimingsolution......................51
4.10PhasebinnedlightcurveoftheXMM-NewtonEPIC-pnobservationrevolu-
tion1086...................................52
4.11Fouriercoefficientsfromthelightcurvesofthe16XMM-NewtonEPIC-pn
observationsofRXJ0720.4−3125......................53
˙24.12TheZvaluesintheP−fplane......................54
14.13PhaseresidualsofRXJ0720.4−3125afterapplyingthetimingsolution...54

5.1PhaseresidualsofRXJ0720.4−3125afterapplyingthetimingsolution
shownwithsineandabs(sine)fits......................60
5.2ThestringlengthsderivedfromthephaseresidualsofRXJ0720.4−3125..61
5.3ThephaseresidualsofRXJ0720.4−3125afterapplyingtheglitchsolution.62
5.4SEDofRXJ0720.4−3125...........................64
5.5OrbitalfitofthephaseresidualsofRXJ0720.4−3125...........66
5.6Phaseresolvedevolutionoftemperatureandequivalentwidthof
RXJ0720.4−3125...............................68

6.1Thegeometryofarotatingsphere......................73
6.2Thedifferenttemperaturedistributionsusedinthiswork..........75
6.3Freeprecession................................76
6.4Syntheticlightcurvesofarotatingspherewithtwoantipodalhotspots(I).78
6.5Syntheticlightcurvesofarotatingspherewithtwoantipodalhotspots(II).79
6.6Syntheticlightcurvesofarotatingspherewithtwoantipodalhotspots(III).80
6.7Thepulsedfractiondependingontheinclinationandθ...........81
6.8RelativenumberofpossiblegeometricconfigurationsofRXJ0720.4−3125.82
6.9Fittedphaseresiduals.............................83
6.10Fittedtemperaturevariation.........................84
6.11Fittedtemperaturevariationandphaseresiduals..............86

xvi

ablesTofList

1.1Theinnerstructureofaneutronstar.....................7
1.2Propertiesofthe“MagnificentSeven”...................11

2.1ROSATobservationsofRXJ0720.4−3125..................18
2.2XMM-NewtonobservationsofRXJ0720.4−3125...............19
2.3ChandraobservationsofRXJ0720.4−3125..................27

4.1FitmodelforRXJ0720.4−3125.......................39
4.2SpectralchangesofthephaseaveragedEPIC-pnspectraofRXJ0720.4−3125.39
4.3ThethreenarrowabsorptionfeaturesofRXJ0720.4−3125detectedwith
ChandraHRC-S/LETG...........................46
˙4.4Periodandfderivedfromdifferentmethodsinthiswork,comparedto
previousresults................................50

5.1Fitresultsfromfittingthephaseresidualswithasineorabs(sine).....
5.2OrbitalelementsafterfittingthephaseresidualsofRXJ0720.4−3125...

A.1AllobservationsofRXJ0720.4−3125withTOAsandindividualperiods
listedinchronologicalorder..........................

xvii

5965

98

LIST

OF

ABLEST

xviii

UnitsofList

SinceitismorepracticalinastrophysicstouseSIunitsscaledtoastronomicalvaluesand
itismorecommontousecgsunits,alistofthescaledandcgsunitsthatareusedinthis
work,expressedinthekgssystemisgivenhere(valuesgivenwiththeir1σerrors).

•1AU(astronomicalunit;scaledtotheaveragedistancebetweenSunandEarth)
1AU=1.49597870700(3)×1011m

•1pc(parsec;thedistancethatisrequiredforanobjecttohaveaparallaxangleof
onearcsecondwithrespectto1AU)
1pc=3.085678×1016m≈2.062648×105AU

•1M(Solarrestmass)
1M=1.98892(25)×1030kg

•1MJ(Jovianrestmass)
1MJ=1.8986(25)×1027kg≈1/1047M

•1eV(electronvolt;amountofkineticenergygainedbyafreeelectroninanelectric
volt)1inghavfield1eV=1.60217653(14)×10−19J
•1erg=1gcm2/s2=10−7J=10−7kgm2/s2

•1Gauss=1Vs/cm2=10−4T=10−4Vs/m2
•MJD(modifiedJuliandate)countsthedaysfromNovember17th1858,0:00a.m.

Note,thegravitationalredshiftgrinthisworkfollowsthedefinition
12rcgr=1−2GM.
Oftenthegravitationalredshiftisgivenas

xix

(1)

List

in

of

the

Units

literature

as

well.

gr

=

1−1

xx

2GM2

cr

1

(2)

1

onductiIntro

1.1Thediversityofneutronstars

SincethereportofthefirstneutronstardiscoveredbyJocelynBell[46]in1968,almost
2000moreneutronstarswerefounduptonow.Afurthermilestonewasthediscoveryof
thefirstbinarypulsar[53]duetopulsartimingbyJosephHootonTaylorJr.andRussell
Hulsein1974.Thisextremelyrareconfiguration(nowadaysonlyninebinarypulsarsare
known,see[118])enablesustoprobegeneralrelativityandwasafirstindirectproofforthe
existenceofgravitationalwaves.Theaccordancebetweenthepredictedandtheobserved
behaviouroftheorbitalelementsisastunningconfirmationofEinstein’stheory(see[119]
forareview).Moreover,forthefirsttimeneutronstarmassescouldbemeasureddirectly.
Mostmassesoftheknownbinarypulsarsareclosetothecanonicalvalueof1.4M[118]
andmeasuredwithanaccuracybetterthan1%insomecases.Later,thesametechnique
helpedtodetectthefirstobjectswithplanetarymassesorbitinganobjectwithstellarmasses
outsidetheSolarsystembyAleksanderWolszczanandDaleFrailin1992−theso-called
pulsarplanetsaroundPSR1257+12[140].
Alltheseneutronstarsareradiopulsarsthatbuildbyfarthelargestclassofneutronstars.
MostradiopulsarshavedipolemagneticfieldstrengthsofB≈1012Gaussandspinperiods
Pintheorderofasecond.Theagesrangefromafewthousandyearsuptosomehundred
millionyears(Myrs).Withsomesimplificationsaneutronstarcanbeseenasarotating
dipole,thusradiatingenergyandslowlyspinningdown(seenextsection).Thiscanbe
measuredbythetimederivativeoftheperiod,P˙.Ifradiopulsarsarerepresentedinthe
P−P˙diagram,theyroughlyoccupythesameregion,seefigure1.1.
InthebottomleftcorneroftheP−P˙diagramonecanidentifyanotherpopulation,the
millisecondpulsars.Mostmillisecondpulsarsarecomponentsofbinarysystems.They
gainedmomentumduetomassaccretionfromtheirstellarcompanionandthusspunupin
thepast.Withtime,neutronstarscooldownand/ortheradiosignalgetsweaker,hence,

1

INTRODUCTION1.

Figure1.1:TheP−P˙diagramofallneutronstarsforwhichthesequantitiesareknownwith
linesofconstantcharacteristicage(dotted,derivedfromequation1.6)andconstantdipole
magneticfieldstrength(dashed,derivedfromequation1.4).Thedataforthe“Magnificent
Seven”(M7)1aretakenfrom[38;65;66;67;127],allotherdataaretakenfromtheATNF
database[85].RXJ0720.4−3125(RXJ0720)ismarkedasaredstar.

theybecomeinvisiblebutlatercanbeobservedduetotheiraccretion.Theseobjectsare
called“recycledpulsars”.Althoughtheaccretingmillisecondpulsarsalsoemitinother
wavelengthsthanradio,theywillalsobenamedradiopulsarsinthiswork.
ThelaunchofX-rayandγ-raytelescopesinthelastdecadesopenedanewwindowto
neutronstarscienceandallowedtodiscovernewclasses(see[102]andreferencestherein
eview).rarfoOneofthesenewclassesarethesoftgammarepeaters(SGR).Theyhavespinperiodsof
afewsecondsandareconsideredtobeyoungobjects(someofthemareassociatedwith
supernovaremnants)andburstinγ-rays.SomeSGRsshowquasiperiodicoscillations
duringgiant(luminosity≥1043erg/s)flareswithfrequenciesofabouttensofHertz(Hz).
VerysimilartotheSGRsaretheanomalousX-raypulsars(AXPs)sinceSGRsinquiescence
havethesameproperties.AXPshavespinperiodsofafewsecondsandseveralshowa
hardtail(10−150keV)intheirspectra.Probably,SGRsandAXPsaredifferentstagesor
manifestationsofthesameclassofobjects.Bothhavemagneticfieldsof≈1014Gaussand
theX-rayluminosityisseveralordersofmagnitudeslargerthantheenergylossfromthe
1http://www.atnf.csiro.au/research/pulsar/psrcat/;fromMay1st,2010

2

1.2Observablepropertiesofneutronstars

spin-down,andlikelyoriginatesfromthemagneticfielddecaywhencethetermmagnetars.
Rotatingradiotransients(RRATs)areneutronstarsthatemitshortburstsintheradio
band.ThatmakesitchallengingtomeasuretheirPandP˙.SincetheRRATsroughly
occupythesameregionastheradioquiet“MagnificentSeven”(hereafterM7)inthe
P−P˙diagram,aconnectionofbothisdiscussedwithinthecommunity.TheM7will
bewidelydiscussedinsection1.3.NotethatAXPs/SGRs,RRATsandtheM7aremuch
differenttotheordinaryradiopulsarssincetheyarehighlymagnetisedandmostofthem
areknowntoemitinoptical,X-rayandγ-rays.

1.2Observablepropertiesofneutronstars

fieldsmagneticandAges1.2.1Assumingthatthemainenergylossofapulsariscausedbytheradiationfromarotating
dipolefield,asproposedby[95],thelossofrotationalenergy
dErot=Iωω˙(1.1)
dt

equalsthatofarotatingdipole

dEBB2dipR6ω4sin2α
dt=−6c2,(1.2)
whereωisthespinfrequency,Bdipthemagneticfieldstrengthatthemagneticpole,Rthe
radiusoftheneutronstar,Iitsmomentofinertia,αtheanglebetweenrotationaxisand
magneticpoleaxisandcisthespeedoflightinvacuum.
Settingequation1.1equaltoequation1.2leadstoanequationwiththegeneralform

ω˙=const×ωn(1.3)
wherenisthebrakingindexwithn=3inthecaseofadipole.
Fromequation1.1andequation1.2anexpressionforBdipcanbederivedusingtypical
valuesofR=10kmandM=1.4M,

Bdip≈3.2×1019PP˙Gauss.(1.4)
Chargedparticlesmaygiverisetospectralfeaturesrelatedtocyclotronabsorption.Gravi-
tationalredshiftedcyclotronlinescouldbemeasuredattheenergy
1eBEp=mpc1−rs/R(1.5)

3

INTRODUCTION1.

wherempisthemassoftheparticle,eistheparticlecharge(equalstheelementarycharge
forprotons,electronsandpositrons),isthereducedPlanck’sconstantandrsisthe
Schwarzschildradius.Equation1.5deliversanalternativeestimatetoequation1.4forthe
strength.fieldmagneticSincetheneutronstarspinsdownandassumingthattheinitialspinfrequencyismuch
largerthanthepresentone,thecharacteristicageisgivenby

τ=n−11PP˙(1.6)
derivedfromintegratingequation1.3.Equation1.6andequation1.4areusedforthelines
ofconstantagesandconstantmagneticfieldsinfigure1.1.
However,iftheneutronstarisnotspherical,buthasanon-axisymmetricshapewiththe
ellipticity1,thelossofmomentumduetogravitationalradiationfromthegravitational
quadrupoleterm(assumingahomogeneousdensity)is

dEGW=32GI22ω6(1.7)
5c5dtwhereGisthegravitationalconstant,andmighthavevaluesof10−9to10−6[97].With
thecontributionfromequation1.7,thebrakingindexcouldbeupton=7[139].Inreality
thebrakingindexisinfluencedbyacombinationofdipoleandgravitationalradiation.The
measuredvaluesofthebrakingindexfromfivedifferentpulsarsshowthatnvariesatleast
withinafactoroftwo[81],butliesbelown=3,indicatingtheabsenceofgravitational
radiation.Brakingindicesbelown=3aree.g.explainedbypulsarwinds[141;143].
GlitcheschangePandP˙andmimicadifferentage,themagneticfieldisnotaperfect
dipoleandpossiblemotionofthepoleswithrespecttothesurfaceoftheneutronstar
influencesnsignificantly[82].Sincethemagneticfieldissupposedtobemuchstronger
atbirthoftheneutronstar(atleastformagnetars),thermalpropertiesofthecrustand
thestructureofthemagneticfieldarechangingandinfluenceeachother.Thisleadstoa
significantevolutionofthebrakingindexnfromn=2ton=4forneutronstarsyounger
than0.1Myrs,upton=10fora1Myroldneutronstar,see[100],figure10therein.
Inadditiontheremightbesomeothermechanismsinfluencingnandτ.Thereforeτgives
anupperlimitwhiletracingbackyoungandhotneutronstarstotheirassumedbirthsites
giveskinematicagesbelowτ[121;122]thatmightbemorereliable.

eraturestempandRadii1.2.2MeasuredneutronstarmassesfrombinarypulsarsvaryfromM=1.1MtoM=1.4M
[118],whiletheoreticalpredictionsgiveamaximummassofM=2.7M[117]forextreme
1=(I1−I2)/I3

4

1.2Observablepropertiesofneutronstars

EquationsofState(hereafterEoSs).TheexpectedradiiareintherangefromR=8km
toR=12km[75].Inanycase,neutronstarsarerelativisticobjectsandtheradiiseen
fromadistantobserver(R∞)differfromtheintrinsicneutronstarradiifollowing

RR∞=1−rs/R,(1.8)
henceneutronstarsappearlarger.Duetothegravitationalredshiftneutronstarsalso
appearcooleratinfinity,i.e.thetemperatureseenbyadistantobserveris

T∞=T×1−rs/R.
Thus,forablackbodythemeasuredluminosityisgivenby

42L∞=L×(1−rs/R)=4πσR∞T∞,
whereσistheStefan-Bolzmannconstant.

(1.9)

(1.10)

1.2.3Composition,structureandtheirconstraintsfromobserva-
tionsAsthenamesuggests,afirstapproximationtodescribeneutronstarsisacompositionof
pureneutrons.TheEoSofafullydegeneratedpureidealneutrongaswasusedin[94]and
simpleassumptionsalreadydelivertherightmagnitudesformassesandradii.However,
withincreasingdensitytheinteractionsbetweentheparticleshavetobetakenintoaccount
andtheneutronsbecomesuperfluid.Forevenhigherdensitiesneutronsandprotonsmay
turnintoapioncondensateorotherstagesofmatter,suchasdeconfinedquarks.Thus,
neutronstarshavetobetreatedashighlynon-homogeneousobjectshavingashellstructure
−eachshellwithitsownspecialproperties.Sincethisisanownpartofmicro/particle
physics,onlyabriefoverviewoftheissuesimportantforobservationsisgivenhere.
Thegeneralpicture[117]isthataneutronstariscoveredwithafewcentimeterthin
butopticallythickhydrogenatmosphereonthesurface(densityρ≤106g/cm3).The
atmosphereisleftoverfromthesupernovaeventand/orgatheredfromaccretionandmay
alsocontainionisedoxygenandiron[87].Thisatmosphereshouldbeidentifieddueto
dominantabsorptionlinesinthespectra,evenforhighlymagnetisedneutronstars[87].
Thephysicalpropertiesofthesurfaceareaffectedbythetemperatureandthemagnetic
field.Theoutercrust(ρ≤4.3×1011g/cm3)belowtheatmosphereconsistsofheavynucleiwith
alargeneutronfractionandarelativisticdegeneratedelectrongas,likeforwhitedwarfs.In
theinnercrusttheneutronsturnintoasuperfluidgas(ρ≤2×1014g/cm3)thatbecomesa

5

INTRODUCTION1.

superfluidneutronliquidmixedwithsuperfluidprotonsaboveρ=2.5×1014g/cm3.When
aneutronstarisformed,itcoolsdownvianeutrinoemissionandbecomesisothermalafter
≈102yrsbeforeemergingthefollowingneutrinocoolingstage(≈102yrsto105yrs)and
startstocoolviaphotonemissionafterafew105yrs.Sincesuperfluidityhasasignificant
influenceontheheatcapacityandneutrinoemission(thatthemselvesinfluencecooling),
thecriticaltemperature(thatisonlyroughlyknown)toswitchtosuperfluidity,depending
onthedensity,couldbeconstrainedfromobservationsbymeasuringthecurrentneutron
startemperatureanddeterminingitsageiftheneutronstarisyoung(i.e.hot)enoughand
[37].emittingthermallyUptonucleardensity(ρnuc≈2.8×1014g/cm3)thephysicsofnucleon-nucleoninteraction
iswellunderstoodandnucleon-nucleonscatteringisconstrained.However,beyonddensities
aroundρ≈1015g/cm3itisnotclearwhathappens:theneutronsmayformstrangematter
(hyperons,kaonsorfreequarks),orpioncondensatesorevenpurequarkmatter.Ifthe
entirestarconsistsofquarkmatter,itiscalledabarequarkstar(sometimes“quarkstar”
and“strangestar”areusedsynonymously,althoughhyperonsandkaonsbearstrangeness,
too).Ifonlythecoreconsistsofquarksbutthecrustofordinarymatter(neutronsmixed
withprotons),itiscalledahybridstar.Quarkstarsarecurrentlyhypothetic,butinprinciple
theycouldbedistinguishedfromneutronstars[7;8].
Finally,theEoSgivesaconfigurationofthecompactness,i.etheratioofradiusandmass
(R/M),forwhichtheneutronstarisstable.OftenthefunctionofcompactnessR/Mitself
iscalledEoSintheliterature,sincethisisthebasicobservable.Selfboundquarkstarshave
fundamentaldifferenttrajectoriesoftheEoS(i.e.R/M)comparedtoordinaryneutron
starsbecausetheydonotneedgravitationalpressuretostaystable.
Generally,ifthechangeofpressurestronglyinfluencesthedensity,theEoSiscalledsoft,
ifthechangeofpressuredoesnotaffectthedensitymuch,theEoSiscalledstiff,i.e.stiff
EoSsleadtostarswithlargerradiiandmaximummasses.Apossiblestructureofaneutron
starforastiffandasoftEoSislistedintable1.1.
AsmallsetofEoSsisshowninfigure1.2,notethedifferencebetweenneutronstarsand
quarkstars.Inprinciple,thenumberofvalidEoSscouldbeconstrainedbymeasuringthe
radius(e.g.fromcoolingneutronstarsusingequation1.10)andmass(fromtheredshift
ofspectrallines)forasingleneutronstarindependently.However,onlyroughestimates
forlimits(dashedlinesandthelightgreenregioninfigure1.2anddiscussionin[76])are
availableandforbinarypulsarsonlymasses(noradii)aremeasured.

6

1.3Abriefoverviewonthe“MagnificentSeven”
Table1.1:Theinnerstructureofaneutronstar[117]forasoftandastiffEoS.The
bonoundathebriesoundaoftheriesdaiffreerentgiven.layersaBothreneutronmeasuredstawithrsresphaveectatomasstheofsurfaceM=and1.4theM.densitiesThe
EoS,comprespositionectivelyand.ForstructuredetailsforofthethesoftEoSs,andseestiff[117],EoSissectionderived9.3.fromtherein.the“Reid”and“TNI”
EoSstiffEoSsoftouteratmospherecrust(?)outeratmospherecrust(?)
ρ≤20×−010.814gkm/cm3ρ≤4.03−×0.10311kmg/cm3
heavyinnernuclei,crustelectronsheavyinnernuclei,crustelectrons
0.8−1.8km0.3−0.9km
ρ=2×1014−5.6×1014g/cm3ρ=4.3×1011−2×1014g/cm3
superfluidneutrons&protons,electronsheavynuclei,electrons,superfluidneutrons
recoouterρ≥0.29−×∼101410g/kmcm3
superfluidneutrons&protons,electrons
recorecoρ=5.6×101.148−−91..893km×1015g/cm3ρ=∼1.1028−×∼101215gkm/cm3
pioncondensate?,solid?,quarkmatter?pioncondensate?,solid?,quarkmatter?
1.3Abriefoverviewonthe“MagnificentSeven”
ThefirstidentifiedandbrightestmemberoftheM7,RXJ1856.4−3754,wasdiscoveredby
[135]inROSATdata.Aftertheidentificationofanopticalcounterpart[134]andthedirect
measurementofthetrigonometricalparallax[133],itwasquiteclearthatRXJ1856.4−3754
isaneutronstar.Sincethen,sixfurthersuchobjectswerediscoveredinROSATdatasoon,
butthenumberoftheseobjectsremainedconstantsince2001[147].Onlytwofurther
candidates[99;113]1werepublishedbynow.However,severaldozensofsuchobjects
shouldbestillhiddeninROSATdata,aspredictedbypopulationsynthesisstudies[104].
OftentheM7arecalledXDINS,i.e.X-raydimisolatedneutronstarsalthoughtheyare
actuallybrightinX-raybecauseoftheirproximity.SomeoftheM7spectrashowoneor
twobroadabsorptionfeatures.Thesefeaturesaresupposedtobecyclotronresonances
fromchargedparticles(protons,electrons),thusitispossibletoinferthemagneticfield
strengthboth,fromequation1.5andequation1.4sincePandP˙isknownformostM7.
Indeed,magneticfieldstrengthswithvalues≈1013Gaussfromthedifferentmethodsare
ingoodagreement(regardingthesimplicityoftheassumptionsasdiscussedintheprevious
section)fortheindividualsources,iftheabsorptionfeaturesarecausedbyprotoncyclotron
most1likRecentlyelya,therecycledobjectpulsarcalledwithap“Calvera”eriodof[113]0.059wass[152].confirmedtobeanisolatedneutronstar,butitis
7

INTRODUCTION1.

Figure1.2:Stablemass-radiustrajectoriesfromdifferentEoSs(blacklines,greenlinesfor
selfboundquarkstars).Thefigureisobtainedfrom[76],figure2therein.Forthenotation
anddetailsoftheEoSssee[76].TheorangelinesgiveR∞accordingtoequation1.8.The
upperleftregionsarenotpermittedfromtheradiusbeingsmallerthanrs(GR),central
pressureisalwaysfinite(P≤∞)andbycausality.

resonances.However,theoriginofthesefeaturesisactuallyunclear.
TheM7areeitherradioquietorradioemissiondetectionsareambiguousorcouldnotbe
confirmed[56;71;83;84].However,theM7exhibitX-raypulsationsbetween3sand12s.
Suchlongspinperiodsleadtonarrowradiobeams,decreasingtheprobabilitytoobserve
aradiopulse.AllM7areisolated,i.e.theyarenotassociatedwithasupernovaremnant,
donotbelongtoabinarysystemandnocompanionsarefoundsofar[105].Fromthe
characteristicage(equation1.6),thekinematicage[122]andfromcoolingcurves[36;37]
agesofafewMyrsorevenlessarederived.Inmostcases,theM7wereidentifiedwithfaint
blueopticalcounterparts.Intriguingly,allofthem(ifmeasured)exhibitanopticalexcess,
theiropticalfluxexceedsbyafactoroftentothirty(RXJ2143.0+0654)theextrapolation
atlowenergiesofthebest-fittingX-rayblackbody,suggestingthattheopticalemission
originatesfromalarger,coolerarea,whiletheX-raysoriginatefromasmaller,hotterpart
ofthesurface.ForRXJ1856.4−3754andRXJ0720.4−3125atrigonometricparallaxcould
bemeasured,fortheotherM7distanceestimatesarederivedfrombrightnessand/orab-
sorptionduetotheinterstellarmedium(ISM)[107].AllM7arecloseby,i.e.locatedwithin
500pc(accordingto[89],themaximumdistanceofRXJ1308.6+2127couldbeupto
700pc,howeveramorerecentandmorereliableestimate[122]yieldsadistancewithin

8

1.3Abriefoverviewonthe“MagnificentSeven”

).cp500TheX-rayspectrafitbestwithpurethermal(i.e.blackbody)radiation.Ifaneutron
staraccretesmatterfromtheISM,itcanbere-heated.Accretionrequiresrelativelydense
phasesoftheISM[11](thatcanbeexcludedfromthelowabsorptionvaluesNH,see
section4.1,derivedfromtheX-rayspectra),lowspatialvelocities(thataretoohighfor
thoseM7,RXJ1856.4−3754andRXJ0720.4−3125,withmeasuredpropermotionsand
parallaxes[68;69;70;91;122;133])and/orlongrotationperiods(thatarestilltooshort
foraccretion[136]eveninthecaseoftheM7althoughtheirspinperiodsarelargecompared
tothosefromotherneutronstars,seefigure1.1).Thus,theM7arelikelycoolingneutron
starsratherthanre-heatedduetoaccretionfromtheISM.
ThebasicobservablepropertiesofallM7arelistedintable1.2.
IftheM7areindeedthermallyemitting,i.e.arecoolingneutronstars,theyofferustheop-
portunitytostudymatteratextremeconditions(densityatnucleardensity,B≈1013Gauss
andtemperaturesaround106K)directly.Sincewecanlookontotheirsurface,spectral
lineswouldenableustomeasurethegravitationalredshifttodeterminethecompactnessof
theobject.Fromknowndistance,luminosityandmeasuredtemperaturetheradiuscanbe
obtainedusingequation1.10,iftheemissionisthatofablackbody.Neverbefore,radius
andmass(i.e.compactness)ofasingleneutronstarcouldbemeasuredatonce.1Anesti-
mateforthecompactnesswouldgiveconstraintsforthevariousnumberofEoSs.Having
ageandtemperature,constraintsforcoolingmodelscouldbederived,suchasinputsfrom
microphysicsandquantummechanics(coolingduetoneutrinoemission,cross-sections,
neutronandprotonsuperfluidityeffects,compositionetc.).
HowimportanttheastrophysicalinputfromtheinvestigationsoftheM7iscanbeseen
fromthehistoryofitsbrightestmember,RXJ1856.4−3754.Afteritsdiscovery,thefirst
measureddistanceofRXJ1856.4−3754waspublishedtobe61−+98pc[131],inferringara-
diusofR∞=3.3km.ThisradiusistoosmallandincompatiblewithanyknownEoS,
evenforthoseusingexoticquarkmatter.Later,havingnewobservations,thedistance
measurementwasrevisedtobetwicethisvalue[133],butstilltheX-rayspectrafitwith
R∞=5.2kmnormalisedtoa140±40pcdistance[16].This,andtheabsenceofpul-
sations[26;111]ledtotheassumptionthatRXJ1856.4−3754isaselfboundquarkstar,
ratherthananeutronstar[26;126;142].However,itisarguedthattheX-rayspectra
systematicallyunderestimatetheradius[133]andtherealvaluewouldbeR∞=11km.A
fewyearslater,thedistanceofRXJ1856.4−3754wasrevisedagaintobe178−+2217pc[89].
Then,followingtheargumentationin[133],theradiuswouldbetoolargeeventofitthe
stiffesthadronic(ordinaryneutronsandprotons)EoS.Nowadays,thedistanceisagaines-
timatedtobe123−+1115pc[132].Inthiscase,theX-rayfluxmayoriginatefromahotpolar
1Forthelow-massX-raybinaryEXO0748−676thegravitationalredshiftgr=1.35wasmeasuredfrom
ironandoxygenlines[18],butcouldnotbeconfirmed.

9

INTRODUCTION1.

cap,i.e.alimitedpartofthesurfacewithR∞=4.4km(note,theemittingareaisnot
necessarilyofacircularshape)andtheopticalexcessiscausedbythecoolersurfaceparts
withR∞=17km[15].Thisissupportedbythedetectionofweakpulsations(pulsed
fraction≈1%)intheX-rays[127].TheM7areoneoftherareclassesofneutronstars
thatarecurrentlyusefultoputconstraintsontheEoSasdiscussedhere.
Surprisingly,theX-rayspectraofRXJ1856.4−3754arefreeofanyspectralfeatures[15;16],
althoughitwasexpectedtofindstrongabsorptionlinesabove0.5keVduetohighlyionised
ironoroxygen(seethedetaileddiscussionin[16]).Moreover,alsotheotherM7donot
exhibitformallyexpectedabsorptionfeatures(exceptthecyclotronlines)fromtheirhy-
potheticatmosphere.Thus,themodelingandunderstandingoftheM7spectraisstill
[87].challenging

1.43125−J0720.4RX

1.4.1Spectralandtemporalvariations
TheneutronstarRXJ0720.4−3125wasdiscoveredby[39]asX-raysource,havinga8.391s
pulseperiodandwasidentifiedwithafaintblueopticalstarin[28;70;74;88].Thedistance
wasdeterminedtobe360−+17090pc[69]fromdirectparallaxmeasurementsusingHubbleob-
servations.AmongtheM7,RXJ0720.4−3125hasauniqueplaceinasmuchitshowssignificantvari-
ationsinitssurfacetemperature,intheequivalentwidthofanabsorptionfeatureseenin
theX-rayspectrumandinthesizeoftheemittingarea[22;38;51]overtimescalesof
years.SuchvariationsareunknownfortheotherM7.
RXJ0720.4−3125exhibitsahardnessratiovariationandaphaseshiftbetweentheflux
andthehardnessratio(bothfoldedwiththe8.391spulseperiod)discoveredby[20]in
XMM-Newtondata,seefigure1.3.Lateron,itwasshown[22]thattheenergy-dependent
changeinthepulseprofileisaccompaniedbyalongtermchangeoftheX-rayspectrum.
Thedependenceofthepulseprofilesontheenergywasconfirmedby[43]andaphase
lagbetweensoft(0.12−0.4keV)andhard(0.4−1.0keV)photonswasalsoreported.A
longtermperiodofPpre≈7.5yrs[41]wasfoundinthespectralvariations(seefigure1.4
1.5).figureandTheconstantspin-downP˙ofRXJ0720.4−3125wasfirstestimatedtobe≈10−14s/sby
[151]andamorerecenttimingsolutionusingfurtherobservationswaspresentedin[19].
Thephasecoherenttimingsolutionsin[63]and[129]havebeencomputedincludingeither
datafromROSAT,ChandraandXMM-Newton(thesocalled“alldata”solution),oralso
ChandradataonlyandalldataexceptROSAT,see[129].Applyingatimingsolutionwith

10

]τyr/-223--mas[5.1058.0.5512.3332.4.
popticalmotionerropmag27=26=≥27=25=27=
8.26]24=1.4.equationfromageracteristicchaThe[]
BVB50ccdBBB
][5.m0.
10ink-−-−.053.-
Myrs54..diptτ.209.3.05.07.7.
2MyrsB≥[dip1814.35..14--35.0.3
.leavailabwhen,B10≤
]G131[inG21..36
kccy6.26.6/4/9-
t]and1.5equationusingcalculatedisdistance
[]634590+105−6700390+1115−215430
B1356.0.≈
108cp−+170−−−−
agekinematicthethanrgerlais˙P13360698.24055.76120..39041.
123[325325ccyB]s/s923-≤−τ10[]s45.039.037.131.88006.043.
?[.8Seven”.“MagnificenttheofertiesProp502231254123212737540654
kPTeV[344−1192101026937639102
95]851.2:ableTthatNote1.6.equationusingcalculatedisObjectJ0420.0RXJ0720.4RXJ0806.4RXJ1308.6RXJ1605.3+3249RXJ1856.4RXJ2143.0RX
ba−−−+−+

11

1.43125−J0720.4RX

107]86;[40;5022:−129]122;69;63;51;43;41;39;[28;3125:−107]65;42;[40;4123:−122]116;115;89;64;[61;2127:+134]133;132;127;122;68;[15;3754:−153]149;147;107;[67;0654:+
J0420.0RXrforef.J0720.4RXrforef.J0806.4RXrforef.J1308.6RXrforef.150]128;122;107;90;[62;J1605.3+3249:RXrforef.J1856.4RXrforef.J2143.0RXrforef.ab
17741223RBSRBS

INTRODUCTION1.

Figure1.3:Thephaseshiftbetweenthetotalflux(0.12−1.2keV,upperpanel)andthe
hardnessratio(HR=Counts0.12−0.4keV/Counts0.4−0.8keV)reportedin[20](seefigure1
thetherein)verticalusinglinetheinbothXMM-Newtonpanels,indicatingobservationthe0078.phaseTheshift.phaseAlloferrorsthearePmaximumoissonisian.shownby

constantspin-downdoesnotonlyleadtovariablephaselagsbetweensoftandhardpho-
tonsintheXMM-NewtonEPIC-pndata,alsothephaseresidualsincludingallobservations
ofRXJ0720.4−3125availableatthistime(untilMJD=53700days,i.e.November12th,
2005)showalongtermvariation,probablyfollowingasine,likeinthespectralchanges
(figure1.4)withasimilarlongtermperiodPpre=7.88±0.01yrs,showninfigure1.6,and
[38].

1.4.2Interpretingthespectralandtemporalvariations
ThesignificantvariationsofRXJ0720.4−3125meritsmoreinvestigationsandtwomain
possibleexplanationswereproposed:RXJ0720.4−3125isafreeprecessingneutronstar
[22;38;41;43],orthebehaviourofRXJ0720.4−3125couldbeexplainedbyaglitchevent
[129].SupposingthattheX-raysoriginatefromhotpolarcapsonRXJ0720.4−3125thatcover
onlyafractionofthemuchcooler(thusinvisibleinX-rays)entiresurface,precessionwould
causeanadvanced(theneutronstarprecessestowardstheobserver)andaretarded(the
neutronstarprecessesbackwardswithrespecttotheobserver)signal,whereastheresiduals
wouldfollowasine[92].Theresidualsarejusttheadditionaltimeneededforaspotto

12

1.4

3125−J0720.4RX

respFigureonding1.4:radiusVaofriationtheofsizeblackofbtheodyemittingtempaeraturereaof(kTRX),J0720.4equivalent−3125widthas(repEoWrted)andinco[43].r-
ThedataobtainedfromXMM-NewtonEPIC-pnobservationsinfullframemodeandthin
filter(seeexplanationinsection2.2)aremarkedasdotsandareusedfortheerrorweighted
sinefit.OpencirclesrefertoXMM-NewtonEPIC-pnobservationsindifferentmodes,see
[41;43].Theerrorsofthedatamarkthe90%confidenceintervals,whiletheerrorsofthe
longtermperiodPprederivedfromthesinefitdenote1σ.

13

1.INTRODUCTION

Figure1.5:TheXMM-NewtonspectraofRXJ0720.4−3125withthelowestandhighest
measuredtemperatures(T=86.5±0.4eVandT=94.7±0.5eVforrevolution0078and
0815,respectively)sofar.ThedotsrepresentthemeasureddatawithPoissonianerrors,the
linescorrespondtothebestfittingmodel(blackbodywithabroadabsorptionfeaturearound
0.3keV),see[22;38;41]fordetails.

appearinthelineofsight(andviceversafortheotherspot).
Duringprecessiontheobserverwouldseedifferentpartsofthesurfacethatwouldcause
changesinthespectralproperties(ifthehotspotsaredifferentintemperatureandsize),if
two,roughlyantipodal,hotspotswouldbothcontributetotheX-rayemission.Thephase
residualscausedfrombothhotspotswouldbeshiftedbyPpre/2:ifonehotspotprecesses
towardstheobserverandappears(orlargerpartsofthespotbecomevisible),thesecond
hotspotmovesbackwardswithrespecttotheobserveranddisappears(orsmallerparts
arevisible).Sincethetiminganalysisisnotsensitivetowhichofthehotspotsiscausing
theresiduals,thephaseresidualsqualitativelymayhavetheshapeofanabs(sine),having
twicetheperiodofthecorrespondingsine(twopeaksfromtwodifferenthotspots).More-
over,thismodelalsowouldexplainthevariablephaseshiftbetweenhard(mainlyemitted
fromthehotterspot)andsoftphotons(mainlyemittedfromthecoolerspot)seeninthe
XMM-NewtonEPIC-pndata.DuringthefirstobservationsaroundMJD≈52000days,the
hardphotonslagthesoftphotons,then,aroundMJD=52800days,thesoftphotonslag
thehardphotons.Unfortunately,onlywithXMM-NewtonEPIC-pndataitispossibleto
dividethephotonsintoahardandasoftbandwithsufficientstatistics(seesection2.2),

14

J0720.4RX1.43125−

Figure1.6:PhaseresidualsofRXJ0720.4−3125derivedfromdifferenttelescopesandde-
tectorsaspresentedin[38]usingthephasecoherenttimingsolution(constantspin-down)
from[63].ThelongtermperiodPpre=7.88±0.01yrsderivedfromtheerrorweightedsine
fitissimilartothatfoundfromthespectralvariations(seefigure1.4).Allerrorsdenote1σ.
NotethesystematicphaseshiftbetweenthesoftandthehardbandintheXMM-Newton
data.EPIC-pn

thusmoredataandanongoingmonitoringofRXJ0720.4−3125isneededtofollowthis
.furtherehaviourbAlternatively,[129]proposedaglitcheventthatoccurredaroundMJD=52800dayscausing
thebehaviourofRXJ0720.4−3125.Aglitchcouldbecausedbyanaccretionevent,anim-
pactofamassiveobject,orastarquakeinthecoolingneutronstarcrust.Aglitchleadsto
ajumpintheperiod,thespinfrequencysuddenlyincreasesandtheneutronstarcontinues
spinningdown.Suchglitchesareknownfrommanyyoungradiopulsarsandcanoccurup
toafewtimesperyear[55;137;146],i.e.arenotunusualforyoungpulsars.Thephase
coherenttimingsolutionincludingaglitchin[129]wellexplainsthetimingbehaviourin
theobservationsavailableatthattime.Itisarguedthataglitchwouldreleaseenergyand
thechangesinthetemperatureareactuallyajump,thatwillbefollowedbyaslow,maybe
exponential,coolinginthefutureandjustlookssinusoidalinthedataavailableatwinter
2005(MJD=53700days).Fromthejumpinthespinfrequencythegainofmomentum
canbeestimatedthatreferstoahypotheticimpactmassof1020−1021g,themassofan
[129].asteroid

15

INTRODUCTION1.

Whiletheglitchhypothesisdoesnotexplainthevariablephaselagbetweenhardand
softphotons(seefigure1.6)andwhythetotalluminosityofRXJ0720.4−3125remains
constant,freeprecession1maycontradicttheoreticalpredictions,sinceitisexpectedthat
neutronstarsconsistofsuperfluidmatterundertheircrust[78].
Precessingneutronstarswouldemitgravitationalwavesaccordingtoequation1.7.
Althoughthegravitationalwaveswithaperiodofafewyearslikeinthecaseof
RXJ0720.4−3125cannotbemeasuredyetandinthenearfuture,provingprecessionwould
showthatsuchclassesofgravitationalwaveemittersthatmaycontributetothegravita-
tionalwavebackground(maybewithmorecapableprecessionperiods)existinprinciple.
Then,assumptionsaboutthephysicsofsuperfluidsinneutronstarshavetobereconsidered
[34].

1Precessionpoweredbyacompanionisalmostcertainlyexcluded,seesection5.1.1

16

2

reductiondataandData

ThisworkhasmadeuseofdifferentX-raytelescopes.Themainscientificresultsare
obtainedwithXMM-NewtonandChandra(both,timingandspectroscopy),andtheROSAT
dataareusedforsomeconsiderationsregardingthetiminganalysis.RXJ0720.4−3125has
alsobeenobservedwithotherX-raytelescopes(e.g.BeppoSaxorEinstein);however,they
didnotcontributeadditionalinformationtothiswork,thusarenotdiscussedhere.
Inordertounderstandtheselectioncriteriaappliedtothedatafromthedifferenttelescopes
inlaterstagesofthework,hereabriefoverviewoftheX-raytelescopes,theirinstruments
andpropertiesisgiven.

2.1TROSA

TheGermanR¨ontgenSatellit(X-raysatelliteROSAT,[124])waslaunchedonJune1st1990
andthemissionwasleadbytheMax-Planck-Institutf¨urextraterrestrischePhysik(MPE).
ROSATworkeduntilFebruary1999.Thefirstsixmonthsafterlaunchweredevotedto
theAllSkySurvey.TheROSATmissiondeliveredfundamentalinsightsintothephysics
ofcompactobjects.Duringthemission,allM7knowntoday[38]werediscovered.X-
rayemissionfromsomeradiopulsarswasalreadydetectedwiththeEinsteinsatellitebut
ROSATgaveaclearerpictureofthefaintX-rayemissionproducedbythecoolingsurface
ofnearbyisolatedneutronstars.
ThetwomaininstrumentsonboardwerethePositionSensitiveProportionalCounter
(PSPC)withafieldofviewoftwodegreesandaneffectiveareaof≈240cm2at1keV;
andtheHighResolutionImager(HRI,[21]),havingafieldofviewof38’withaneffective
areaof≈80cm2at1keV.ThespatialresolutionoftheHRIdenotes2”.Both,PSPC
andHRI,operatefrom0.1−2.5keV.AfurtherinstrumentistheWideFieldCamera
(0.062−0.206keV)thatisnotimportantforthiswork,thusisnotintroducedhere.
Duetolowstatisticsandlowenergyresolution,theROSATdatacouldnotbedividedinto

17

2.DATAANDDATAREDUCTION

Table2.1:ROSATobservationsofRXJ0720.4−3125inchronologicalorder.Fordetailson
[19].seeobservationsTROSAObs.Id.InstrumenttotalcountsMJDStartDateEffective
[days]exp[osureks]
allskysurveyPSPC725481761990Oct11−
rp300338n00PSPC5374492581993Sep273.22
rh300508n00HRI1259501991996Apr253.13
rh180100n00HRI1197502111996May73.57
rh300508n01HRI493503541996Sep271.41
rh400884n00HRI13381503911996Nov333.57
h400944n00HRI3054509241998Apr203.57

twoenergybands,asdoneforXMM-NewtonandChandradata(seenextsections).The
photonsfromthePSPCweretakenfromchannelstento90(100−900eV)andforthe
HRIfromchannelsonetoeight.ThelowcountrateintheROSATdatacausesproblems
fortiming,aswillbeseenlater.ThereducedandbarycentriccorrectedROSATdatawere
adoptedfrom[19].Detailsofthedatareductioncanbefoundtherein.Thephotonarrival
timesintheROSATeventfilesarecountedfromtheindividualobservationday(minus
halfadaytostartatnoon),whiletheXMM-NewtonandChandraphotonarrivaltimes
arecountedfromMJD=50814days(January,1st1998,0:00),thustheROSATphoton
arrivaltimesweremodifiedtofitwiththephotonarrivaltimesfromtheothertelescopes.
AllROSATobservationsofRXJ0720.4−3125arelistedintable2.1.

2.2XMM-Newton

TheXMM-NewtonsatellitecarriesthreeX-raytelescopes[54]andwaslaunchedonDecem-
ber10th1999.Itisthesecondcornerstonemissionofthe“Horizon2000ScienceProgram”
oftheESAandisstillactive.Threemaininstrumentsareonboard:theEuropeanPhoton
ImagingCamera(EPIC),theReflectingGratingSpectrometer(RGS)andtheOptical
Monitor(OM).TheOMisnotrelevantforthethesisandthuswillnotbeintroducedhere.
TheEPICconsistsof3CCDcameras:theEPIC-pn[120]andtwoEPIC-MOS[125]cam-
eras,eachonebehindamulti-mirrortelescope.EachX-raytelescopehasatotalgeometric
mirrorareaof1550cm2,i.e.4650cm2intotal.However,sinceonlyapartoftheincoming
lightfallsontotheMOSdetectors,theeffectiveareasareactuallylowerthanthatofthe
pndetector.TheobservationsofXMM-Newtonareassignedwiththesatelliterevolution
er.numb(“rev.”)

18

XMM-Newton2.2

Table2.2:XMM-NewtonobservationsofRXJ0720.4−3125inchronologicalorder.The
countsofbothRGSaregivenfor0.35−0.9keV.
rev.InstrumentsetupCountsCountsMJDStartDateEffective
(120−400eV)(400−1000eV)exposure
[ks]ys][da0078EPIC-pnFFthin241783115287516772000May1358.60
EPIC-MOS1FFthin696234397761.98
EPIC-MOS2SWthin680104081861.99
48.8915900RGS149.0015481RGS20175EPIC-pnFFmedium10349155743518702000Nov2125.65
EPIC-MOS1LWmedium157651166218.00
30.258711RGS129.137901RGS20533EPIC-pnFFthin13795172150525852002Nov628.38
EPIC-MOS1FFthin279872189229.99
EPIC-MOS2FFthin291692219229.99
29.618541RGS128.877952RGS20534EPIC-pnFFthin14505776095525872002Nov830.18
EPIC-MOS1FFthin281682211231.80
EPIC-MOS2FFthin289542276831.79
31.228764RGS130.228225RGS20622EPIC-pnSWthick12319994655527622003May272.79
EPIC-MOS1FFmedium212041874129.98
EPIC-MOS1FFthin284332375433.59
EPIC-MOS2FFmedium219881965029.99
EPIC-MOS2FFthin309012441333.59
74.7822414RGS174.7221433RGS20711EPIC-pnSWmedium8315160557529402003Oct2724.90
EPIC-MOS1FFthin108411193713.90
EPIC-MOS1LWthin105471176915.71
EPIC-MOS2FFthin116491239213.91
EPIC-MOS2LWthin119431238215.71
44.7714726RGS144.7713477RGS20815EPIC-pnFFthin13068393280531472004May2241.30
EPIC-MOS1FFthin358534117845.21
EPIC-MOS2FFthin359154231845.22
44.9117351RGS144.9116270RGS20986EPIC-pnFFthin181754131146534882005Apr2851.43
EPIC-MOS1SWthin324003647553.05
EPIC-MOS2SWthin344563826653.06
53.1018884RGS153.0818398RGS21060EPIC-pnFFthin175481120913536362005Sep2351.14
EPIC-MOS1SWthin337103707052.76
EPIC-MOS2SWthin339773770652.77
52.8618656RGS152.8317519RGS21086EPIC-pnFFthin167725117828536872005Nov1237.84
EPIC-MOS1SWthin252652709139.46
EPIC-MOS2SWthin250452758039.47
39.5712083RGS139.5510812RGS21181EPIC-pnFFthin8901559524538772006May2220.04
EPIC-MOS1SWthin136521421921.66
EPIC-MOS2SWthin150451504821.66
21.826715RGS121.796125RGS21265EPIC-pnFFthin8985260883540442006Nov520.04
EPIC-MOS1FFthin124141229621.61
EPIC-MOS2FFthin152911465321.62
21.826255RGS121.815789RGS21356EPIC-pnFFthin8941157483542262007May520.04
EPIC-MOS1FFthin166901668521.61
EPIC-MOS2FFthin171471681821.62
21.796588RGS121.785797RGS21454EPIC-pnFFthin10291764833544212007Nov1723.06
EPIC-MOS1FFthin186741819724.62
EPIC-MOS2FFthin190291841624.62
24.816953RGS124.816054RGS21700EPIC-pnFFthin3708530806549132009Mar2110.84
EPIC-MOS1FFthin114811187617.69
EPIC-MOS2FFthin119361155617.69
RGS121.79654521.796719RGS21792EPIC-pnFFthin6540748105550962009Sep2217.90
EPIC-MOS1SWthin125241191919.22
EPIC-MOS2SWthin127241199319.24
19.215368RGS119.215437RGS2

19

2.DATAANDDATAREDUCTION

Figure2.1:ViewontheEPIC-pndetector(120−1200eV)infullframemode(revolution
is0078,RXleft)J0720.4and−3125smallandwindothewbmorightdestreak(revolutioniscaused0622,byright).theThereadoutbrightoftheobjectdetectointher.centreNote,
thatnootherbrightobjectinfluencesthedataintheselectedenergyband.

EPIC-pn2.2.1

TheEPIC-pndetectorisaback-illuminatedCCDchiphavingtwelve(4×3)singlechip
panels,eachofithas64columns(with200pixel,188ofthemareused)withitsown
readoutnode.Generally,thisleadstobettertimeresolutionthanfortheMOS1andMOS2
detectors.TheCCDarrayhasatotalsizeof376×384pixel(188×64foreachofthe
twelvepanels),eachpixelcorrespondsto4.1”.Thereadoutfortheentirechip(fullframe
mode,hereafterFFmode)hasatimeresolutionof73.4ms,whileaspatiallyrestricted
readoutmodeincreasesthetimeresolution.Furtherreadoutmodesarethelargewindow
mode(LW)with48ms(198×384pixel)andthesmallwindowmode(SW,63×64pixel)
with6msreadouttime.TheobservationsperformedwithEPIC-pnaredoneintheFF
andSWmode,seefigure2.1.SinceRXJ0720.4−3125hasaperiodof8.39s,thetime
resolutionoftheinstrumentisfullysufficient.Otherreadoutmodesarethetimingmode
andtheburstmodewithatimeresolutionof0.03msand7µs,respectively.Theeffective
areaofthepndetectoramounts≈1400cm2at1.5keV.
IfaphotonimpactsontheCCDitcausesachargecloudthatisameasureofenergy,
i.e.theEPIC-pndetectorcanbeusedforspectroscopy.RXJ0720.4−3125isarelatively
brightX-raysourceandanimpactoftwolow-energyphotonswithintheCCDframetime
canmimicahigh-energyevent.Thisphenomenoniscalledphotonpile-up.Thepile-up
dependsonthereadoutmode,i.e.decreasesforfasterreadoutmodes.Evenforthefull
framemode,thepile-upisnegligibleforRXJ0720.4−3125.
ToreducetheincidenceofopticallightallRXJ0720.4−3125observationsperformedwith

20

XMM-Newton2.2

Figure2.2:ViewontheMOSdetector(120−1200eV,bothMOSareequal,onlyrotated)
infullframe(revolution0078,MOS1,left),largewindow(revolution0175,MOS1,middle)
andsmallwindow(revolution0078,MOS2,right)mode.

XMM-Newtonaredonewithafilter,wherethethinfilterisfullysufficientinthiscase.
RXJ0720.4−3125wasconsideredtobeaconstantsourcelikeRXJ1856.4−3754andwas
usedforcalibrationissues.Therefore,atthebeginningofthemission,observationsin
mediumandthickfilterweredone.Thickerfiltersmainlyblocksofterphotonsbelow
≈0.4keVcomparedtothethinfilter.
ThebandpassoftheEPIC-pndetectoris0.10−15keV,accordingtopreviouspublications
[38;41;43]photonsfrom0.12−1.2keVwhereusedinthiswork.Thespectralresolution
is≈100eVforsingle-pixeleventsat1.0keVbutgetsworseforlowerenergies.

EPIC-MOS2andEPIC-MOS12.2.2

TheMOSdetectorsarebothfront-illuminatedandconsistofanarrayofsevenquadratic
CCDarrays(onepixelcorrespondsto1.1”).Bandpassandspectralresolutionforthe
MOSdetectorsarecomparabletothepndetector.ThesamesetoffiltersasforEPIC-pn
isavailable.InFFmode(600×600pixel)thetimeresolutionis2.6s,i.e.30%ofthe
pulseperiodofRXJ0720.4−3125.FortheLW(300×300pixel)andtheSW(100×100
pixel)modethetimeresolutionsare0.9sand0.3s,respectively.Afurtherreadoutmode
istheMOStimingmode(1.75ms).AlldataforRXJ0720.4−3125areobtainedfrom
observationsdoneintheFF,LWandSWmode,seefigure2.2.

RGS2andRGS12.2.3

IncontrasttothepnandMOSimagingdetectors,theRGS[23]aregratingspectrometers,
i.e.thedispersionangleoftheincidentlightdependsonthephotonenergy.ForbothRGS
thefirstandsecondordersarerelevant,whilethecountrateinthethirdorderisabout
eighttimeslessthanforthesecondorder.Actually,followingthedesignofthedetector,
the1stand2ndordersarethe−1stand−2ndorders,respectively.Thebandpassesforboth
RGSare0.35−2.5keV(1storder)and0.62−2.5keV(2ndorder).

21

2.DATAANDDATAREDUCTION

Figure2.3:TheRGS2spectrumofRXJ0720.4−3125fromtheXMM-Newtonobservation
reprevolutionresentsthe0078.bestThefitfailmodelureofofachipblackfourboisdyrespwithaonsibleGaussianfortheabsodatarptiongapline,andseethesolidtable4.1line
insection4.1.TheerrorsarePoissonian,seealsofigure1.5forcomparison.

TheRGSaresuitableforhighresolutionspectroscopyofbrightsourceswitharesolution
of3.2eVand2.0eVat1keVforthe1standthe2ndorder,respectively.
DuringtheoperationofXMM-Newton,chipsevenofRGS1(0.90−1.18keV)andchip
fourofRGS2(0.52−0.62keV)failed.WhileRXJ0720.4−3125hasalowcountrate
around1.0keV(seefigure1.5)andthefailureofchipseveninRGS1isnegligible,the
failureofchipfourinRGS2causesasignificantgapinthespectrumofRXJ0720.4−3125
2.3).(figure

dataXMM-NewtonofReduction2.2.4

AtthebeginningoftheworkinDecember2007,13XMM-Newtonobservationsof
RXJ0720.4−3125wereperformedandavailableinthearchive.Fromthese13observations,
thefirst11havebeenreducedandanalysedbefore.InNovember2007,theobservation
duringrevolution1454hadbeenexecuted.These14observationshavebeenanalysedand
reprocessedwiththestandardXMM-NewtonScienceAnalysisSystem(SAS)version7.1.0.
InMarch2009anotherXMM-Newtonobservationwasperformed[130](revolution1700)
andfinallyinSeptember2009themostrecentobservationofRXJ0720.4−3125(revolution

22

XMM-Newton2.2

Figure2.4:Thespatialdispersionplot(upperpanel)andenergydispersion(lowerpanel)
plot(bananaoflikRGS1.ecurvesTheinbluethelineslowerindicapanel)tetheandthedefaultcalibrationextractionsourcregionses(shoforrtthehosourcerizontalphotonsregions
inthelowerpanel).Chipsevenisdefectandexcluded.

Figure2.5:ThezerothorderimageofRXJ0720.4−3125obtainedfromtheChandraobser-
HRC-S/LETG.using5582vation

23

2.DATAANDDATAREDUCTION

1792)couldbeadded[49].ThelasttwodatasetswereanalysedwiththeSASversion
9.0.0,butfollowingthesameprocedureasforthepreviousobservations.Ourteamplans
tocontinuethemonitoringofRXJ0720.4−3125andthelastXMM-Newtonproposal[50]
wasaccepted,butnotexecutedsofar(priorityC).Allobservationsarelistedintable2.2.
Thesoftwarefordatareductionanddatapreparationforspectroscopywereadoptedfrom
FrankHaberl(see[41;43])andthecodeswereonlyslightlymodifiedforMOSandRGS
reduction.dataThepndatawasanalysedusingtheepchaincommand,theMOSdatausingemchain.To
reducethecontaminationofthedatabyincreasedfluxesofsoftprotonsinthesolarwind,
alldatasetspassedthefilteringbytheGoodTimeIntervall(GTI)filesthatweregenerated
duringthestandarddatareductionprocess.However,fortheobservationrevolution1700
bothMOShave30%backgroundflaringtime,whilealmost40%flaringtimeforthepnde-
tectorwasreportedintheobservationprotocol.TheMOSexposureswereinterruptedand
re-started(1.5ksscheduledobservations,afterwards12ksasunscheduled)duringflaring
sothat5kswerefilteredoutbytheGTIfiles,producingsufficientlycleandata.Inthecase
ofpntheobservationwasnotinterruptedandthefirsthalfoftheobservationwashighly
contaminated.TheGTIfilesstillleftcontaminatedtimeintervals,thusforthisobservation
onlythesecondhalfoftheobservationwasusedafterpassingtheGTIfilters.
Finally,fortimingpurposes,thebarycentriccorrection(regardingallleapsecondsadded
duringtheyears)wasappliedandthephotonsweredividedintoasoft(120−400eV)and
ahard(400−1000eV)energyband(seesection3.3).
MostphotonsarerecordedinasingleCCDpixel,butsomeeventsaresplittedbetween
differentCCD-pixels(iftwo“doubles”,ifthree“triples”andiffour“quadruples”)andare
flaggedbydifferentpatternnumbers.Sucheventshavetoberecognisedtoreconstruct
asingleenergyvalue.Note,thathigherpatternsareidentifiedwithpile-up,siliconfluo-
rescenceorcosmicrays(see[120]foramoredetailedexplanation).ForallXMM-Newton
CCDdetectorssingleeventswereusedforspectroscopyandwerecollectedwithinacircular
regionof30”(pn)and8”(MOS)radius(i.e.thesourceplusbackgroundphotons).The
backgroundphotons,neededforbackgroundcorrectionofthespectra,wereobtainedfrom
acircularregionofthesamesize,locatedonthesamechipasthesourcephotons.This
wasnotpossibleforMOSSWobservations,thusthebackgroundphotonsweretakenfrom
chip.ouringneighbaThedatareductionoftheRGSdatawasperformedwiththeSASversionsmentionedabove,
usingthergsproccommand.AftertheapplicationofthestandardGTIfilesthephotons
forthespectrawereobtainedfromthedefaultRGSextractionregionsshowninfigure2.4.

24

Chandra2.3

Figure2.6:ThefirstordersofRXJ0720.4−3125obtainedfromtheChandraobservation
w5582ouldbeusinglocatedonHRC-S/LETG.theleftBothsite),otherderstaworesupverticalerimpwhiteosed(theshadedzerothstripesorinderbisothcutpanelsoutaandre
Uppcausederbypanegapsl:btheetweesourcenthephotonsdetectoarrechips.indicatedbytheblackhorizontalstripe(highercount
rate).Lopluswerbackgroundpanel:Thephotonoverlaids,thetwdefaultobow-tieextractionshapedaregions.reasareTheusedcentralfortheregionisbackgroundusedforphotons.source

Chandra2.3

TheChandraspacecraftwaslaunchedonJuly23rd1999byNASAandisstillactive.
Chandrahoststwoimagingandreadoutdevices:theAdvancedCCDImagingSpectrometer
(ACIS,[31])andtheHigh-ResolutionCamera(HRC,[73]);andtwogratings:theHigh
EnergyTransmissionGrating(HETG,[24;25])forarangeof0.4−10keVandtheLow
EnergyTransmissionGrating(LETG,[30;58;59])workingat0.07−10keV.Generally,
ChandrafacilitieshaveahigherspatialresolutionthanthoseofXMM-Newtonbutamuch
smallereffectivearea(total800cm2and400cm2at0.25keVand5.0keV,respectively),
i.e.sufferfromalowernumberofphotonscomparedtoXMM-Newtonobservationswith
thesameexposuretime.WhileonXMM-Newtonallinstrumentsobservesimultaneously,
onChandraonlyoneinstrumentcanbeusedatthetime.
TheChandratelescopedoesnotsteadyfixthetargetwhileobserving,butperformsa
dithering.Thisavoidsunexposedareasintheobservedskyfieldduetodetectorstructures
(CCDgaps,deadpixelsetc.).Thedatareductionsoftwaretakestheditheringintoaccount
rrection).coect(asp

HRC-S/LETG2.3.1TheHRCdeviceconsistsoftwodetectors,oneoptimisedforimaging(HRC-I)andonefor
spectroscopyifusedwithgrating(HRC-S).ForRXJ0720.4−3125theHRC-Sdetectorwas
usedincombinationwiththeLETG(i.e.HRC-S/LETG)havinganenergyresolutionof
ΔE/E≥1000between0.08keVand2.0keVforthedispersedphotons(+1stand−1st
orders).Thezerothorderisanimageofthesource.
BothHRCdetectorshaveaspatialresolutionof0.5”,whereasthefieldofviewforHRC-S

25

2.DATAANDDATAREDUCTION

Figure2.7:TheimageofRXJ0720.4−3125inACIS-CCmodefromtheChandraobservation
pixels2774.Thealready≈extraction10to15regiontimes(bluemorerectangle)countsaisrezoomeddetected(redthaninrectangle).thebInrightestthetwoneighbbrightestouring
pixels.

is7×97havinganeffectiveareaof≈30cm2at1keV(50timeslessthanXMM-Newton
EPIC-pnandtwotimeslessasforthe−1stordersofbothRGSintotal).Importantfor
timingisthehightemporalresolutionof16µs,i.e.5000timeshigherthanforEPIC-pn
FFmode.However,duetoawiringerrorintheHRCdetector,thearrivaltimeofanevent
isassociatedwiththearrivaltimeofthefollowingevent1anddecreasesthetimeresolution
tothemeantimebetweentheevents.Sincethearrivaltimeofaphotonisalwaysassigned
tothenextphotonandthepulseperiodofRXJ0720.4−3125isrelativelylarge,thedeter-
minationoftheperiodisnotinfluencedandtheeffectsontimingarenegligible.

CIS-CCA2.3.2

TheACISdetectorhastwoCCDarrayswithatotaloftenchips.Eachchiphasasizeof
1024×1024pixel,whereonepixelcorrespondsto0.5”.Eightchipsarefrontilluminated,
twoarebackilluminatedwithbothconfigurationshavinganeffectiveareaof≈340cm2at
1keV.Inallcases,RXJ0720.4−3125wasobservedintheContinousClock(CC)mode,
1http://cxc.harvard.edu/ciao4.2/caveats/hrc−timing.html

26

Chandra2.3

Table2.3:ChandraobservationsofRXJ0720.4−3125inchronologicalorder.Theidentifier
markthemergeddatasets:observationswiththesametagaremergedintoonedataset.
ThecountsfromChandraHRCdataarenotdividedintohardandsoftband,thereforethe
totalnumbersofcountsarelisted.
Obs.Id.Instrument(120−Counts400eV)(400−Counts1000eV)MJDStartDateexpEffectiveosure
[ks]ys][da17453681HRC-S/LETGHRC-S/LETG93922722515765157520002000FFebeb2126.265.40
3691HRC-S/LETG2660515792000Feb46.12
2774277322AACIS-CCCIS-CC9452134551164615648522485224820012001DecDec5410.6115.01
277122ACIS-CC8761553522502001Dec61.86
27723ACIS-CC35374487522502001Dec64.05
466646673AACIS-CCCIS-CC56062678130945835530115301020042004JanJan7610.124.79
46683ACIS-CC21214918530162004Jan115.16
5305466943ACIS-CCHRC-S/LETG1890132754277530625302320042004FJaneb271935.705.22
467055ACIS-CC572312329532212004Aug310.13
46715ACIS-CC27786318532232004Aug55.15
467346725AACIS-CCCIS-CC2527248360345789532445322720042004AugAug2395.135.12
558167HRC-S/LETG30998533932005Jan2368.20
636455828HRC-S/LETGHRC-S/LETG2221035777536105352320052005AugJun27138.8770.17
636999HRC-S/LETG7696536522005Oct826.26
717710HRC-S/LETG2532536532005Oct98.04
7243724410HRC-S/LETGHRC-S/LETG59314927537185371820052005DecDec141517.1816.29
72451010HRC-S/LETG5249537182005Dec1617.19
7251558411HRC-S/LETGHRC-S/LETG47875321537755371820052006SDecep91710.14.1965
1086112HRC-S/LETG4240548512009Jan2011.91
10701107001312HRC-S/LETGHRC-S/LETG1564714053550865487620092009SFeebp111433.21.8217

i.e.ACIS-CC.Inthismode,thespatialinformationofthephotonsislostandthedata
arereadintoa1×1024pixelimage.Duetothisreadoutmode,theintegrationtime,i.e.
temporalresolution,improvesto2.85ms.

ofReduction2.3.3dataChandraAtthebeginningofthework,26ChandraobservationsperformedinHRC-S/LETGand
ACIS-CCmodewereavailable(lastobservationinSeptember2006).SincetheMPEcon-
tributedtothedevelopmentoftheHRCgratings,GuaranteedTimeObservation(GTO)
couldbeusedtoaddthreemoreobservations.ThemonitoringofRXJ0720.4−3125using
HRCGTOisstillcontinuing.Fortimingpurposes,mostChandraobservationsareexecuted
asshortexposuresofafewks,repeatedseveraltimeswithinafewdays.Theseobservations

27

2.DATAANDDATAREDUCTION

weremergedassumingthatnosignificantchangesinthepropertiesofRXJ0720.4−3125
occurredwithinsuchashorttimescale(incomparisontothelongtermchangesoveryears).
Duetomerging,the29observationswerereducedto13datasets,seetable2.3.
TheChandradatawereanalysedwithCIAO4.1.ForHRC-S/LETGthephotonsofthe
zerothorderwerecollectedfromacircularregionof2”radius,seefigure2.5.Thephotons
frombothfirstorderswerecutoutwithinthestandardLETGspectralextractionwindows
(seefigure2.6),butlimitedto10−60A˚(1240−207eV)andthetwobrightesthorizon-
talpixelstripesonly,tominimisethecontributionofbackgroundnoise.Topreparethe
HRC-S/LETGdataforspectroscopicfittinginXspec(seesection4.1),thebackgroundwas
generatedwiththecommandtg−bkg.
BeforeproceedingwiththeACIS-CCdataitwascheckedthattheobservationswerepro-
cessedwiththeStandardDataProcessing(SDP)versionDS7.6.3.orlatertoguarantee
bestcorrectionsofthereadouttimesanddithering.ThecoordinateaccuracyforallACIS-
CCobservationsisbetterthan0.5”,i.e.onepixel.TheChargeTransferInefficiency
(CTI)correctionwasappliedandthesourcephotonsfromarectangularregioncovering
thebrightestpixels(locatedonchipsevenforallACIS-CCobservations)wereextracted,
2.7.figureseeAsmentionedpreviously,animportantissueforthetimingofRXJ0720.4−3125isthephase
shiftbetweenhardandsoftband.ForHRC,theenergyinformationinthezerothorder
islost.Thisregards40%ofthetotalamountofphotons.Thehardphotonsextracted
fromthetwofirstorderswouldonlyequate20%ofthetotalamountofphotons.However,
fortimingpurposes,thelightcurveshavetobebinnedintenphasebinsormoreanda
lownumberofphotonswouldleadtoalargescatterinthelightcurves,thustheHRC
photonswerenotdividedinthetwobands.Notethatthetotalnumberofphotonsfrom
Chandraobservations(evenifnotdividedinbands)ismuchlowerthanforXMM-Newton
observations(seetable2.2andtable2.3).
Inallcasestheimplementationofthecorrectbadpixelfilewascheckedwiththecommand
plistardlibanditwassetwithpsetardlib,ifnecessary.Thebarycentriccorrectionforthe
HRCandACIS-CCdatawasappliedusingaxbary.Notethattheorbitephemerids,needed
forthebarycentriccorrection,areprovidedas“level=0”datafilesdirectlyafteranobserva-
tionisperformed.However,theseephemeridsareextrapolationsandarenotsufficientfor
pulsartiming,thus“level=1”ephemeridswereusedonly(theseareavailableaweekafter
theobservationisperformed).

28

3

timingrPulsa

ThegoalofpulsartimingistodeterminePandP˙andhigherordersoftheperiodderivatives
yieldingage,magneticfieldstrengthandbrakingindexaccordingtoequation1.6and
equation1.4.Incontrasttoradiopulsartiming,theobservationsofX-raypulsarsdeliver
atableofarrivaltimesforeachsinglephoton,aneventlist.Toaccountforthespecial
requirementsofX-raypulsartimingspecialalgorithms(forperioddetectionsandphase
coherenttiming)arediscussedhere.Thesealgorithmswereimplementedandtestedfor
thisthesisandwerewritteninMatlab1.
Ingeneral,thephaseφofthesignalevolvesas

dφ(t)=2π.(3.1)
)t(PdtIfthesimplemodelwithaconstantspin-downisused,theperiodevolveswithrespectto
areferencetimet0,

P(t)=P(t0)+P˙∙(t−t0).

(3.2)

Usingequation3.2tointegrateequation3.1leadstoanexpressionforthephasedifference

2πP˙
φ(t)−φ(t0)=P˙ln1+P(t0)(t−t0).(3.3)
Anarbitrarycontinuous(i.e.withoutaglitch)phaseevolutioncanberepresentedbya
series

¨˙φ(t)=φ(t0)+f(t−t0)−2f(t−t0)2+6f(t−t0)3...(3.4)
withfbeingthefrequency.Inthiswork,equation3.4wasusedforthephasecoherent
1(R2008a)7.6.0.324version

29

MINGITPULSAR3.

timing(accordingtoequation3.2[63;129],withoutaglitch)onlyuptothesecondorder
wn).spin-do(constantInprinciple,onecouldmeasurePfordifferentobservationsandfitaslopetoderiveP˙.
However,thisisnotpossibleforRXJ0720.4−3125sincetheindividualperiodsfromthe
singleobservationsarenotaccurateenough,aswillbeseenlater.Therefore,moreadvanced
required.readsmetho

timingcoherentPhase3.1

DeterminingtheperiodP0fromthefirstobservationyieldstheerrorΔP0dependingmainly
ontheobservedtimespan,e.g.followingtheerrorestimationin[72].Fromthegivenerror,
onecandeterminethetimespanuntilextrapolationsforthephase(e.g.thephaseofthe
maximumlight)arereliable.ThistimespanislessthanP0/ΔP0cyclescorrespondingto
thelossofoneperiodcycle.Ifthenextobservationlieswithinthistimespan,itslight
curvecanbefoldedintoP0.Thephasedifferenceofthemaximumlightfromthesecond
observationwithrespecttothereferenceobservationresultsfromΔP0,i.e.anewperiod
P1canbefoundtominimisethephaseresidual.ThenewerrorΔP1dependsonthetime
spanbetweenthetwoobservations,i.e.ismuchsmallerthanΔP0.
Thisprocedureisrepeatediterativelyincludingthenextobservationsclosestintime,eval-
uatingtheperiodanditserrorbyminimisingthephaseresiduals.Ifthemodulusofthe
phaseresidualsincreaseswhileevaluatingtheperiod,thephasedifferencecontributedby
P˙becomesimportant,i.e.accordingtoequation3.4asecondtermhastobeincluded.
Toaccomplishphasecoherenttiming,thereferenceobservationshavetobeperformedas
shortexposuresrepeatedtwotothreetimesafewdaysafterthefirstobservation.This
wasdonewiththeACIS-CCobservations4666to4669followedbytheHRC-S/LETG
observation5305correspondingtoabaselineof52days,seetable2.3.

3.2Algorithmsforperioddetections

Sincearrivaltimesofeachsinglephotonaremeasuredandtheeventlistcontainsentries
forsome103to105photons(dependingonexposure,detectorandtelescope)overatime
spanofoneto100ksincludingtimegaps,specialalgorithmshavetobeimplementedfor
perioddetectionandsomepre-workisnecessary.
Theemission/detectionofaphoton(event)followsaPoissoniandistribution,i.e.the
probabilityPforaparticularsequenceofsignalsis

30

3.2Algorithmsforperioddetections

P=Nsinie−si(3.5)
!ni=1iifsiistheexpectednumberofcountsperbinandniisthemeasurednumberofcountsper
binattheendoftheexperiment.ThetotalnumberofbinsisNwithrespecttoafinite
area,energyrangeandtimeresolutionofthedetector,i.e.si=W(xi;yi;νi;ti)δxδyδνδt.
ThefunctionWhastobeassumed,e.g.forRXJ0720.4−3125,Wseemstobeasinusoid
accordingtofigure1.3,upperpanel.Inthiscase,Whasfourparameters(offset,ampli-
tude,frequency/periodandphase1),orfiveparameters,ifthefrequency/periodischanging
accordingtoequation3.4(again,truncatingafterthesecondorder).Generally,Whasp
parametersandmayhaveanarbitrarycharacter.

2testZ3.2.1nIfphotonsfromaparticulardetectorareainafixedenergybandareextractedandsincethe
samplingdurationtendstozeroforRXJ0720.4−3125,ni=1andNisthetotalnumberof
counts.Following[13]theZn2test(herenisthenumberoforders,followingthecommon
withappliedaswterminology)nN2N2
Zn2=2coskφi+sinkφi(3.6)
Niikwhereφiisthephaseaccordingtoequation3.4.Forasingleobservationthephaseshift
fromP˙isnegligible.TheprobabilitydensityfunctionofZ2nisequaltothatofχ2with2n
degreesoffreedom[13].Thismakesitfeasibletoinfertheerrorsdirectly[110].
TheZn2codewastestedcheckingtheresultsin[63]and[129].

3.2.2Cashstatisticsandmaximumlikelihood
Startingfromequation3.5theCash[17]value(orCvalue;althoughmisleadingoftencalled
”Cashstatistics”or”Cstatistics”)fromthemaximumlikelihoodis
NC=−2lnP=2E−nilnWi.(3.7)
=1iAsbefore,ni=1andEisthetotalnumberofcountsexpectedfromthemodeldistribution.
Following[17],aminimumofCfromequation3.7hastobefoundbyvaryingallparameters
poverasearchgridofqparameters(forexampleq=2ifPandP˙arevaried).This
aswill1beAmplitudeseenlater.andoffsetcanbescaledtogetherandtheactualnumberofparametersisactuallyoneless,

31

MINGITPULSAR3.

minimumvalueofChastobesubtractedfromtheminimumCvaluefoundatanyparticular
pointatthesearchgrid,i.e.ΔC=Cminbest−Cminpart.ΔCisdistributedasχ2withqdegrees
offreedomleadingimmediatelytoconfidenceintervals.
Accordingto[19]andfromequation3.3themodelprescription

W(t)=a01+Acos2πlnP(t)+θ0(3.8)
˙P0Pwasused.Substitutingequation3.8intoequation3.7andcalculatingΔCeliminatesall
scalingfactorsofthemodel,suchasa0,i.e.p=4(notp=5)andq=2ifPandP˙
arevariedandp=3andq=1ifonlyPisvaried,respectively.TheamplitudeAand
thephaseθ0ofthemodelsignalarederivedfollowingtheinstructionsin[151]usingthe
Rayleighpowerforasinusoid,similartotheexpressioninequation3.6.
TheCashstatisticscodewastestedcheckingtheresultsandfiguresin[151](theappendix
therein)andtheresultsin[19].TheindividualperiodsderivedfromtheZn2testandfrom
Cashstatisticsareconsistentforeachobservationandonlydeviatewithintheir1σerrors
fortheROSATobservations.Inmostcaseseventheerrorderivedfromtheestimationin
[110]equalsthatderivedfromtheconfidenceintervalsusingCashstatistics.Forexample
bothmethods(andbotherrorestimations)yieldaperiodofP=8.391085(85)s(numbers
inparenthesisindicatethe1σerroronthelasttwodigits)withthesameerrorvaluefor
theXMM-Newtonobservationrevolution1454(hardband),seefigure3.1.Estimating
theerrorwiththeformalRayleighresolvingpowerΔP=P2/2/ΔTobservedleadstoa
muchlargererrorofΔP=0.0015s,whiletheerrorestimationin[72]yieldsanerrorof
ΔP≈2.5×10−5s(dependingonthenumberofphasebinsofthephasefoldedlight
curve),thatissmallerbutcomparabletoΔP≈8.5×10−5susingtheestimationin[110]
ortheconfidenceintervalsderivedfromCashstatistics.

lengthString3.2.3Thetwomethodsintroducedforperioddetectionneedamodelprescriptionasinput.
Althoughtheassumptionofasinusoid(e.g.equation3.8andequation3.6)leadsto
sufficientresults(seefigure3.1)inthecaseofRXJ0720.4−3125,thefunctionW(t)may
e.shapanyhaveForeachtrialperiod,thesignalcanbefoldedintophase.Ifthetrialperiodhitsthetrue
value,thephasefoldedlightcurvehasaminimumlength[14],i.e.theexpression

S=(yi−yi−1)2+(xi−xi−1)21/2+(y1−yn)2+(x1−xn)21/2,(3.9)
n−1
=1i

32

3.3Whythehardband?

Figure3.1:Left:TheperiodogramfortheXMM-Newtonobservationrevolution1454of
RXJ0720.4−3125(hardband)derivedfromtheZn2testwiththefirstordern=1only.
Right:Thesameasontheleft,butzoomedinandtheZ12valueisnormalisedtooneto
illustratetheculmilativedensityfunctionderivedfromΔC(blackshadedarea)onthesame
scale.Thehorizontallinesindicatethe1σand2σconfidenceintervalsoftheperiod.

wherexisthephaseandythequantitysuchascountsperphasebini,becomessmall.
Forthewrongperiod,thephasebinnedlightcurvejustequalsnoiseandS,thestring
length,becomeslarge[27].Thisisvalidforanysignalshape.Thestringlengthmethod
hasitsadvantageforsparsedatasetswitharbitrarytimespacingsuchasthemeasured
phaseresidualsofRXJ0720.4−3125,e.g.seefigure1.6.Thestringlengthmethodwas
alsotestedfortheeventfilesoftheindividualobservations.However,theothermethods
aremoreappropriatefortheperioddetectionoftheindividualobservations(seefigure3.2).

3.3Whythehardband?

Inpreviousworks[41;43;51]thephotonsweredividedintoasoft(120−400eV)anda
hardband(400−1000eV)fortheEPIC-pndetectortoillustratethephaseshiftbetween
thesetwobands.Inthissectionthenecessityoftheseparationofthephotonsintotwo
bandsifdatafromdifferentinstrumentsareusedisdemonstratedanditisshownatwhich
energythebandcut-offhastobemadetoaccomplishapropertimingsolution.Suchan
investigationwasnotperformedbefore(e.g.in[63;129])althoughthephaseshiftwas
[22].wnknoalreadySincethevariablephaselagbetweensoftandhardphotons(seefigure1.6)affectsthe
phasecoherenttimingsolutionandinordertominimisesystematicerrorsbetweenEPIC-
pn,MOS1,MOS2andChandradata(seealsothediscussionin[51])arestrictiontothe
hardenergybandseemsuseful.Asmentionedpreviously,HRCobservationshavealow
numberofphotonsandtheenergyinformationofthephotonsinthezerothorderislost.

33

TPULSAR3.MINGI

Figure3.2:Left:TheperiodogramfortheXMM-Newtonobservationrevolution1454of
RXJ0720.4−3125(hardband)derivedfromthestringlengthmethod.Thestringlength
valueisscaledaccordingto[27].
Right:Thesameastheleftpanel,butzoomedin.Both,theZ12valueandthestringlength,
arenormalisedtoonetoillustratetheculmilativedensityfunction(C.D.F.)derivedfromΔC
scale.sametheon

ThereforeallphotonsfromtheHRCdatawereincluded.
ThespectralresolutionoftheMOSdetectorsis≈100eVinthesoftband[125].Taken
atthesametime,thephaseresidualsfromtheXMM-Newtonobservationsshouldbecom-
parabletothoseoftheChandraobservations.However,thisworksonlywhentakinginto
accountdifferentenergyresponse,spectralresolutionandthephaseshiftbetweenhardand
softphotons(softerphotonsarelessprominentintheMOS,HRCandACISdatathanin
thepndata),influencingtheresiduals.Thiswasshownin[51],figure1thereinand[38],
therein.7figureThisstatementwascheckedusingthoseChandraobservationsperformedcloseintimeto
XMM-Newtonobservations:TheHRCobservation5582(June1st,2005)isclosetothe
XMM-Newtonobservationrevolution0986(April28th,2005),theHRCobservations6369
and7177(October8th/9th,2005)areclosetotheXMM-Newtonobservationrevolution
1060(September23rd,2005),theHRCobservations7243−7245(December14th−17th,
2005)areclosetotheXMM-Newtonobservationrevolution1086(November11th/12th,
2005),theHRCobservations10861and10700(January20thandFebruary14th,2009)
areclosetotheXMM-Newtonobservationrevolution1700(March21st,2009)andthe
HRCobservation10701(September11th,2009)isclosetotheXMM-Newtonobservation
revolution1792(September22nd,2009);seealsotable2.2andtable2.3.
AssumingthatthetimingpropertiesofRXJ0720.4−3125donotchangesignificantlywithin
atimespanofamonth,thetimingresiduals(usingthe“alldata”timingsolutionin[129]
accordingtoequation3.4)oftheseobservationswerecomparedbychangingthebandcut

34

Figure3.3:Theaccordanceofthe
offphaseenergyresiduals−1000ofeVth)eforhardXMM-Newband(cutton
ChandraEPIC-pn,HRCEPIC-ofMOSRX1&J0720.4−MOS23125foandr
Datadifferentsetstakvaluesenofwiththedifferentenergybandtelescopcut.es
aswerecloseselectedintimeinassuchpawossible.aythatThetheyuppaerre
ofpaneltheshophasewsthesumdifferencesofthe(phaseabsolutegaps)valuesde-
resprivedectfromtotheeachdifferentother,whileinstrumentsthemiddlewith
gapspanelandshowsthethecorrespmedianondingofχ2these/d.o.f.phaseis
presentedinthelowerpanel.

35

3.3Whythehardband?

Figure3.4:Thesameasinfigure3.3,
butusingthesoftband(120eV−cutoff
analysis.therfoenergy)

MINGITPULSAR3.

from200eVto800eVinstepsof10eV.Forexample,ifthebandcutisat600eV,there
aretwobandsof120−600eVand600−1000eV.Duetothelimitedenergyresolution,
thesebandcutscouldnotbeappliedfortheHRCobservations.
Then,thephaseresidualswerecalculatedaccordingtoequation3.4byfittingasine(see
[129])tothephasefoldedlightcurves(12phasebins)forpn,MOS1andMOS2andHRC
foreachbandcut.Afterwards,thesumoftheabsolutevaluesandthemedianofthephase
gapsofthephaseresidualsoftheharderbandfromthedifferentdetectorswerecalculated.
Havingthephaseresidualsandtheirerrors,χ2/d.o.fwascalculatedshowingthedegreeof
accordanceoftheresultsfromthedifferentdetectors.Inallthreecases,aminimum(i.e.
bestagreement)wasreachedwhenchoosingabandcutbetween300eVand400eV,i.e.
havingtwobandsof120−400eVand400−1000eV(figure3.3)andusingtheharder
band.1Forbandcutsoflowerenergiesthedifferentdetectorresponsesforthesoftphotons
causelargerphasegapsowingtothephaseshiftbetweenhardandsoftphotonsandthe
roughenergyresolutionoftheEPICdetectors,whileforbandcutsathigherenergiesthe
numberofphotonsdecreasesandthestatisticsworsens.
Ifthesamewasdone,butkeepingthesoftbandphotons(seefigure3.4),thebestagree-
mentofthedifferentinstrumentswasachievedifnobandcutwasapplied(asdonefor
previoustimingsolutions,e.g.[19;63;129;151]).Buteventhelowestχ2/d.o.fvaluewas
morethantwotimeslargerthaninthecasewhenphotonsbetween400−1000eVwere
used.Thechoiceofthehardband(400−1000eV)reducesinstrumentaldiscrepanciesofthe
differentdetectorsasmuchaspossible.

1Forconsistencywithpreviouswork[41;43;51],thecut-offenergyissetto400eV.

36

4

Results

4.1Spectralproperties

EPIC-pn4.1.1

Ascanbeseenfromfigure1.4,thespectralpropertiesofRXJ0720.4−3125followasinu-
soidaltrenduntil2005.Thefurtherdevelopmentwasinvestigatedbyreducingandanalysing
thenewdataobtainedfromXMM-Newton.
In[41;43;51]theEPIC-pnspectrawerefittedusingXspecwiththemodelphabs×
(bbodyrad+gaussian),where“gaussian”representsthebroadabsorptionfeature(allow-
ingnegativenormalisation)seeninthespectraand“bbodyrad”theemissionofaperfect
blackbodyemittingatacertaintemperaturewithanormalisationfactortocalculatethe
sizeoftheemittingarea(scaledtoadistance,hereandin[41;43;51]always300pc).
Thespectrumisattenuatedbyabsorptionduetotheinterstellarmedium(ISM),whichis
modeledusing“phabs”.Toavoidsystematicerrorsduetocross-calibrationproblems,only
EPIC-pndataobtainedinfullframemodewiththinfilterwereconsidered.Thefitmodelis
listedindetailintable4.1.Sincethismodelwasusedpreviouslyin[41;43;51]itiscalled
the“standardmodel”inthiswork.
Xspecprovidesanumberofmodelssimulatingtheemissionofneutronstars(e.g.“nsa”1,
“nsgrav”2,“nsatmos”3),butnoneofthemfitsthedata(χ2/d.o.f.≥2.5).Addinganother
componenttothestandardfitmodeldidnotimprovethefitsignificantly.Therefore,the
standardfitmodelwasusedonly.
The13EPIC-pnspectrainfullframemodeandthinfilterwerefittedinonesessionwith
theparametersNH,Eline,σlineleftlinked.Inprinciple,theseparameterscouldchange
The1nmagneticeutronstafieldrastrengthtmosphere:canmobedelssetato0neutronGaussstar,Bwith=a1010hydrogenGaussandatmosphereB=in10a13fixedGaussmagneticmaximum,field.
[98].and[157]see32NeutronNeutronstastarrwithwithhydrogennonmagneticatmhydrospheogerenwithatmosphereelectronandconductionvariableandsurfacegravitself-irradiation,y,seesee[157].[45].

37

TSRESUL4.

withtime,butitwouldnotinfluencethemainresult,asshownlater.Theblackbody
temperature(andnormalisation)andthelinenormalisationareleftfreeforeachindividual
spectrum,sincetheyareknowntovary.Insteadofthelinenormalisation,amorecommon
measureofthestrengthofaspectralfeatureistheequivalentwidth(EW),thatisused
1on.furtherAfterincludingthenewdata(revolution1181,1265,1356,1454,1700and1792,seeta-
ble2.2),thespectralpropertiesofRXJ0720.4−3125clearlydonotcontinuetofollowasinu-
soidaltrendfurtherbutseemtoundergoarelativelyfastrisearoundMJD=52800days
followedbyaslowrelaxation.Toavoidcross-calibrationproblemsaserrorsources,the
EPIC-pnobservationsinotherinstrumentsetupswerefittedseparately,howeverthespec-
tralpropertiesfollowwellthetrendseenintheobservationsperformedinfullframemode
filter.thinwithThevaluesoftheparameterswhicharecommontoallspectraare(errorsdenote90%
confidence):

•NH=1.040±0.035×1020/cm2

•Eline=302.1±4.6eV

•σline=76.3±3.3eV

andarefullyconsistentwithpreviousvalues[41].Fittingthese13EPIC-pnspectrain
onesessionyieldsχ2/d.o.f=1.28.Totesttherobustnessofthefitresults,thefitswere
performedindifferentways:theElineandtheNHvaluewereallowedtovarywithtime(i.e.
foreachspectrumindividually).IfthelineenergyElinewasnotfixed,itshowedthesame
trendasthetemperature:ajumparoundMJD=52800days(from150eVto250eV)
followedbyaslowdecrease,whileNHfollowedthetrendofthesizeoftheemittingarea
andequivalentwidthanddecreasedfrom1.1∙1020/cm2to0.48∙1020/cm2.However,the
NHvalueandElinearestronglycoupled.Achangeinthelineenergycanbecompensated
forbyavariationoftheNHvalue.Inaddition,thisapproachcauseslargererrorbarssince
thedataarenotsufficienttofittoomanyfreeparameters.Inanycase,thebehaviourof
thespectralvariationsintemperature,equivalentwidthandsizeoftheemittingareaisnot
significantlyinfluencedusingthesedifferentvariancesorthestandardfittingprocedureused
in[41]andinthiswork,butatemporalchangeofElineand/orNHcannotbeexcluded.
Thetrendsofthetemperature,equivalentwidthandsizeoftheemittingareaareillustrated
infigure4.1andtable4.2andtheEPIC-pn(fullframemodeandthinfilter)spectraof
RXJ0720.4−3125areshowninfigure4.2.Thespectralpropertiesobtainedfromthe
EW1(Ifλ)I0=is(1the−I(intensitλ)/Iy0)ofdλ.thecontinuum,theequivalentwidthisgivenwith

38

4.1Spectralproperties

Table4.1:Thestandardfitmodelphabs×(bbodyrad+gaussian)usedforthe
RXJ0720.4−3125spectrainthisandprevious[41;43;51]works.
componentparameterunit
22212bbphabsodyradcolumntemperatdensitureykNTH10k/eVcm
normalisation(km/10kpc)2
3gaussianlinelineenergywidthEσlinekkeVeV
normalisationphotons/s/cm2
T(seeablealso4.2:figureSpectral4.1).AllchangesobservationsofthearephaseperfoaveragedrmedinfullEPIC-pnframespecmotradeofandRXwithJ0720.4thin−filter,3125
unlesswritteninitalic(inotherinstrumentsetups,seetable2.2).Theerrorsdenotethe90%
interval.confidenceorbit[MdaJysD][EeVW][keVT][kmradius]
0.+4007801755167851870−+54..16−+33..588686..05±±00..7444..9080±±00..1409
−3+4.5.8
053405335258752585−−1913..76−−+444...3668888..17±±00..5544..6471±±00..1010
071152940−67.7−+4+22...37792.0±0.6−
098608155348953148−−5758..21−−+333...5999494..47±±00..4544..3428±±00..0708
9.+3106010865363653687−−5455..53−−+333...5599393..18±±00..4444..4936±±00..0807
9.+4126511815404553877−−5350..07−−+444...4859293..71±±00..6644..5243±±00..1110
0.+5135614545422654421−−4443..16−−+444...4779192..94±±00..6644..4944±±00..1010
1.+5179217005509654912−−3844..38−−+554...2689191..39±±00..6744..5151±±00..1112

observationperformedduringrevolution0622isnotlistedintable4.2,sincethethickfilter
wasused,whichstronglyreducesthenumberofeventsatlowestenergies.

RGSandEPIC-MOS4.1.2Inadditiontothepndata,theMOS1andMOS2andtheRGS1andRGS2datawere
investigated.SincetheMOSdetectorsarelesssensitiveinthesoftband[125],onlyphotons
above400eVcouldbeusedforthespectralfitting.Forthisreason,theinformationof
thebroadabsorptionfeature(Eline=302.1±4.6eV)islostandnoconclusionscould
bederived.Thevaluesforthetemperatureshaveerrors≈3eV(90%confidence),i.e.
aretoolargetoseeaclearvariation.Moreover,theinstrumentsetupsfortheMOS

39

4.

TSRESUL

Figure

4.1:

Long

thefromobtained

mrte

variations

of

the

ulsep

inobservationsEPIC-pn13

circlesshowdataobtainedfrom

l.leveconfidence90%denote

the

other

phase

averaged

fulldemoframe

EPIC-pn

40

ectrasp

of

thinwith

observations

(see

RX

3125−J0720.4

enOp(dots).filter

table

2.2).

rErro

rsba

4.1Spectralproperties

Figure4.2:AllXMM-NewtonEPIC-pnspectraofRXJ0720.4−3125performedinfullframe
modewiththinfilter.Thespectraarefittedwiththestandardfitmodel[41;43;51],see
4.1.table

detectorsvarymuchmorethanforpn(seetable2.2),i.e.preventsdirectcomparisonofthe
differenttemperatures,sothatonlythreeorfourobservations(notnecessarilycontiguous)
aredirectlycomparable.Moreover,theMOSdetectorresponsechangeswithtimethat
introducesanothersourceforsystematicuncertainties.
InthecaseofRGS1andRGS2,onlyphotonsabove350eVcouldbeused,i.e.again
itwasnotpossibletoderivethevaluesfortheequivalentwidthofthebroadabsorption
feature.ThespectralresolutionofthetwoRGSismuchbetterthanforEPIC(see[23]
andsection2.2).Duetothelowersensitivity,theRGSdatawereco-addedby[44]using
rgscombineonlyallowingtoinvestigateatotalaveragespectrum,butwithhighenergy
resolution.Anarrowabsorptionfeature(EW=−1.35±0.30eV)around0.57keVwas
foundinthetotalspectrum.
Sincetheworkof[44],threenewXMM-Newtonobservationswereperformed(seetable2.2)
thatimprovestatistics.ThenewRGSobservationswereco-addedinthesamewayas
describedin[44].Onlyfirstorderswereconsidered,sincethesecondordersareweak.
TheRGS2detectordoesnotprovidespectralinformationintherequiredenergyband(see
figure2.3),thuscouldnotbeused.Intotal,theexposuretimesumsupto600ks(50ks
[44]).inthanremoFirst,thestandardfitmodel(table4.1)wasappliedtotheco-addedRGSspectrum,then
theparameterslistedintable4.1werekeptfixedandafurtherGaussianabsorptionfeature

41

TSRESUL4.

Figure4.3:Theco-addedRGS1(firstorderonly)spectrumofRXJ0720.4−3125inthe
upperpanelwithatotalexposureof600ks.Theblacklinerepresentsthefitfromthe
standardmodel(seetable4.1),whiletheredlineshowsthestandardfitmodelplusanarrow
absorptionfeatureseenat0.5692±0.0022keVwithEW=−1.055−+00..042106eV(errorsdenote
90%confidencelevel),seealso[44]forcomparism.Thefitresidualsfromthestandardfit
areshowninthelowerpanel.

(representingthenarrowabsorptionline)wasincluded.IncludingtherecentXMM-Newton
observations,thelinewasconfirmedat0.5692±0.0022keVwithEW=−1.055−+00..042106eV
andσ=3.5±1.8eV(errorsdenote90%confidencelevel),seefigure4.3.Theinfluence
ofthelineonthequalityofthespectralfitisnegligible:applyingthestandardmodel,the
fityieldsχ2/d.o.f.=1.17,includingthenarrowabsorptionfeature,χ2/d.o.f.decreasesto
1.16.Though,sincetherearenodetectorfeaturesinthisenergyrange,thelinedetection
seemsreliable.However,anabsorptionlinearound0.48keV,asclaimedby[44],couldnot
confirmed.eb

HRC-S/LETGChandra4.1.3

ToverifythespectralchangesofRXJ0720.4−3125detectedwithEPIC-pntheChandra
HRC-S/LETGspectraperformedcloseintimetoeachother(seetable2.3)weremergedto
improvethestatistics.Thisresultsinnineindividual(merged)spectra.TheHRC-S/LETG
spectrawereaddedusingtheCIAOcommandaddgratingorderstoaddthetwofirstorders
(allotherordershaveanegligiblecountnumber)andaddgratingspectratoaddtheHRC-

42

4.1Spectralproperties

S/LETGspectra.ThefitprocedurefollowedthatforEPIC-pnusingthestandardfitmodel
.ec12XspinAlthoughtheerrorsforthetemperatureswereagainlargerthanforEPIC-pndata,the
temperaturecouldbederivedfromnineobservationsperformedinthesameinstrument
setup.Thetemperaturevariationsclearlydonotfollowasinefortheobservationsperformed
after2005(MJD=53700days),seefigure4.4.Thedifferentspectraareshownin
figure4.5.DuetothelackofcountscomparedtotheEPIC-pndata,itwasnotpossible
toobtainreliableestimatesforthevariablevaluesoftheequivalentwidth(ofthebroad
absorptionlineat0.3keV)andsizesoftheemittingarea,sincetheresultingerrorsaretoo
large.Thevaluesoftheparameterswhicharecommontoallspectraare(errorsdenote
confidence):90%

•NH=0.67±0.13×1020/cm2
•Eline=258±40eV
•σline=67±25eV
Theninespectrafittedinonesessionyieldχ2/d.o.f=0.54.Formally,NHderivedfrom
theChandraHRC-S/LETGspectraisnotconsistentwiththevalueobtainedfromEPIC-pn.
ThisdeviationiscausedbythelowervalueofEline=258±40eVcomparedtothevalue
obtainedwiththeXMM-NewtonEPIC-pnspectra(Eline=302.1±4.6eV),althoughthey
areconsistent.Asaresult,NHhasalowervalueaswell,sinceNHandElinearestrongly
coupled,asdiscussedpreviously.
Fromtheresultsoftheco-addedRGSspectraitwasobvioustotakethenextstepand
co-addallChandraHRC-S/LETGspectra.Altogether,theco-addedHRC-S/LETGspectra
have450ksexposuretime(seetable2.3).Afterfittingthefinalaveragespectrumwith
Xspec12usingthestandardfitmodel,thefollowingresultswereobtained(errorsdenote
interval):confidence90%the•NH=0.857±0.090×1020/cm2
•Eline=255±32eV
•σline=76±23eV
•kTaver=92.0±1.4eV
•Raver=4.8±1.6km
•EWaver=−39−+1019eV.

43

TSRESUL4.

Figure4.4:ThetemperatureevolutionofRXJ0720.4−3125includingthemostrecentXMM-
NewtonandChandraobservations.TheChandraspectraweremergedaccordingtothetags
intable2.3.Thedashedcurverepresentsthesinefitin[41]andfigure1.4thatisnot
consistentwiththenewobservations.Allspectraarefittedwiththestandardmodel,see
[41;43;51]andtable4.1.

withχ2/d.o.f=1.08.
Now,NHisinbetteragreementwiththevaluederivedfromtheEPIC-pnspectra,butstill
it.withconsistentnotInadditiontothenarrowabsorptionfeaturefoundby[44],twootherlinesthatseemtobe
evenmoresignificantwithrespecttothecontinuum,weredetected.Sinceallthreelines
areratherweak,foracross-checkChandrapipelineproductswereusedaswellasrepro-
cesseddatafortheco-addedspectrumtogetherwithtwodifferentXspecabsorptionmodels
(phabsandtbabs)fortheISM.Inallcases,thelineswerepresent,seefigure4.6.Tofitthe
lines,theparametersfromthestandardmodelwerefixedandaGaussianabsorptionline
(representingthenarrowabsorptionfeature)wasaddedandfitted,thenallparameterswere
setfreeandfittedagain.Theparametersofthethreelinesarelistedintable4.3.Likefor
theco-addedRGS1spectra,theinclusionofthenewabsorptionlinesdidnotsignificantly
improvethefit,sincethefeaturesareweakandthevalueofχ2/d.o.f.isdominatedbythe
restofthespectrum.χ2/d.o.f.fromtheco-addedHRC-S/LETGspectradecreasedfrom
1.08to1.03.
Toensurethatthenewdetectedlinesarenotuncalibratedinstrumentalfeatures,allavail-

44

4.1Spectralproperties

Figure4.5:TheChandraHRC-S/LETGspectraofRXJ0720.4−3125,mergedaccordingto
thetagsintable2.3.Allspectraarefittedwiththestandardmodel,see[41;43;51]and
4.1.table

ableHRC-S/LETGspectraofRXJ1856.4−3754wereco-addedforcomparison.Nosignif-
icantspectralfeatureswerefoundsofarfromRXJ1856.4−3754[15;16].Theco-added
HRC-S/LETGspectrumofRXJ1856.4−3754(500kstotalexposuretime)wasfittedin
XspecwithasingleblackbodyabsorbedbytheISM(modelphabs).Indeed,thethreeab-
sorptionlinesfoundinthespectrumofRXJ0720.4−3125arenotpresentinthespectrum
ofRXJ1856.4−3754(illustratedbythefitresidualsinfigure4.7)thathasmuchbetter
statistics.Intriguingly,theabsorptionlinefoundat0.48keVfitstotheOVIIKαresonancelinehaving
aredshiftof1.17,asclaimedin[44].Anabsorptionfeatureat0.65keV(OVIIIatrest,see
[44])remainsundetected,probablyduetothelackofphotonsinthisenergyrange.How-
ever,theabsorptionfeatureat0.53keVishardtoreconcilewithhighlyionisedoxygen,
eitheratrestorwithagravitationalredshiftof1.17.Morelikely,thisabsorptionfeature
originatesfromneutraloxygenintheISMsinceitisclosetotheK-edgewithstrongsub-
edgesat0.538keV,seethediscussionin[60],section4.1.3.therein.Thus,thisfeature
mightbearesultofinexactmodelingoftheedgeorindicatesanoverabundanceofoxygen
inthedirectionofRXJ0720.4−3125.
Theinterpretationofthethreeabsorptionfeaturesmeritsmoreinvestigationsinthefuture
andthepresenceofsuchlinesshouldalsobecheckedfortheotherM7aswell.

45

TSRESUL4.

Figure4.6:Thesameasinfigure4.3,butobtainedfromtheco-addedHRC-S/LETG
0sp.57kectrumeVof(seeRXalsoJ0720.4table−4.3)3125.areThemuchbthreeetternaseenrrowinabsothefitrptionresidualsfeatures(lowater0.48panel),0.53thanandin
thespectrumitself(upperpanel).

Table4.3:ThethreenarrowabsorptionfeaturesofRXJ0720.4−3125detectedintheco-
addedChandraHRC-S/LETGspectra.Thethirdlinecorrespondstotheabsorptionfeature
foundby[44]intheXMM-NewtonRGSdata,theothertwolineswereundetectedbefore.
Allerrorsdenote90%confidencelevel.
energywavelengthσEW
[keV][A˚][eV][eV]
0.4842±0.001725.606−+00..0900904.5±1.8−1.52−+00..4325
0.5313±0.001223.336−+00..0530533.8±1.3−2.10−+01..1120
0.5663±0.003121.890−+00..1202408.2±3.4−2.78−+01..4810

Timing4.2

4.2.1Individualperiods,lightcurvesandphasedetermination

Asdescribedpreviously,theavailableXMM-NewtonandChandraACIS-CCobservations
weredividedintohardandsoftphotonsandthoseChandraobservationscloseintime
weremergedintoonedataset(seetable2.3).Afterthismerging71datasetswere
obtained:16fromXMM-NewtonEPIC-pnand36fromEPIC-MOS1/MOS2(theXMM-
Newtonobservationsrevolution0622and0711fromMayandOctober2003,respectively,

46

Timing4.2

Figure4.7:Thefitresidualsfromtheco-addedHRC-S/LETGspectraofRXJ1856.4−3754
(upperpanel)afterapplyingtheblackbodymodel[15;16]andfromtheco-addedHRC-
S/LETGspectraofRXJ0720.4−3125(middlepanel)afterapplyingthestandardmodel,see
[41;residuals43;51]oftheandsptableectra4.1.ofRXTheloJ1856.4cati−onsof3754)thearenamarrorkwedabsowithrptionthedashedfeaturesred(notlinesseenandinthethe
fittedGaussianabsorptionlinesareindicatedwitharedsolidline.Thefitresidualsvanish
aftertheinclusionofthreeabsorptionlines(bottom).

havefourMOSdatasetseach),6ROSATdatasets(pointingsonly)and13(mergedfrom
29)datasetsfromChandraobservations.
Touseadatasetfortiming,thephotonarrivaltimeshavetobefoldedintophase,thus
thecorrectperiodhastobedetected.Iftheperiodogramispopulatedbyequallydominant
aliases,thephasefoldingisambiguousandsuchobservationshavetobetakenwithcare,
thusinafirststeptheperiodwasdeterminedusingtheZ12testforeachofthe71data

47

TSRESUL4.

setsindividually(errorsarecalculatedusingtheapproachin[110]).SincetheROSATdata
havealowcountnumber,theseobservationsyieldlargeperioderrorsandshowaliases,
hencewereexcludedforthefirsttimingsolution.Fortheobservationswithmorethan
≈104photons,theperioddeterminationbecomesmorecertain(seetableA.1).Mostof
theindividualperiodsareconsistentwiththesinglespin-downmodelwithin1σerrorsand
allofthemareconsistentwithin2σerrors,seefigure4.8.TheperiodoftheChandraHRC-
S/LETGobservation7251showsalargediscrepancywithrespecttotheotherobservations
(seetableA.1),probablycausedbythesmallnumberofphotonsgivingnotenoughstatistics
forareliableperioddetermination.Unfortunately,thisobservationisnotcloseintimeto
theotherChandraHRC-S/LETGobservationsandcouldnotbemerged.LiketheROSAT
data,thisobservationwasexcludedaswell,i.e.finally64observationswereused.
Inpreviousworks[63;129],thephasefoldedlightcurvesofRXJ0720.4−3125werefitted
withasinusoid,howeveritisknown[43]thatthelightcurvesarenotbestrepresentedbya
sinefunctionandgenerallyexhibitamorecomplicatedshape[109]dependingonemission
geometry.Indeed,theFouriercoefficientsofthelightcurvesprovideinformationaboutthe
sizeandthelocationoftheemittingarea−apuresineisonlyaspecialcase.Totake
thisintoaccountandtoderiveamoreaccuratephasedetermination,thelightcurveswere
fittedusingacombinationofthreeFourierharmonics:

3F(φ)=Aksin(kφ)+Bkcos(kφ)(4.1)
=0kwherek=0correspondstotheconstantoffset.Inthefollowing,eachtermisdenoted
assinkorcosk,e.g.sin1abbreviatesA1sin(1φ),cos1abbreviatesB1cos(1φ).The
contributionofcos1isnegligible(thephaseiszeroatthereferencetime,andacosine
termwouldimplyaphaseshift),thesuminequation4.1startsalwayswithsin1,whilethe
remainingtwotermscanbesin2+sin3,cos2+sin3orcos2+sin2,andsoon.Thelight
curveswerefittedwiththesumofthreeterms,nottointroducetoomanyfitparameters,
andtermswithk>3werenotused,i.e.onlythreetermsintotal.Thecombinationthat
fitstheindividuallightcurvewiththelowestvalueofχ2/d.o.f.wasusedforthephase
determination.In[63],thereferencepointforthephasetobezeroandtheinitialperiodwastakenfromthe
combinedChandraACIS-CCobservations4666to4669withtheHRCobservation5305,
coveringatotaltimespanof52days.Thisdatasetproducesaliasesintheperiodogram
causedbythetimegapsbetweentheobservations.ThreepeakswithZ12≈140were
detected:P1=8.39036664(53)s,P2=8.39111600(50)sandP3=8.39188114(53)s.
P2yieldsformallythelargestZ12valueandisconsistentwiththereferenceperiodP=
8.39111590(50)sfrom[63](numbersinparenthesesindicate1σerrorsusingtheerror

48

Timing4.2

[110]).inestimationTheotherobservationsweresortedwithincreasingtime,takingasreferencetimethatof
[63](“alldata”solution).Inprinciple,theACIS-CCobservations4670to4673combined
withtheHRCobservation5581couldaswellbeusedasstartingpoint.However,thetime
gaptotheobservation5581istoolargeandtheperioddeterminedfromtheACIS-CC
observations4670to4673isnotaccurateenoughtokeepthephasecycles.
Basedonthereferenceperiod,thephaseofthemaximuminthephasebinnedlightcurve
wascalculatedfittingtheFourierseries(equation4.1)fromthereferenceobservationand
fromtheobservationnexttoitintime.Then,theperiodisvariedwithinitserrorsinorder
tominimisethephasedifference,assumingthattheperiodintheseobservationsisnot
changingandthenextobservationwasadded.Assuminganinitialguessforf˙intherange
between−15and−5×10−16Hz/s,thechangeintheperiodduetothesecularspin-down
becomescomparabletotheperioderrorafter150daysfromthereferencetime.Thenthe
periodandf˙werevariedwithintheirerrorsinordertominimisethesumofthesquared
phaseresidualsweightedbytheirerrorsfromthelightcurvefit.Thenextobservationwas
thenaddedandthewholeprocedurewasrepeated,findingnewvaluesoftheperiodand
f˙.Theperioderrordecreaseswiththegrowingtimespantothereferencepointfollowing
thegeneralapproachin[72],whiletheerroroff˙iscalculatedfromthedifferentvalues
off˙obtainedbyvaryingthephaseresidualswithintheir1σerrorsduringthisiterative
cedure.ropTheconvergenceofthetimingparametersisillustratedinfigure4.9.Ifadifferentinitial
periodischosen(e.g.P1orP3),thephaseresidualsaresmallaroundthereferencepoint,
butgrowwithlargertimedistanceandfinallyscatterarbitrarilybetween0.5and−0.5.
DeterminingthephaseresidualswiththeFourierseriesleadstoanimprovementofthe
χ2/d.o.f.forthelightcurves(seeforexamplefigure4.10)andtoabetterdetermination
ofthephaseshift.Thephaseofthemaximumlightdeliversthetimeofthemaximumlight
closesttothemiddleoftheobservation,thetimeofarrival(TOA),see[63;129].Fitting
thelightcurveswithonlythreeFourierharmonicsisjustifiedsinceinmostofthecasessome
Fouriercoefficientsarenegligible(seethecoefficientsfromthephasefoldedlightcurves
oftheEPIC-pnobservationsinfigure4.11asanexample).Thetemporalevolutionofthe
Fouriercoefficientsindicatesthesubstantialchangeofthelightcurves(seealso[52]),i.e.
oftheobservedgeometryoftheemission[109],asalreadyreportedin[22;41].

utionssolTiming4.2.2Thephasecoherenttimingwasperformedbybinningthelightcurvesinto10,12,16,18
and20phasebins.In[63;129]thelightcurvesofRXJ0720.4−3125werefoldedinto16
phasebins,alsofortheMOSdata.Ifthenumberofphasebinsislarge,thelightcurves

49

TSRESUL4.

4erroFigurerbars4.8:denoteLeft:the1σIndividualpuncertainteriodsy,seefrom[110].observationsSquareswithmarkmopreeriodsthan10derivedfromphotons.XMM-The
NewtonEPIC-MOS1andMOS2observations(hardband),dotsEPIC-pnobservations(hard
Theband),verticalcirclesdottedChandralineshowsHRC-S/LETGthereferenceandAtimeCIS-CCgivendatain(ha[129]rdban(“alld)anddata”starssolution)ROSATanddata.the
horizontaldashedlineindicatestheperiodevolutionderivedfromthe“alldata”solutionin
[129].Right:ThesameasleftbutusingthesoftbandforEPIC-MOS1andMOS2,EPIC-pnand
data.CIS-CCA

Table4.4:Periodandf˙derivedfromdifferentmethodsinthiswork,comparedtoprevious
results.excluded.ForAlltheerrorstimingcorrespsolutionondinto1thisσwork,confidencethe(foChandrartheZHRC2solutionobservationsee7251[110]wawithsalwerroaysrs
1scaledtoχ2/d.o.f.).
2˙solution×per10−iod7[−s]8.391115f×10−16[Hz/s]r[sms]d.o.fχ/d.o.f
thiswork,hardband

“allwithoutdata”ROSAT33..362(39)336(22)−−99..946(74)961(67)00..60626470−−33
2withoutChandra3.310(22)−9.940(71)0.6158−3
ZZ21“allwithoutdata”ROSAT23..96(13)09(14)−−910..992(61)047(34)00..58736470−−33
Z112withoutChandra3.09(13)−9.980(36)0.7258−3
thiswork,softband

“alldata”3.429(22)−9.956(72)0.5070−3
Z12“alldata”3.31(62)−9.959(17)0.5070−3
previouswork(appliedtothehardband)

[129](“alldata”)2.670(84)−9.88(13)0.9770−3
[63][129](“all(withoutdata”)ROSAT)32..20(13)846(77)−−99..74(04)918(15)01..64307064−−33
[63](Chandra)3.05(16)−9.97(06)0.6412−3

50

454747644651

4039

812075657

Timing4.2

duringFigurethe4.9:iterativeEvolutionproofcessf˙app(upperroachingpanel),theperiofinaldtiming(middle)solutionandph(maaserkedresidualwiths(lodottedwerlines).panel)
ThedataisobtainedfromthetimingsolutionwithoutROSATdataforthehardband.All
errorsdenote1σ.

intheChandradatascatterduetothesmallcountratecomparedtoXMM-Newtonwhile
toofewbinsresultinaninsufficienttimeresolution.ThetimeresolutionfortheMOS
detectorsis0.3s(smallwindow),0.9s(largewindow)and2.6s(fullframe),i.e.lessthan
onephasebin.Thisiscompensatedforbythelargenumberofphotons.Thebesttiming
solutionregardingthelowestmeanofthephaseresidualsforallobservations(excluding
ROSATdataandtheHRCobservation7251)wasderivedfor12phasebins.
Fittingthephasefoldedlightcurveswithapuresinusoid,thefinalvaluesofthetiming
solutionforthehardbandareP=8.3911153307(22)sandf˙=−9.933(52)×10−16Hz/s
forthephasecoherenttimingsolution.Thiscorrespondstoχ2/d.o.f.=12.7forthetiming

51

TSRESUL4.

Figure4.10:Phasebinned(40bins)lightcurve(400−1000eV)oftheXMM-Newton
EPIC-pnobservationrevolution1086(November2005)foldedduringthetimingprocedure.
ThesolidlinerepresentsthecombinationofthreeFourierharmonicschosenforthephase
determination.Thephaseshiftdiffersslightlyfromthatofthesinefit(dottedline).The
dashedlineshowsthatfittingonlywiththesecondharmonic(cosine)isnotalwayssufficient.
TheerrorbarsdenotePoissonianerrors.

solutionandfortheindividuallightcurvefitsχ2/d.o.f.=2.29onaverage.
FittingthelightcurveswithavariablecombinationofthethreeFourierharmonics,didnot
changetheresultsignificantly:P=8.3911153362(39)sandf˙=−9.946(74)×10−16Hz/s;
howeverthephaseresidualshavesmallererrors(seee.g.figure4.10)andthereforethetim-
ingsolutionautomaticallyyieldsalargervalueofχ2/d.o.f.=47.Thelightcurvesfitwith
χ2/d.o.f.=1.23onaverage.
TheperiodsdeterminedfromtheROSATdata[19;151]differsignificantlyfromtheref-
erenceperiodP2(seetableA.1)butinclusionoftheROSATdata(table2.1)extends
thetimespanofobservationsfrom≈9.6yrsto≈16.5yrsandenlargesthedataset
from64to70observations.Thephasecoherenttimingsolution(fittingthelightcurves
withavariablecombinationofthethreeFourierharmonics)includingROSATdatare-
sultsinP=8.3911153336(22)sandf˙=−9.961(67)×10−16Hz/sfor12phasebins.
Thiscorrespondstoχ2/d.o.f.=45forthetimingsolutionandthelightcurvesfitwith
χ2/d.o.f.=1.17onaverage.
WhentheChandradatawereexcluded,buttheROSATdatawerestillused(58data

52

4.2

Timing

Figure4.11:Fouriercoefficientsfromthephasefoldedlightcurvesofthe16XMM-Newton
EPIC-pnobservationsofRXJ0720.4−3125.Thedesignationofthecoefficientsfollowthat
4.1.equationin

setsoutof70)andthesamereferencetimewaschosenasbefore,thetimingsolution

resultedin(againfittingthelightcurveswithacombinationofthefirstthreeFourierhar-
monics)P=8.3911153310(22)sandf˙=−9.940(71)×10−16Hz/sfor12phasebins

thatcorrespondstoχ2/d.o.f.=47forthetimingsolutionandforthelightcurvefits

53

TSRESUL4.

˙2FigureChandra4.12:observationsTheZ1values(excludinginthetheP−HRCfplaneobservationderived7251)fromoftheRXJ0720.4XMM-Newton,−3125ROSAcompaTandred
totheresultsofthephasecoherenttimingsolutionsinthiswork.Thepeakislocatedat
P=solutions8.derive391115309(14)dwithoutsandChanf˙dra=data−9.(op992(61)en×circle),10−16withoutHz/s.ROSATheTthreedata(star)differentandtimingusing
box),XMM-Newton,butbecomeROSAvisibleTandenlargingChandratheredobservationsbox(sho(dot)wninarethenotupperresolvedleftponanel);thissthecalevalues(red
arederivedlistedfromintabletheha4.4.rdTheband(erro400rs−denote1000eVthe).formal1σuncertainty.Alltimingsolutionsare

Figure4.13:PhaseresidualsofRXJ0720.4−3125afterapplyingthetimingsolutionderived
withouttheROSATobservationsandwithouttheChandraHRCobservation7251(marked
asafilledcircle)appliedtoallobservations.

54

Timing4.2

χ2/d.o.f.=1.21wasobtainedonaverage.
Toverifythecorrectnessofthetimingsolutions,theZ12methodwasappliedtothesame
combinationofobservationsasforthephasecoherenttimingsolutions.Usingall70
datasets,themaximumpeak(Z12=8263)islocatedatP=8.391115309(14)sand
f˙=−9.992(61)×10−16Hz/s,seefigure4.12.Theerrorsoftheperiodandf˙areobtained
fromtheequationin[110],wherethevaluescorrespondtothemaximumpeakinthecentre
toχ2/d.o.f..
ofthe1σconfidenceregion.Inthisregionthepeakissymmetricandtheerrorsarescaled
Toshowthedifferenceofthetimingsolutionsinthedifferentbands,aphasecoherent
timingsolutionforthesoftband(includingall70datasets)wasalsoperformed.Allresults
arelistedintable4.4.
Afterthenewphasecoherenttimingsolutionswithconstantspin-downwereapplied,the
dataofRXJ0720.4−3125stillexhibitlargephaseresiduals,seeforexamplefigure4.13in
comparisontofigure1.6.DuetotheFourierseriesfitting,theerrorsofthephaseresiduals
aresmallerthanpreviously(figure1.6),sincethelightcurvesfitbetter.However,the
smallererrorsformallyincreaseχ2/d.o.f.ofthetimingsolution.Thetrendofthephase
residualsdiffersonlyslightlyforthedifferenttimingsolutions.Notethephasegapbetween
thehardandthesoftbandoftheXMM-NewtonEPIC-pndataandthebetteraccordance
oftheresultsfromthehardbandtotheotherinstrumentsachievedbytheband-cutat
400eV,asshowninfigure4.13.

55

4.

TSRESUL

56

5

Discussion

Inthischaptertheresultsofthisworkaresummarisedanddiscussedtogiveanoverview.
Thefocusisputonthetimingresults.Twomainexplanationsforthebehaviourof
RXJ0720.4−3125arecompeting:precessionandtheglitchhypothesis.However,inprin-
cipletherearemoreexplanationsthatappearedduringtheworkandthatwillbediscussed
hereaswell.Thesefurthertheoriesareexaminedfortheiradvantagesanddisadvantages.
Forcompletenessandforcomparisontopreviousworks[41;51],theresultsfromphase
resolvedspectroscopyarediscussedhereaswell.

5.1Updatedinterpretationofthespectralandtempo-
ralvariationsofRXJ0720.4−3125

Precession5.1.1

FreeprecessionofRXJ0720.4−3125wasfirstproposedby[22]andmoreevidences
werefoundwithnewdata[41;43]yieldingaprecessionperiodofPres≈7yrs.If
RXJ0720.4−3125precesses,itwouldcauseanadvanced(theNSprecessestowardsthe
observer)andaretarded(theNSprecessesbackwardswithrespecttotheobserver)signal,
wherethetimingresidualswouldfollowasine[92],asdiscussedinsection1.4.2.Fortwo
hotspotsonthesurfaceofRXJ0720.4−3125thephaseresidualsqualitativelymayhavethe
shapeofanabs(sine),havingtwicetheperiodofthecorrespondingsine(Pres≈14yrs),
sincethetimingisnotsensitivetowhichhotspotiscausingtheresidualsandprecessing
towards/backwardsthelineofsight.Thereisevidenceforsuchalongerperiodseenin
thevariablephaselagsbetweenhardandsoftphotons,see[41;43;51]andfigure4.13.
However,ithastobeshownwhetherthisscenariocanexplainthespectralbehaviourseen
infigure4.1aswell.Formally,alsothespectralchangeswouldthenundergoaperiodic
behaviourhavingPres≈2×7yrs.AlongtermperiodofPres≈14yrscouldexplainwhy

57

DISCUSSION5.

thespectralchangesdonotshowaperiodictrend(figure4.1)yet,sincethetimespanof
theXMM-Newtonobservationswouldcoverlessthanonecycleinthiscase.
Indeed,thephaseresidualsinfigure4.13seemtofollowaperiodicpattern.Ifthephase
residualsincludingthemostrecentdataarefittedwithanerrorweightedsineorabs(sine),
thelongtermperiodsare7−9yrsor14−18yrs,respectively.Thefitresultsarelisted
intable5.1andshowninfigure5.1(forthetimingsolutionwithoutROSATdata).In
allcases,thefityieldsformallyunacceptablevaluesforχ2/d.o.f.However,evenreducing
thesystematicerrorsfromthedifferentinstrumentsduetoenergyselection(hardphotons),
stillsomeChandradatapointsdeviatefromthephaseresidualsderivedfromXMM-Newton
datacloseintime,suggestingthatthesystematicerrorislargerthanthestatisticalerrors.
Thus,scalingtheerrorswithafactoroftwo,thevaluesforχ2/d.o.freachfrom1.3to2.4.
Moreover,ifthetwohotspotshaveslightlydifferentproperties,thetwohumpsinthesine
orabs(sine)arenotequal,thatalsoworsenstheformalχ2/d.o.fvalue(seechapter6).
ThenewturningpointofthephaseresidualswouldhavebeenatMJD=55387−+107100days
(firsthalfofJuly2010)oratMJD=55240−+88days(firsthalfofFebruary2010)forthe
sineortheabs(sine)fit,respectively(seefigure5.1).
Sincethesineandtheabs(sine)fitsresultinunacceptablevaluesforχ2/d.o.fandboth
assumeacertainshapeoftheperiodicpattern,thestringlengthalgorithmthatmakesno
assumptionfortheshapeandispredestinedforsparsedatawasimplementedtosearch
foralongtermperiod.Thestringlengthofthephaseresidualsreachaminimumfora
longtermperiodbetween6and8yrswithanabsoluteminimumat≈6.8yrs.Although
thisminimumisnotsharp,apuresinewouldalsocauseabroadminimumsincethephase
residualsaresparsewithvariabletimegapsbetweentheobservations.Ifthephaseresiduals
didnotfollowaperiodicpattern,thestringlengthperiodogramwouldlookdifferent.The
resultsareshowninfigure5.2.
Freeprecessionmayoccuriftheneutronstarhasanellipticshapewithellipticity,preces-
sionperiodPresandspinperiodP,whichroughlyfollowtherelationP∼Pres×[57]fora
rigidbody.Thisleadsto≈10−8forRXJ0720.4−3125.Althoughdeformationcausedby
centrifugalforcesarehighlydependentontheEquationofState(EoS),RXJ0720.4−3125
hasafartoolargespinperiod,sothatthispossiblesourceofdeformationcancertainlybe
excluded,see[57],equations13to15therein.
Motivatedbytheobservationofglitchesinradiopulsars,neutronstarsaresupposedto
hostafluidinteriorundertheircrust.Thisinteriorwouldinteractwiththeinnercrust
andwouldcausedampingoffreeprecessionduetomutualfriction[5].Inthecaseof
RXJ0720.4−3125,freeprecessionwouldhavebeendampedafter130to3500yrs(again,
stronglydependentontheEoS),atleastahundredtimeslessthantheneutronstar’s
[122].age

58

5.1UpdatedretationinterpofthespectralandtempraloRXriationsvaJ0720.4−of3125Tableobservations5.1:Fitusedforesultsrthefromcurrentfittingtimingthephasesolutionsaresidualsreusedwithforathesinefitsoofrtheabs(sine).longtermOnlyperiothoseds.
Allerrorsdenote1σ.
longtermfitPresrmsd.o.fχ2/d.o.f
[yrs][s]
”data“allsine7.30±0.370.2970−57.8
abs(sine)14.35±0.310.3170−58.6
TROSAwithoutsineabs(sine)178..9148±±00..212400..19216464−−5556..35
Chandrawithoutsineabs(sine)147..2641±±00..183000..33315858−−5589..77

Precessioncausedbyanunseenperturberislikelyexcluded:ifrpisthedistanceoftheper-
turber(havingthemassMp)totheneutronstarandθpistheinclinationtotheperturbers
orbit,thentheperturbermassrequiredforboundprecessionwouldbe(seealso[80])
2π8Mp=3GPPrescosθprp3.(5.1)
IncludingthevaluesofRXJ0720.4−3125(Pres=14yrs,=10−8),theperturbermass
wouldscalewithMp≈5×10−11×(rp/1km)3×M.Indeed,therequiredperturber
masswouldbearoundsomeM,ifitwaslocatedat∼3×103kmfromtheneutronstar.
However,atthisdistancetheperturbercouldnotbecomposedbyordinarymatter,buthas
tobeeitheranotherneutronstarorablackhole.Moreover,aperturberofafewJovian
masseswouldbelocatedevencloser(atafew102km)totheneutronstar.
IfRXJ0720.4−3125showsprecession(thatisstronglysupportedbythevariablephaseshift
betweensoftandhardphotons),thensomethingpreventsdamping(seee.g.section5.1.3)
ortheprecessionwascausedrecently,i.e.withinthelastfewthousandyears.Certainly,
RXJ0720.4−3125doesnotshowboundprecession.

othesishypglitchThe5.1.2Anotherhypothesistoexplainthephaseresidualsisaglitcheventthatwouldchangethe
spinperiodandthespin-down.Applyingthe“alldata”glitchsolutionproposedin[129]
withaglitchthatoccurredattg=52866dayssignificantlyreducesthephaseresiduals
fortheobservationsavailableatthistime(MJD=53500days).However,includingthe
mostrecentXMM-NewtonandChandraobservationsfromthiswork,theresidualsgrowto
largervalues.Therefore,anewparameterwasintroducedbyfittingaparabolicslopeto

59

DISCUSSION5.

Figure5.1:PhaseresidualsofRXJ0720.4−3125afterapplyingthetimingsolutionderived
withouttheROSATobservationsandwithouttheChandraHRCobservation7251(marked
asafilledcircle)toallobservations.Thebestfitswithasineandanabs(sine)model(only
theobservationsusedinthecurrenttimingsolutionareusedforthefits)arealsoshown
(seetable5.1).Symbolsfollowthoseinfigure4.8andfigure4.13,allerrorbarsdenote1σ.

theglitchsolutionin[129]withthephysicalmeaningofapost-glitchcorrectionf˙cforthe
spin-down,whilekeepingtheparameters,asvalidbeforetg,constant.Theerrorweighted
fitforthehardbandusingalldata(andfittingthelightcurveswithapuresinetobe
consistentwith[129])yieldsf˙c=−1.11±0.10×10−17Hz/s(errorsindicate1σ)that
significantlyreducesthephaseresiduals.In[129]thepost-glitchspin-downwascalculated
tobef˙old=−1.040±0.030×10−15Hz/s,i.e.thecorrectedvalueisf˙new=f˙c+f˙old.All
otherparameters(spinperiodandspin-downbeforetg,spinperiodaftertgandtgitself)
areequaltothosein[129].Comparedtothesineandabs(sine)fits,thenewglitchsolution
formallyfitsbetter(χ2/d.o.f=2.8,rms=0.31s),seefigure5.3.
AglitchwouldexplainthesuddenriseofthetemperaturearoundMJD=53000days,
followedbyaslowcool-down.However,theglitchesknownfromradiopulsars(here,no
temperaturescanbemeasured)haverelaxationtimes(inthetiming)ofsometensor
afewhundreddays,whileRXJ0720.4−3125hasnotreacheditsinitialtemperaturefor
sevenyears.Figure4.1indicatesthatthetemperaturerisealreadybeganoneyearbefore
tg(MJD=52500days)andjustacceleratedattg.Whilethehardnessinthespectra
changed,thetotalX-rayluminosity(120−1000eV)stayedconstant.Bothfactswould

60

5.1Updatedinterpretationofthespectralandtemporalvariationsof
3125−J0720.4RX

Figure5.2:Thestringlengthsderivedfromthephaseresiduals(takingallerrorsintoac-
count)showninfigure5.1,representedbyblacklines,comparedtothestringlengthsifthe
phaseresidualswouldhavebeenproducedbyapuresine(red)andrandomly(blueline).

notexcludeaglitch,butthechangingphasegapbetweenhardandsoftphotonsandthe
decreaseofthesizeoftheemittingareaatthesametimecannoteasilybeexplainedby
del.moglitchthe

5.1.3Tkachenkowaves

Freeprecessioninaneutronstarissupposedtobedamped[57;79],buttheremightbea
mechanismthatpreventsprecessionfrombeingdamped.In1970,Tkachenkowaves(that
arestandingsoundwavespropagatinginthelatticeofneutronvortices)wereproposed
toexplainthelongtermperiodicvariationsoftheCrabpulsar[112].Suchphenomena
areobservedinsuperfluidheliumunderlaboratoryconditions[123].Recentlyitwaspro-
posed[103]thataglitchgeneratedTkachenkowavesinRXJ0720.4−3125thatleadsto
precessionwiththeprecessionperiodPp(Pp∼P/)equaltotheperiodofthestanding
TkachenkowavePT(i.e.theperiodsareinresonance).SincetheTkachenkowaveprop-
agatesparalleltotheneutronstar’sspinaxisandtheneutronstar’smomentofinertiais
non-symmetric,i.e.>0,Tkachenkowavesperiodicallychangethespinfrequency.
Assumingthattheneutronstariscomposedofacrustwithanegligiblemomentofinertia
andasuperfluidinteriorbelowit,onlyconsistingofneutrons,theperiodoftheTkachenko

61

5.

DISCUSSION

Figure5.3:Upperpanel:ThephaseresidualsofRXJ0720.4−3125afterapplyingthe
glitchsolution(“alldata”)in[129].Theglitchtimetg=52866daysismarkedasdotted
verticalline.Accordingtoequation3.4,thedeviantpointsaftertgarefittedwithanerror
cowightedrresppaondingrabtoolicapslopeost-glitch(solidcoline,rrectiondottedofpaf˙rab=olic−1.lines11(10)×indicating10−17theHz1σ/s.confidencerange.)
cLowerpanel:Thephaseresidualsafterapplyingthepost-glitchf˙correction.Symbolsfollow
4.8.figureinthose

62

5.1Updatedwaveinyearswouldbe

retationinterpofthespectralandtempraloRXriationsvaJ0720.4−of3125RP
PT∼1.77×10km×1s,(5.2)
see[112].InthecaseofRXJ0720.4−3125,equation5.2yieldsalongtermperiodof
5−7yrsforreasonableradii.Itshouldbementionedthatequation5.2onlyaccountsfor
thefifthharmonicoftheTkachenkowave,following[112].Afterthelongtermvariations
oftheCrabpulsarcouldnotbeverified,Tkachenkowavesdidnotplayaroleinastrophysics
foralongtime.Onlyrecently,Tkachenkowaveswereinvestigatedinmoredetail[93].In
contrasttoasuperfluidsphere,in[93]themodesarecalculatedforashelloftwosuperfluids
fordifferentshearviscositiesofnormalmattercouplingtothesuperfluids.Generally,the
periodsderivedforstrongcouplingarelargerthanpredictedbyequation5.2andthemutual
frictionmaybetooweaktodamptheoscillation.Hence,evenalongtermperiodof15yrs
forRXJ0720.4−3125couldbeexplainedinthisway.Severalradiopulsarsshowquasi-
periodicstructuresintheirtimingbehaviour.These“periods”areafactorofafewtoo
largetoobeyequation5.2,butcouldbeexplainedbyTkachenkowavesinprinciple−just
withastrongcouplingofthenormalmattertothesuperfluidorforalowerharmonicthan
thatusedforequation5.2.
TheprobabilitytoobserveaglitchcausingprecessionviaTkachenkowavesseemstobe
low[103].In[145],alongtermperiodicoscillationwithaperiodofapproximatelyoneyear
wasobservedintheglitchingradiopulsarPSRB2334+61afterremovingthe(nonphase
coherent)glitchsolution.Thus,Tkachenkowavesmeritmoredetailedinvestigationsand
acollaboration(withSergeiPopovandArmenSedrakian)hasalreadystarted.

5.1.4Circumstellarand/orfallbackdisk
Itisdiscussedin[3;4]thatsomeneutronstarsmaybesurroundedbyafallbackdebrisdisk
thatisleftoverfromthesupernovaevent.Evidenceforsuchafallbackdiskwasdiscovered
aroundtheneutronstar4U0142+61[138].Sincethediscoveryofanarrowabsorption
featureintheXMM-NewtonRGSspectraofRXJ0720.4−3125[44]thatlikelyoriginates
fromhighlyionisedoxygen(andthepresenceofmaybetwofurthernarrowabsorption
featuresfoundintheChandraHRC-S/LETGspectrainthiswork)thereisevidencefora
fallbackdisksurroundingRXJ0720.4−3125aswell.
Theinterpretationofsuchafeatureisapriorinotclear(seealsothediscussionin[44]):
Ifthelineoriginatesfromtheneutronstaratmosphere,itisredshiftedbyafactorof1.11
(M=1M,R=16km)to2.00(M=2M,R=8km)andtheionitselfisnotknown.
DuetotheStark-effect,pressureandtemperature,thelinesshouldbebroadened[96]to
sometensofeVandsplittedbytheZeeman-effect,dependingontheatomicnumberZ.

63

5.DISCUSSION

Figure5.4:SpectralenergydistributionofRXJ0720.4−3125fromthenearinfraredtoX-
rays.ThesolidlinerepresentsthemodelspectrafromXMM-NewtonEPIC-pnfittedwiththe
aredatapobtainedointsfromfromthetheobservationsXMM-NewtonrevolutionEPIC-pn0078(seeobservationalsotablerevolution2.2).The0815blackwithdatathepbroadoints
16boabsodyrptionemissionfeaturefrombseenothatX-ra300yeV(observations7.25×10withoutHz).anyabThesorptiondashedforlinesTeff=indicate86.5±the0.4blackeV
and94.7±0.5eV,respectively.TheUandBmagnitudesarelistedin[91],theVband
magnitudeistakenfrom[28],Rfrom[74]andtheHbandmagnitudegivestheupperlimit
[105].tordingacco

TheπlinesareshiftedbyΔEπ∼0.1keV×(B/1011Gauss)2×(26/Z)2whiletheσlines
areshiftedbyΔEσ=(11/5)Eπandthecentreisalsoshiftedtowardshigherenergiesby
ΔE∼0.17keV×(B/1011Gauss)2×(26/Z)2.Moreover,thecentreshiftdependsonthe
electrondensity,see[114].
Thedetectedlineenergyof0.57keVfitstoOVIIorOVI[47]withoutgravitationalredshift.
SuchlinesaredetectedinsomeGalacticlow-massX-raybinaries[144].Thus,thelinelikely
originatesfromtheinterstellarorcircumstellarmedium.Ifhighlyionisedoxygenispresent
closetotheneutronstarsurface,OVIIIat0.653keVshouldappearat0.57keVwitha
reasonableredshiftof1.16(or1.17)andthecorrespondingOVIIKαresonancelineshould
appearat0.49keV.In[44]itisargued,thatsuchanabsorptionfeatureprobablycouldbe
seen.WhilethisabsorptionfeaturecouldnotbedetectedintheRGSdatainthiswork,an
absorptionlineattheparticularenergyintheChandraHRC-S/LETGdatawasfound.In
addition,afurtherabsorptionfeatureat0.53keVwasfoundintheChandraHRC-S/LETG

64

5.1UpdatedretationinterpofthespectralandtempraloRXriationsvaJ0720.4−of3125Table5.2:OrbitalelementsafterfittingthephaseresidualsofRXJ0720.4−3125infigure5.1
withanorbitalsolution.Allerrorsdenote1σ.
valueelementrbitaloperiod2530±130days
6.93±0.35yrs
eccentricity0.93±0.10
long.ofascendingnode−0.45±0.32rad
periast.passage[MJD]50220±130days
aComp×sin(i)3.8±2.3AU
a×sin(i)0.0026±0.0016AU
χ2/d.o.f640/(70−7)=10.2
massfunction/sin3(i)3.3±6.3×10−7MJ

data(seefigure4.6)thatlikelyoriginatesfromtheK-edgeofneutraloxygenOI[60]at
rest.Thisindicatesanoverabundanceofneutraloxygeninthelineofsightormightbea
resultofinexactmodelingoftheedge.
AllM7aredimintheopticalbands(seetable1.2),butthemeasuredopticalfluxesare
5to10timeslargerthanexpectedbyextrapolatingtheblackbodyX-rayspectrum.For
RBS1774theopticalexcessisevenafactorof≈30,see[153].Itisshownin[44]
thatanambientmedium/cloudaroundRXJ0720.4−3125couldexplaintheopticalexcess
(figure5.4)foracertainsetofparameters(Note,thatRXJ1856.4−3754alsoexhibitsan
opticalexcess,butnodiskcouldbedetected[108].Theopticalexcesscanalsobeexplained
byacondensedhydrogenatmosphere,see[48;155;156],andnotmandatorywithadisk.).
IfthiscloudordiskhasapatchystructureandorbitsaroundRXJ0720.4−3125,itmay
accountalsoforthespectralirregularities.Afallbackdiskcouldeasilyleadtoanaccretion
eventbytheimpactofanasteroid,asproposedby[129]fortheglitchevent.Eventuallya
diskmayblockradioemission,asshownin[29],unlessRXJ0720.4−3125isanoff-beam
pulsarwhichismorelikely.
CertainlyafallbackdiskdoesnotexplainallpeculiaritiesofRXJ0720.4−3125,e.g.(again)
thevariablephaseshiftbetweenhardandsoftphotons,butadetectionornon-detection
wouldruleoutsomepossibilities.Adebrisdiskheatedbytheneutronstarwouldhave
temperaturesabout100to1250K(lastnumberreferstothelimitforevaporationof
dust)foradistanceof0.67to6.7AU,respectively,hencewouldbedetectableinthenear
infrared[6].ThereforeaSpitzerobservationwasproposed(andaccepted)[106],butnot
et.yexecuted

onmotiOrbital5.1.5Neutronstarsthathostplanets,orbetterhostobjectswithplanetarymasses,arearare
configurationbutareclearlydetectedinafewcases,seee.g.[9;140].Ifaplanetorbited

65

DISCUSSION5.

Figure5.5:ErrorweightedorbitalfitofthephaseresidualsofRXJ0720.4−3125.The
symbolsfollowthoseinfigure5.1andfigure4.8.

aroundRXJ0720.4−3125,itwouldcauseorbitalmotionoftheneutronstararoundthe
commonbarycenter.Thiswobblingwouldcausetimedelaysinthearrivaltimesofthe
pulses,sincethelightneedsmoretimetotraveltheadditionalwayfromtheprojectionof
thesemimajoraxis(havinganinclinationioftheorbitalplane)withrespecttoadistant
observer.Viceversa,theorbitalmotioncausesanadvancedsignalforadifferentorbital
phase.Dependingontheorientationandtheeccentricityoftheorbit,thephaseresiduals
donotnecessarilyfollowasinusoid.
SincethelongtermperiodofRXJ0720.4−3125isonatimescaleofyearsandtheneutron
starmassshouldbecomparabletoasolarmass,thepossiblecompanionshouldhavea
mass,MComp,ofaboutsomeJovianmasses.Non-detectionsintheH-band[105]downto
22.9magyieldanupperlimitofMComp=15MJforRXJ0720.4−3125,ifthecompanion
formedtogetherwiththeneutronstarafterthesupernova1Myrsagoandstillcoolsdown.
ThislimitforMCompisvalidforadistanceof360pcofRXJ0720.4−3125totheSun.
Fittingthephaseresidualsshowninfigure5.1withorbitalmotionyieldsMComp×sin(i)=
0.93MJassuminganeutronstarmassofM=1.4M.Theinclinationoftheorbitis
unknown,butassuminganuniformdistribution,theprobabilityislessthan4%thatsuch
ahypotheticcompanionwouldhaveamassabove15MJ(inclinationlessthan3.6◦),i.e.
couldhavebeendetectedin[105].Thus,acompanioncouldstillbeundetectedbydirect

66

5.2Phaseresolvedspectroscopy

imaging.Thefitresultisshowninfigure5.5andtheorbitalparametersarelistedintable5.2.To
obtainareasonablefit,itisnecessarytocoveratleasttwocycles,i.e.thephaseresiduals
obtainedfromtheROSATdataareincludedfortheorbitalfit.
Thefittedorbitishighlyeccentric,i.e.ishardtodetermine,thustheorbitalelements
havelargeerrorsandthefitcorrespondstoχ2/d.o.f=10.2,thatisevenworsethanthe
sineandabs(sine)fitslistedintable5.1.Sincetheorbitalmotionalsodoesnotexplain
thevariablephaseshiftbetweenhardandsoftphotonsandthefityieldslargeerrors,the
companionhypothesismightbeunlikely.Fortunately,whensearchingforafallbackdisk
withSpitzer[106],anobjecthavingafewJovianmassescanalsobedetected,ifexisting.

5.2Phaseresolvedspectroscopy

ThevaluesofthespectralpropertiesofRXJ0720.4−3125intable4.2arederivedfromthe
spinphaseaveragedspectra.Whilerotating,RXJ0720.4−3125exhibitsdifferentpartsof
itssurfacedependingontherotationphase.Thespectralpropertiesforacertainrotation
phasemightbedifferentfromthevalueslistedintable4.2.Toderiveaphaseresolved
evolutionofthespectralproperties,acertaintimingsolutionhastobeappliedtoassign
thephotoneventswithaphasevalue.
In[41],figure4therein,suchaninvestigationwasperformedusingthe“alldata”phase
coherenttimingsolutionin[63].Withinthisthesis,anupdatedtimingsolutionderivedby
includingthemostrecentobservationsisnowavailable,aswellasatimingsolutioninclud-
ingaglitcheventthatoccurredatMJD=52866days[129]butcorrected,asdiscussedin
section5.1.2.Theassignmentoftheeventsbyaphasevaluedependsontheappliedtiming
solutionandthusinfluencesthetrendofthephaseresolvedspectralvalues.Therefore,in
additiontotheothertimingsolutions,thephasewascalculatedusingtheperiodsofthein-
dividualobservations(seetableA.1,forthehardband,tobeinaccordancewiththetiming
solutionderivedinthisworkandthecorrectedglitchsolutiondiscussedinsection5.1.2)
withthereferencepointsettothetimeofmaximumlightclosesttothemiddleofthe
individualobservation.Inthiscase,eachobservationisindependentfromtheothers(thus,
nof˙isrequired).Thisavoidsthatanpulseprofileobtainedfromanobservation,thatis
notwellrepresentedbyacertaintimingsolution,isshiftedandsmearedoutforthephase
resolvedspectralfitting(i.e.nochangewithinarotationcyclecanbeseen,althoughit
exists).Accordingto[41]theXMM-NewtonEPIC-pnobservationsperformedinfullframemode
withthinfilterwereusedonly(seetable2.2).Thephasevaluesforeachphotonarrival
timewerecalculatedfromthefourdifferenttimingsolutionsmentionedbefore.Likein[41],

67

DISCUSSION5.

ofFigureRXJ0720.45.6:−Phase3125fromresolvedthe(fivespectraphasederivedbins)withevolutionofXMM-NewtontemperatureEPIC-pnandinfullequivalentframemowidthde
withthinfilterfordifferenttimingsolutions.Thecurvesobtainedfromthedataofrevolution
the0078(firstequivalentwidthobservation),)and0815revolution(spectra1792with(mosthighestrecentvaluesdata,ofseetemptableerature2.2)aandreshomownduluswithof
(mathickrkedblackredfolines.rTherevolutionsquares0078,indicate0815theand1792averageforbvaluesetteraccovisibirdinglity)tomarktablephase4.2,0the.0−circles0.2,
whiletheellipsoidaltracksevolvecounter-clockwise.Allerrorsdenote1σuncertainty,see
also[41],figure4therein,and[51],figure12therein.
UppUppererleft:right:AfterAfterapplyingapplyingthethetimingsolutionsolutionfromfromthisw[63],ork“all(withoutdata”ROSAsolutionTdata),therein.seesec-
[52].and4.2.2tionLowerleft:Afterapplyingthecorrectedglitchsolutiondiscussedinsection5.1.2and[52]
calculation.phasetherfoLowerright:Thephasewasderivedfromtheindividualobservationswherethemaximum
lightissettozerophase.

thephotonsweredividedbyphaseinfivebins(0.0−0.2,0.2−0.4,0.4−0.6,0.4−0.8
and0.8−1.0),i.e.65spectrawereobtained(13observations,eachdividedinfivephase
bins).Thesespectrawerefittedsimultaneouslywiththestandardfitmodel(seetable4.1)
withNH,σlineandElinekeptfree,butfittedwiththesamevaluesforall65spectra.All
otherparameterswereallowedtovaryforall65spectra,seesection4.1,[41]and[51].

68

5.2Phaseresolvedspectroscopy

Dependingonthetimingsolution,thespectrafitwithχ2/d.o.f.=1.13−1.14.Theevo-
lutionoftheequivalentwidthversustemperaturefollowsanellipsoidaltrackthatevolves
counter-clockwiseduringarotationcycle.Thevariationsofequivalentwidthversustem-
peratureforthedifferenttimingsolutionsareshowninfigure5.6.
Generally,theellipsoidaltracksmovedfromlowtemperaturesandlowernegativevaluesfor
theequivalentwidth(revolution0078)tohighertemperaturesandlargernegativevalues
fortheequivalentwidthandreachedtheirmaximumatrevolution0815(thisbehaviour
coversatimespanoffouryears).Sincethen,theellipsoidaltracksmovedslowly,but
steadilytowardstotheirinitialposition,buthavenotreachedityet(forfiveyears).During
thisevolution,thephaseaveragedvalues,aslistedintable4.2,movedalongastraight
line(fromrevolution0078torevolution0815)andmovedbackonthesametrajectory.
Whiletheellipsoidaltracksexhibitedaslimshape(revolution0078,0533and0534)atthe
beginningofthemission,theybecamebroader(untilrevolution0815)andnowseemto
becomeslimagain.Theexactshapeofthetrackandthemaximumvaluesreachedduring
arotationcycledependonthechosentimingsolution(seefigure5.6),whilethegeneral
trendisindependentfromthetimingsolution.
Intheaveragespectrumofrevolution0078,theequivalentwidthisconsistentwithzero,
butreachesextremevaluesinbothdirections,thatarenotconsistentwithzerofordiffer-
entphases,duringtherotationcycle.Theequivalentwidthevenisformallyinemission
(anabsoluteoffsetcouldhoweverbecausedbycalibrationuncertainties),alsoduringthe
revolutions0533and0534,ratherthanabsorptionforsomephases.
Theellipsoidaltracksseeninfigure5.6showthepresenceofcoolerandhotterpartsof
theneutronstars’surface,butfromtheirevolutionitisnotpossibletojudgewhetherthey
showalongtermcyclicbehaviourormovebacktotheinitialconditions,comingfroman
deviation.unique

69

5.

DISCUSSION

70

6

Modellingafreeprecessingneutron
rsta

Althoughthereisnofinalconclusionabouttheoriginofthespectralandtemporalchanges
ofRXJ0720.4−3125yet,forvariousreasonsdiscussedinchapter5,freeprecessionseems
morelikelythantheotherhypothesesmentionedinthiswork.Hereitissimulatedwhether
allchangescouldbetheproductoffreeprecession(ofaspherewithtwohotspotswhich
maynotlieexactlyantipodal)withonesetofgeometricalparameters.Theseparameters
arecompactness,spotsizesandtheirangularshiftwithrespecttoeachother,thetemper-
aturedistributionandtheviewingandprecessionangle.Aprecessingspherewithallthese
(thenfixed)parametersshouldreproducethechangesinthetemperatureandobservedsize
oftheemissionarea,thepulsedfractionandthephaseshiftbetweensoftandhardphotons.
SuchamodelwastestedforRXJ0720.4−3125byRobertoTurollain[154].However,it
wasnotpossibletoreproduceallpropertieswithonesinglesetofparametersatonceand
theparameterspaceistoolargetobescannedsystematically.Theintentionofthemodel
presentedhereistocreateasimplifiedbutfastercodetoscantheparameterspace.The
aimofthismodelingistostartfrombasicassumptionsandtoclarifywhethertheobserv-
ablepropertiescanbereproducedinprinciple(qualitatively),namelythenon-sinusoidal
variationsinthespectralpropertieswhileaperiodicpatterninthetimingbehaviourisseen.
Whensuchageometricconfigurationisfound,themodelalsoshouldobeythepulsedfrac-
tionandtheshapeofthelightcurves.Theresultsofthismodelthencouldbeusedfora
moreconstrainedinvestigationwiththemoredetailedmodelin[154].
ThesoftwareforthesimulationinthisworkwaswritteninMatlab.Thedetailsofthecodes
andthephysicalinputarediscussedhere.

71

6.MODELLINGAFREEPRECESSINGNEUTRONSTAR

delmoThe6.1

6.1.1Thegeometryoftheproblem
Tomodeltheemissiongeometryofaneutronstarwithtwohotspotsonitssurface,the
designationfortheparametersgivenin[109]andillustratedinfigure6.1isadopted.In
contrastto[109],wherethespothasaninfinitesmallsize,bothhotspotsareextended
inthiswork,sinceitisknownthatthesizeoftheemittingareaofRXJ0720.4−3125
correspondstoafewkmradius.
Ifzisthespinaxesoftheneutronstar,θistheanglebetweentheunitvectorn,that
pointsfromthecentreoftheneutronstartothecentreofthehotspot,andtheneutron
star’sspinaxis.Thespinaxisisseenbyadistantobserverwithaninclinationi.Whena
photonleavesthehotspotwiththeangleαwithrespectton,i.e.hastheinitialdirection
k0,itisinfluencedbygravity(leadingtolightbending),thuswillhavetheangleψ=α
withrespecttonatinfinity.Thefinaldirectionofthelightsignalisexpressedbythevector
k.Bydefinition,cos(ψ)=k∙n,thatyields

cos(ψ)=cos(i)cos(θ)+sin(i)sin(θ)cos(φ).(6.1)
Asseenfromfigure6.1,theangleφdenotesthespinphase,i.e.φ=2πt/Pwithφ=0
att=0withthehotspotfacingtheobserver.ψaccountsfortheapparentinclinationof
ot.sphottheFortheantipodalhotspot,onlyθ=π−θantipodalandφ=π+φantipodalhastobe
substituted,withtherestrictionthatthefluxequalszero,ifcos(α)<0.Usually,thehot
spotsarenotexactlyantipodal.Thereforetheshiftanglesθoffandφoffthataccountto
theoffsetofthesecondhotspotfromtheantipodalpositionareintroduced.

inputPhysical6.1.26.1.2.1Lightbendingandlightemission
Toconnecttheobservedlightpathtotheemissionfromthesurface,anexpressionleading
fromαtoψhastobefound.Theapproximation
cos(α)≈rs+1−rscos(ψ)(6.2)
RRwhichwasderivedby[10]wasadopted(usingtheSchwarzschildmetricwithrsbeing
theSchwarzschildradiusandRistheradiusoftheneutronstar).Theerrormadeby
equation6.2dependsoncompactnessandtheemissionangleα.Foranyemissionangle,
thiserrorislessthan10%iftheneutronstarexceedstwiceitsSchwarzschildradiusand

72

6.MODELLINGAFREEPRECESSINGNEUTRONSTAR

dF=N1−rsEcos(α)dcos(α)dS,(6.4)
dµRwhereNisanormalisationconstant(accountingfordistance,numberofphotonsand
constantfactors)andµ=cos(ψ).Withequation6.2,equation6.4canbeintegrated
(here:summed)accordingtothevariablesshowninfigure6.1.
Eachsurfaceelementhasagiventemperatureandemitslikeablackbodyandthelight
curveisobtainedbysummingupthecontributionsofeachsurfaceelementatthedifferent
spinphasesaccordingtoequation6.1.

6.1.2.2Temperaturedistributions
Thetemperaturedistributiononthesurfaceofanisolatedneutronstarisaffectedbythe
localmagneticfieldandiscurrentlynotfullyunderstood.Dependingonthemagneticfield
geometryanddifferentsurfaceconditions,variousmodelswereproposed[1;32;33;35;
101;148].Eachtemperaturedistributionitselfincludesfreeparametersanditisnotexactly
knownwhichdescriptionisvalidforRXJ0720.4−3125.Thusinthisworkthreedifferent
simpletemperaturedistributionswereimplemented.Theyareaprioryassumedandnot
derivedfromthemagneticfieldself-consistently.Sincetheradiusoftheneutronstarisjust
anormalisationfactorinthiscase,theradiusofacircularhotspotismeasuredbytheangle
Ξ.Thesimplesttemperaturedistributionisuniform:T(ξ)=T0ifξ≤Ξ,withrespect
tothecentreofthehotspot,andT(ξ)=0elsewhere.AnotherapproachisaGaussian
distributionwithT(ξ)=T0exp[−0.5(ξ/Ξ)2].Probablythemostrealisticdistribution
accordingto[35]isT(ξ)=T0|cos(ξ)|0.5.Herethelasttemperaturedistributionisnamed
“magnetic”,sinceitisanapproximationderivedfromthemagneticdipolefieldgeometry.
Unliketheothertwotemperaturedistributions,thisdistributionhasnosizeinthesenseofΞ
andisvalidfortheentiresurface.Alltemperaturedistributionsareillustratedinfigure6.2.
Asitwasshowninsection3.3,thephaseresidualsofRXJ0720.4−3125measuredwith
differentinstrumentsareinbestagreement,ifonlythehardbandof400−1000eVisused.
Thebroadabsorptionfeatureat300eVmightbeexplainedasacyclotronline.However,
thephysicaloriginofthislineisactuallyunclear,butthemechanismthatcausesthisline
hastobeknowntoimplementthisline(anditsvariation)correctly.Therefore,theline
wasnotincludedinthemodelandtheinvestigationsweremostlylimitedtothehardband
(wheretheinfluenceofthelineismuchlessthaninthesoftband).

6.1.2.3Freeprecession
Boundprecessioncausedbyacompanion(liketheEarth-Moonsystem)isprobablyan
unlikelyscenarioforRXJ0720.4−3125,asdiscussedinsection5.1.1,thusthisworkfocuses

74

delmoThe6.1

Figure6.2:Thedifferenttemperaturedistributionsusedinthiswork.Fromlefttoright:
uniform,◦Gaussian,◦“magnetic”.◦Inallthreeexamples,thecentraltemperatureequals100eV,
Ξ=20,φ=50andθ=80.

onfreeprecession.Fromthespectralvariationsitishardtodistinguishbetweenbound
precession,freeprecessionandnutation.
Freeprecessionoccurs,ifthespinaxisωoftheneutronstardoesnotcoincidewiththeaxis
ofsymmetry,s(herethenotationin[77]isadopted).LetLbethevectorofthe(total)
conservedmomentum,then,atanytimeω,sandLspanaplane.TheanglebetweenL
andωscaleswiththeellipticity,i.e.practicallyωandLarethesameaxis.
Inthisregimetwonewangleswereintroduced,theconstantwobbleangleθwbetweenLand
sandχthatisspannedbetweensandn,seefigure6.3.Anobserveronthesurfaceofthe
neutronstarwouldobserveacircularmotionofωaboutswiththeprecessionperiod[77].
Iftheobserversatontheemittingpolehe/shewouldseeωmovingaroundhim/herifθw
islargerthanχandhe/shewouldsitoutsideofthiscircle,ifθwissmallerthanχ.Both
caseswouldcausedifferentphaseresidualsforadistantobserver.Duetoprecession,the
spinphaseismeasuredtobeφ+ΔφwiththephaseshiftΔφ.Sincetheapproachthat
θwissmallisusedin[77]butthecontributionsfromtwohotspots(anddifferentsurface
elements)withdifferentlatitudesareneeded,themoregeneralequationsderivedin[92]
wereimplementedtocalculatethephaseshiftΔφ:

cos(χ)sin(θw)−[1−cos(θw)]sin(χ)sin(ωpt)
tan(Δφ)=sin(χ)cos(ωpt)+[cos(χ)sin(θw)+sin(χ)cos(θw)sin(ωpt)]tan(ωpt)(6.5)
ifχ>θw,and
sin(χ)cos(ωpt)
tan(Δφ)=−cos(χ)sin(θw)+sin(χ)cos(θw)sin(ωpt)(6.6)
ifχ<θw,whereωptistheprecessionphase.
Forthecode,thismeansthatθnewvarieswiththeamplitudeθwduringtheprecession
cycle,asitwouldbeseenbyadistantobserverwithθnew=θw+χ(accordingtofigure6.1
andfigure6.3),whereχcorrespondstothe“old”θinfigure6.1.Inthecaseofbound
precession,theinclinationvariesintimewiththeprecessionperiod,butθisconstantsince
thespinaxisrevolvesinaconealongtheprecessionaxis.

75

6.2Procedureandfitresults

precession)andthecodewastestedfirstwithone,laterwithtwohotspots.
Generally,lightbendingsmoothsthelightcurves,sincepartsoftheneutronstararevisible
thatwouldbeinvisiblewithoutrelativisticeffects.Forsomevaluesofthecompactness,
thelightcurvesundergosignificantchanges(seefigure6.4).Ifthehotspotshavedifferent
propertiesthatdeviatemuchfromeachother(e.g.sizeandtemperature),eachhotspot
willdominatethelightcurveinadifferentenergyband.Thecoolerspotappearswitha
phaseshiftof180◦relativetothehotterspot.Thisleadstoaphasegapoftheresiduals
betweentwobands,asillustratedinfigure6.4.ForRXJ0720.4−3125thepropertiesofthe
hotspotsmightbelessdifferentasinthecaseofthemodeledgeometryproducingthelight
curveseeninfigure6.4,butneverthelesswillproduceaphasegapbetweenhardandsoft
photons.However,thisphasegapwillbeconstantintimeandanadditionalmotion(e.g.
precession)needstobesuperimposedontotherotationtoproducevariablephasegaps
asseeninthephaseresidualsofRXJ0720.4−3125(figure4.13).Thegeneralinfluenceof
differentgeometriesisshowninfigure6.5andfigure6.6.Fromthelightcurvesonly,itis
notpossibletodistinguishbetweenfreeprecessionandboundprecession(figure6.5),since
theyqualitativelyundergothesamechanges.
ThelightcurvesofRXJ0720.4−3125arealmostsinusoidalandthepulsedfractionhas
valuesaround11%(120−1000eV)thatlimitspossibleconfigurationsforthesurface
geometry.Iftheinclinationhasvaluesaround90◦,θcannotbemuchlargerthan20◦,
otherwisethepulsedfractionwouldbetoolargeorthetemperatureprofileontheedgeof
thespothastobeverysmooth.Ontheotherhand,theinclinationcannotbefarfrom
90◦.Iftheinclinationwasclosetozero,i.e.RXJ0720.4−3125wouldbeseenpoleon,no
rotation(i.e.pulsations)wouldbevisibleforanyvaluesofθ.Moreover,thepulsedfraction
isalsoinfluencedbythepropertiesofthehotspotsthemselves,asillustratedinfigure6.7.

6.2Procedureandfitresults

IfthereisacombinationofthegeometricalpropertiesofRXJ0720.4−3125,thatfitsthe
firstXMM-Newtonobservationrevolution0078,thiscombinationshouldreproducethe
observablechangesoftheotherXMM-Newtonobservations,justbyvaryingtheobserved
latitudeofthehotspots(butkeepingsize,temperatureandtemperatureprofile)according
angle.obblewthetoThepossiblecombinationsthatfittheobservationrevolution0078areexploredusinga
MonteCarlosimulationfortheinclinationangelsfromi=20◦toi=135◦foreach
temperatureprofile.Theinclinationvaluesareincrementedwith10◦stepsize.Foreachin-
clinationandtemperaturedistributionupto105runswereperformedandthosegeometrical
propertieswerestored,thatfittheobservedtemperature(differencelessthanthemeasured

77

6.MODELLINGAFREEPRECESSINGNEUTRONSTAR

Figure6.4:Left:Syntheticlightcurveofarotatingspherewithtwoantipodalhotspotsfo◦r
differentvaluesofthecompactness.Therotationaxisisseenundertheinclinationi=80
andtheanglebetweenspotcentreandrotationaxisamountsθ=20◦.Thetemperature
distributionis“magnetic”(T1=100eVandT2=90eV).Notethatforsmallvaluesofthe
compactnessthehumpofthesecondhotspotcanbeseenexplicitly.
Right:Syntheticlightcurveofarotatingspherewithtwoantipodalhotspotsfordifferent
energybandsseenfrom90◦inclination.Here,M=1.4M,R=10kmandθ=20◦.The
propertiesofthetwohotspotshaveextremedifferentvalues(T1=150eVandT2=80eV,
Ξ1=5◦andΞ2=30◦)anddominatethelightcurveinthethreeenergybandsdifferently.
ThetemperatureprofileisGaussian.

error),pulsedfractionandFouriercoefficients(χ2/d.o.f.lessthanthevalueoftheobserved
lightcurves)ofthehardband.AlthoughaMonteCarlosimulationisnoteffective,itavoids
tofitalocalminimumandthecodeisfastenoughtoperform105runswithinoneortwo
days(singlecoreCPU),dependingonspotsizeandtemperaturedistribution,onanordinary
machine.Allrunswereperformedforafixedcompactness(M=1.4MandR=10km)
with40timestepswithinarotationcycleandasurfacegridof5◦×5◦size.
Thenumberofcombinationsofthegeometricalpropertiesthatfitrevolution0078strongly
dependsontheinclination:outof6.5×104runs,450fitcombinationsarefoundfori=90◦,
butonly150fori=50◦.Thesystemofsuitableparametersishighlydegenerated,e.g.a
largespotsizesmoothsthelightcurveandraisesthetemperature.Thiscanbecompen-
satedforbyalowercentraltemperatureandadifferentspotlocation.Adistributionof
possiblecombinationsofthegeometricalpropertiesofRXJ0720.4−3125(fori=80◦)is
showninfigure6.8.Iftheinclinationissignificantlylessthani=80◦andθ≈10◦−20◦,
thepropertiesofthesecond(coolerandlarger)hotspotbecomelessrestrictedbecauseit
isseenonlypartly,whilethepropertiesofthehotterspotbecomemorefixed.Somecombi-
nationsofthegeometricalpropertiesthatfite.g.i=80◦forrevolution0078alsofitvalues
aroundi=75◦ori=85◦(evenforahigherresolvedsurfacegrid,e.g.1◦×1◦)aswellas
theobservationsrevolution0533and0534,sincethetemperaturesoftheseobservations
arenotmuchdifferent.

78

6.2Procedureandfitresults

Figure6.5:Syntheticlightcurvesofarotatingspherewithtwoantipodalhotspotsinthe
hardband(400−1000eV)comparedtothelightcurvesofRXJ0720.4−3125.
Upperpanel:Lightcurvesforvariableinclinationbetween0◦(lightcurvewithhighestpulsed
fraction)and110◦(lightcurveswithlowestpulsedfraction)thatcouldbecausedbybound
precession.ThelightcurvesareobtainedforM=1.4M,R=10km,θ=5◦,T1=120eV
andT2=85eV,Ξ1=10◦andΞ2=30◦,φoff=120◦usinganuniformtemperatureprofile.
Middlepanel:Lightcurvesobtainedforthesamegeometryasintheupperpanel,butfor
constantinclination(i=50◦)andvariable“observed”θ=5◦−110◦asitwouldbethecase
offreeprecession(seefigure6.3)thatwouldcorrespondtoawobbleangleof50◦.
Lowerpanel:ObservedlightcurvesofRXJ0720.4−3125inthehardbandforallXMM-
NewtonobservationsperformedwithEPIC-pninfullframemodeandthinfilter(revolution
numbersarelistedinthelegend).

79

6.MODELLINGAFREEPRECESSINGNEUTRONSTAR

Figureemitting6.6:hotspTheots(redsyntheticaccountslightforcurvesthe(blackcontributionlines)ofofatherotatinghotterandspheresmallerwithsptwotoanddifferentblue
fromthelargerandcoolerspot)havingaGaussiantemperatureprofile.
Topleft:Twoantipodalhotspotswiththesamesize(radiusofΞ=5◦),havingT1=100eV
andT2=80eV,respectively.Thecentreofthehotter◦spotisθ=15◦inclinedfromthe
rotationaxisandtheviewangle(inclination)isi=90.Theneutronstarmasscorresponds
TtoopM=right1.:4MTheandsametheaspradiusreviouslyseen,butfromthethecosurfaceolerhotisRsp=ot10iskm.shiftedbyφoff=180◦in
longitudefromitspreviouslocation.
Bottomleft:Thesameasinthetopleftpanel,buttheneutronstarmasscorrespondsto
M=2.0MandtheradiusseenfromthesurfaceisR=8km.Thus,duetolightbending,
alargerpartofthesurfaceisseenandthepulseheightislower.
Bottomright:Thesameasinthetop◦leftpanel,butT1=100eVandT2=95eV,while
ithe=70◦centre.Noteofthethathotterthissppulseotispθrofile=50significantlyinclinedfromdeviatesthefromrotationapureaxisandsinusoid.theinclinationis

Thenextstepwastofindawobbleangleandprecessionperiodthatfitsallobservations.
Thiswasinvestigatedbyfittingallcombinationsofthegeometricalpropertiesfoundfor
revolution0078totheotherobservationsbyfittingthechangesintemperature,thelight
curvesandcalculatingthephaseresidualsaccordingtoequation6.5,equation6.6and
equation6.7.Toavoidtomissonepossiblecombination,afurtherMonteCarlosimula-
tionwasstartedsimultaneouslythatwasindependentfromtheothercombinationsofthe

80

6.2Procedureandfitresults

Figure6.7:Thepulsedfractiondependingontheinclinationandθ.Theneutronstarmass
coLeft:rrespForondstwotoMantip=o1dal.4hotMspandotsthehavingradbiusothseenT=from100theeVandsurfaceanisRangula=r10sizekm.ofΞ=30◦.
Rightangula:rFosizertofwoΞhot=15sp◦otsandwiththeTco1=oler120hotspeVotandhasT2an=angula100reV.sizeofTheΞ=hotter30◦.spotThehacosoleran
◦◦photosition.spotisInbshiftedothbyFiguresφoffthe=G60inaussianlongitudtempeeratureandθoff=distribution40inwaslatitudused.efromSeethealsoantipfigureodal7
in[12]forcomparison.

geometricalproperties.Thewobbleangleθwisvariedfromθw=10◦toθw=65◦,the
precessionperiodfromeither5to10yrsor12to20yrs.
Nocombinationwasfoundthatfitthevariabletemperature,thelightcurves(withpulsed
fractionandFouriercoefficients)andthephaseresidualswithonefixedsetofparame-
ters.Twomaineffectsworkcontradictory:ifthetemperaturehastochangefrom86eV
to94eV(seefigure4.4),thepulsedfractiondoesnotstayaround11%butincreasesto
valuesofabout30%andthephaseresidualsdonotfit.Ifthephaseresidualshavefit,the
temperaturealmoststaysconstant.Whilesolutionswithi≈80◦arepreferedforthebest
fitofthephaseresiduals,thetemperaturevariationsfitbestwithi≈130◦foracomparable
hotspotgeometryandprecessionparameters.Generally,asmallerwobbleangleisrequired
fortheGaussiantemperatureprofilewithlargedifferencesinthecentraltemperaturesof
thetwohotspotsandsmallspotsizes.However,thisincreasesthepulsedfraction,while
foranuniformtemperaturedistributionthetemperaturegradientwithinthespotsistoo
small(partlythereisagradient“seen”foradistantobserverduetolightbending)togen-
eratelargechangesinthetemperaturewithoutalargewobbleangle(thatdoesnotobey
theobservedphaseresiduals).Inthecaseofthemagnetictemperaturedistribution,the
temperaturegradientissomethinginbetweenthatofthetwoothertemperatureprofiles,
buttheadditionalfreedomofthespotsizeismissing.
Toaccountforthesediscrepancies,separatefitsforthechangesinthetemperatureand
thephaseresidualswereperformed.Theyarediscussedinthefollowingsections.

81

6.

MODELLING

A

FREE

PRECESSING

NNEUTRO

ARST

Figure6.8:Relativenumberofpossiblegeometricconfigurationsofthehotspotsonthe
aturesurfaceofoftheRXJ0720.4XMM-Newton−3125thatobservationfittherevolutionobserved0078pulsepinrofile,thehardpulsed(400−fraction1000andeV)tempband.er-
◦Inthisassumed.case,TheasolidGaussianlinealwtempayseraturerefersptorofilethefoprroptheertieshotofspthotseandhotteranspot,inclinationwhileofthe80dashedwas
linereferstothecoolerspot.Thehorizontalaxisdenotes(fromtoptobottom):T;
angularsizeofthehotspots;anglebetweenrotationaxisandcentreofthehotterspotcentr(θe)
andlongitudetheangulafromrtheshiftantip(θofofdal)inposition.latitudefromtheantipodalposition;angularshift(φoff)in

82

6.2Procedureandfitresults

Figure6.9:Upperpanel:Phaseresidualsthatexhibitadoublehumpwithdifferentsize
andavariablephaseshiftbetweenhardandsoftphotons,likeobservedforRXJ0720.4−3125.
Thephaseresidualswereobtainedforthemagnetictemperatureprofilewithtwoantipodal
hotspots,whereT1=90eVandT2=82eV,i=90◦,θ=20◦andθw=30◦.
Lowerpanel:BestfitofthephaseresidualsfortheXMM-NewtonEPIC-pnobservations
(hardband)derivedwithT1=126eVandT2=101eV,Ξ1=17.3◦andΞ2=34.5◦,
i=80◦,θ=14.9◦andθw=27.4◦.Thetwohotspots(Gaussiantemperatureprofile)
arenotexactlyantipodal,θoff=7.6◦andφoff=−5.4◦.Thefittedprecessionperiod
is13.87yrs.Thephaseresidualsfromfigure4.13derivedfromotherdataareshownfor
orientationandwerenotusedforthefit.

residualsphasetheFitting6.2.1

Itcanbeshownthatvariouscombinationsofgeometricalmodelparameterscanproducea
variablephaseshiftbetweenhardandsoftphotonsandtwohumpsinthelong-termtrend
ofthephaseresidualsasseenfromRXJ0720.4−3125.Beforereachingthelocalmaximum,
thehardphotonslagthesoftphotons.Then,atthelocalmaximum,thephasedifference

83

6.MODELLINGAFREEPRECESSINGNEUTRONSTAR

Figure6.10:ThebestfitofthetemperaturevariationsofRXJ0720.4−3125usingallXMM-
NewtonEPIC-pndatainfullframemodeandthinfilter,seealsofigure4.1.Thegeometrical
propertiesareT1=129eVandT2=95eV,i=136◦,θ=23.9◦andθw=15.6◦.
Thetwohotspots(magnetictemperatureprofile)arenotantipodal,θoff=−81.4◦and
φoff=−20.1◦.Theprecessionperiodcorrespondsto14.48yrs.

betweenhardandsoftphotonsissmall.Subsequently,thesoftphotonslagthehardpho-
tonswhilethephaseresidualsreachtheirlargestvalues(globalmaximum).Alsothephase
differencebetweenhardandsoftphotonsreachesthemaximumattheglobalmaximum.
Anexampleisshowninfigure6.9,upperpanel.Thesephenomenaareexactlyobserved
fromRXJ0720.4−3125,whentheXMM-Newtonobservationscoverthetwomaxima.Only
theXMM-NewtonEPIC-pninstrumentissensitiveenoughthatthisvaraiblephaseshiftcan
beobserved,thusthesedatawereusedtoperformafitofthephaseresiduals.
Thebestfityieldsaprecessionperiodof13.87yrsandisshowninfigure6.9,lowerpanel.
Generally,allobservedeffectscanbereproducedandthecontributionsofthetwosingle
hotspotsvarywiththeirvisibility(i.e.precessioncycle).Formally,thefityieldsanunac-
ceptablevalueofχ2/d.o.f.=9.2,butequation6.5andequation6.6onlyaccountforthe
timedelayanddisregardgeometricaleffectsinthelightcurve,likeshowninfigure6.4right
panel,whenadifferentviewontheneutronstarleadstodifferentcontributionsofthetwo
hotspotsinthelightcurvesthatchangethelocationofthelightcurvemaximum.The
contributionofthiseffectcannotexactlybeevaluatedforthecaseofRXJ0720.4−3125
(sincethetrueemissiongeometryisstillunknown),butanestimatebasedonthegeomet-
ricalpropertiesusedforthefitinfigure6.9yieldsthatχ2/d.o.f.canbeuptoafactor
offivesmaller,ifthiseffectistakenintoaccount.Moreover,thepresenceofspin-down
torques[2]degradesthefit.Thus,freeprecessioneasilyexplainsthetimingbehaviour
ofRXJ0720.4−3125.However,thegeometricalpropertiesusedforthefitinfigure6.9
generatealmostnovariationsinthetemperature.

84

6.2Procedureandfitresults

6.2.2Fittingthetemperaturevariations
Nocombinationsofgeometricalmodelparameterscouldbefoundthatreproducetheob-
servedtemperaturevariations.Inallsimulatedcases,thetemperaturevariationsaresinu-
soidal,exceptiftheoffsetofthesecondhotspotfromtheantipodalpositionislarge,a
doublesinevariationwithmaximaofdifferentheightscanbecreated.Ifthetwohotspots
arealmostatthesamelocationandhavedifferentproperties,iftheinclinationislarger
than100◦andthewobbleangleistwicethevalueofθ,thetemperaturedoesnotvary
sinusoidal,butstilldiffersmuchfromtheobservedvariations.Eventhebestfits,usingthe
temperaturesobtainedwithXMM-NewtonEPIC-pndatainfullframemodeandthinfilter,
yieldχ2/d.o.f.≥30,seefigure6.10.Ineachcase,thetemperatureundergoeschangesof
afeweV,thepulsedfractionreachestoolargevaluesandthelightcurvescannotbefitted
.erlyroppThetemperatureprofilesdiscussedinsection6.1.2.2allowminimumtemperaturesaround
T(ξ)=0eV(theX-raydataisnotsensitivetotemperaturesbelow≈30eV),forthe
uniformtemperaturedistributionoutsidethespotandfortheothertwodistributionsifthe
surfaceelementislocatedfarenoughfromthespotcenter.Likely,thisisnotthecase
forRXJ0720.4−3125andmayaccountfortheincoherencyofthesimulatedtemperature
variationswiththepulsedfractionandthephaseresiduals.Thus,thetemperatureprofiles
weremodified.Inthecaseoftheuniformtemperaturedistribution,thesurfacetemperature
wassettoTsurf>0eVoutsidethespot(ifξ>Ξ).FortheGaussiantemperatureprofile
T(ξ)=Tsurfifξ>Ξaswell,butifT(ξ)<Tsurfwithinthespot(forlargeTsurfand
smallT0),T(ξ)wassettoTsurf.Thisreducestheeffectivesizeofthespot,butavoidsthe
appearanceofacoldringaroundthespot(thatmightbenon-physical).Forthemagnetic
temperatureprofileT(ξ)wassettoTsurf,ifT(ξ)<Tsurf.
Inadvancetostartanewsimulation,differentvaluesofTsurfupto80eVweretested.
Thesurfaceareaofthespotsisatleastoneorderofmagnitudesmallerthantherestof
thesurface,i.e.largesurfacetemperaturessignificantlyinfluencethespectrum.Onlyif
roughlyTsurf<25eV,thenewsimulationsyieldvaluesofχ2/d.o.f.notmuchlargerthan
thevaluesobtainedfromtheprevioussimulations.
Withthemodifiedtemperatureprofiles,someemissiongeometrieswerefoundthatpro-
ducenon-sinusoidaltemperaturevariations(alsowithalmosttherequiredamplitude)while
producinglargephaseresiduals.Thephaseresidualsreachtheirmaximumwhenthetem-
peraturevariationreachesitsmaximum,likeobservedforRXJ0720.4−3125.However,the
trendofthephaseresidualsisnotdouble-humpedandthetrendofthesimulatedtemper-
atureshasamuchdifferentmorphologythantheobservedone.Thesimulatedlightcurves
donotfitwiththeobserved,butthepulsedfractionvarieswithin15−20%(8−12%for
RXJ0720.4−3125).Thesesimulationsagainyieldaprecessionperiodof13−14yrs.The

85

6.MODELLINGAFREEPRECESSINGNEUTRONSTAR

Figure6.11:Simultaneouslyfittedtemperaturevariationsandphaseresidualsof
RXJ0720.4−3125usingallXMM-NewtonEPIC-pndatainfullframemodeandthinfil-
ter,seealsofigure6.9andfigure6.10.ThegeometricalpropertiesareT1=120eVand
T2=86eV,i=27.5◦,θ=45.5◦andθw=18.3◦.Thetwohotspots(Gaussiantemperature
profile)arenotantipodal,θoff=24◦andφoff=26.6◦.Theprecessionperiodcorresponds
to13.47yrs.ThesurfacetemperatureTsurf=10eV.Thisemissiongeometrydoesnotfit
thedata,butshowsqualitativetrendsobservedforRXJ0720.4−3125.

requiredwobbleangleswereθw≈20◦,i.e.notmuchdifferentfromthatinfigure6.9and
figure6.10,buttheinclinationvalueswere≈30◦.Althoughtheseemissiongeometriesdo
notleadtoacceptablefits(χ2/d.o.f.≈30,seefigure6.11),theyroughlyreproducethe
qualitativevariationsofRXJ0720.4−3125.

86

7

rySumma

Inthisthesis,themostrecentX-rayobservationsofRXJ0720.4−3125wereincludedinthe
spectralandtiminganalysisanditcouldbeshownthatthespectralvariationsexhibitedin
theXMM-NewtonEPIC-pndatadonotcontinuethesinusoidaltrend(figure4.1)asseen
inearlierwork[41].Independentoftheappliedtimingsolution,RXJ0720.4−3125exhibits
asignificantvariablephaselagbetweenhard(400−1000eV)andsoft(120−400eV)
photons.ThiscanonlybeobservedwithXMM-NewtonEPIC-pn,sincethisinstrumenthas
therequiredsensitivityandqualityinthetwoenergybands.Theresultsarepublishedin
[51].BasedonnewXMM-NewtonandChandraobservationsandincludingarchivaldata,anew
phasecoherenttimingsolutionforRXJ0720.4−3125wasderived.Thephaseresiduals
seemtofollowaperiodicpattern.IncludingROSATdata,probablymorethanonecycleof
thislongtermperiodiscoveredbyobservations.However,theROSATdataareambiguous,
sincetheysufferfromalownumberofphotonscomparedtotheobservationsperformed
withChandraandXMM-Newton.Thephaseresidualsfromthedifferenttelescopes,instru-
mentsandsetupsareinbestagreement,whenthehardbandisusedforthephasecoherent
timingsolution.TheresultsoftheupdatedtimingsolutionwereconfirmedwiththeZn2
[52].inpublishedandtestFromco-addedChandraLETGandXMM-NewtonRGShighresolutionspectra,threenar-
rowabsorptionfeatureswereidentified.Anabsorptionfeaturearound0.57keVwasfound
by[44].ThisabsorptionfeaturecouldbeconfirmedincludingmostrecentRGSdata.Two
furtherabsorptionfeatureswereidentifiedintheco-addedChandraHRC-S/LETGdata,
thatarenotdetectedintheco-addedRGSspectra(theRGS1detectorhasstrongintrinsic
featuresattheseenergies,seefigure4.3andsection4.1).
Amodelofaprecessingspherewithtwohotspotsonitssurfacedealingwiththreediffer-
enttemperaturedistributionswasusedtosimulatethespectralandtemporalvariationsof
RXJ0720.4−3125.Whilethetrendofthephaseresidualsandthevariablephaselagbe-

87

SUMMARY7.

tweenhardandsoftphotonscanbereproducedwitha14yrslongtermperiod,themodel

didnotreproducetheobservedchangesinthetemperature.Nocombinationofgeometrical

propertieswasfoundthatfitsthechangesinthetemperature,thetimingbehaviourand

thevariableshapeofthelightcurvessimultaneously.Thereasonmightbethateitherthe

assumedtemperatureprofilesaretoosimpleand/ordonotreflectthetruedistribution,

ortheemissionishighlynon-isotropic(seesection6.1.2.1).Theshapeofthespotsis

unknown,thevariableequivalentwidthofthebroadabsorptionfeature(notmodelledin

thiswork)affectstheshapeofthelightcurvesandthecontributionofspin-downtorques

tothephaseresidualsmaynotbenegligible.Sincethecurrentmodelexplainsmostof

thespectralandtemporalpropertiesobservedforRXJ0720.4−3125(somequalitatively),

amoreadvancedanddetailedmodelisinprogressandmaydeliverafinalexplanation.

88

8

outloandConclusionsok

Fromthehypothesesdiscussedinchapter5,onlyprecession(freeorbound,ortriggeredby
Tkachenkowaves)issuitabletoexplainavariablephasegapbetweenhardandsoftphotons
(orbitalmotionleadstophaseresiduals,butnottovariablephasegapsbetweentwobands).
Evenifaglitchformallybetterfitsthephaseresiduals(seesection5.1.2)thanasinusoid,
anabs(sine)(figure5.1)orthephaseresidualsgeneratedfromthemodelofaprecessing
neutronstar(figure6.9),thevariablephasegapbetweenhardandsoftphotonsisakey
issuethatisclearlyobservedandhastobeexplained.Thebadfitofasineoranabs(sine)
functiontothephaseresidualsofRXJ0720.4−3125indicatesthatsuchanapproximation
istoosimple.Indeed,thesimulationsshowthatasinusoidaltrendinthephaseresidualsis
aspecialcaseandoccursexceptionally(seeequation6.5andequation6.6).Qualitatively,
thetrendinthephaseresidualsandthephaselagbetweenhardandsoftphotonscanbe
explainedbytheprecessionmodel,e.g.seefigure6.9.
However,themodelofafreeprecessingneutronstardoesnotsufficientlyexplainthe
spectralvariations.Itwasnotpossibletogeneratealargechangeinthetemperatureof
≈8eV,asithasbeenobservedintheXMM-NewtonEPIC-pndata,whilekeepingthe
pulsedfractionbetween8%and12%.Theremaybeatleastthreereasonsforthis:First,
thetemperatureprofileoftheneutronstarsurfaceisdifferenttothatassumedinthesim-
ulations(i.e.differentfromuniform,Gaussianor“magnetic”,seefigure6.2).Varyingthe
temperatureprofileinfluencesthepulsedfractionandthewobbleanglerequiredtoproduce
therelativelylargevariationsintheobservedtemperature.Sincethetruetemperature
profileofanX-raypulsarisstillspeculative,see[1;32;33;35;101;148],itmightbe
likelythatthetemperatureprofileofRXJ0720.4−3125isverydifferentfromtheassumed
temperatureprofiles.Second,thehotspotsmaynothaveacircularshape,buttheycan
beellipticortheyarecomposedofnumeroussmallerspots−likesometimesobservedfor
Solarspots.Third,thehotsspotschangetheirlocationandmovewithrespecttothe
surfacewhiletheneutronstarisprecessing(orthemovingspotsmimicprecession).

89

CONCLUSIONS8.KOUTLOOAND

Forthemodeloffreeprecession,thedataarebestfittedwithalongtermperiodof≈14yrs
thatyieldsanellipticityoftheneutronstarof≈2×10−8.Ellipticneutronstarsmay
contributetothedetectablegravitationalwavebackground(i.e.fastspinning,non-spheric
compactobjects).Theexistenceofalongtermprecessingneutronstarimposessomelimits
onthesuperfluidinterior,henceontheequationofstate,seee.g.[5;78;79].
Fromobservations,freeprecessionandboundprecessionarehardlytodistinguish.Bound
precessionrequiresanothercompactobjectorbitingaroundRXJ0720.4−3125.Outof
roughly2000knownradiopulsars,onlyninedoubleneutronstarsareknown[118],i.e.the
probabilitytoobserveadoubleneutronstar(orneutronstar/blackhole)amongtheM7is
10.03.onlyPrecession(nomatterhowitiscaused)ororbitalmotionleaveperiodicpatternsinthe
spectralandtemporalvariation,i.e.canbeconfirmedonlybycontinuedobservations.The
monitoringwithX-raytelescopesisstillongoing(thankstoChandraGTOtimeoftheMPE
andownXMM-Newtonobservations),butdoesnotcoverasufficientlylongtimeinterval.
Ifthelongtermperiodicityisconfirmed,freeprecessionisstronglyfavoured−ifnot,a
glitchmightbealikelyexplanation.Thepresenceofadiskoracompanionwillbechecked
soonwiththeSpitzertelescope[106].
Sincethespectralchangesandthetimingbehaviourareincompatibleinthemodel,intro-
ducedinchapter6,thereisstillthepossibilitythatthespectralvariationsandthetiming
behaviourofRXJ0720.4−3125haveadifferentorigincausedbyothereffects.Theobser-
vationsavailableforthisthesisarestillnotnumerousenoughtodrawafinalconclusion,
butfreeprecessionseemstobethemostlikelyexplanation.
Thenarrowabsorptionfeaturesdetectedintheco-addedXMM-NewtonRGSandChan-
draHRC-S/LETGspectrapointtoanoverabundanceofoxygeninthelineofsightto
RXJ0720.4−3125.Thismightbeanevidenceforthepresenceofacircumstellardisk.At
leastoneoftheselinesexhibitsareasonablegravitationalredshift.Acircumstellardiskmay
accountforsomeobservedpeculiaritiesofRXJ0720.4−3125.Hence,theotherM7haveto
beinvestigatedfortheexistenceofacircumstellardiskand/orfornarrowabsorptionfea-
turesintheirco-addedXMM-NewtonRGSandChandraHRC-S/LETGspectratoderive
usefulconclusionsabouttheinteractionbetweentheM7andtheirenvironment.However,
thisiscurrentlynotpossibleformostoftheM7sincetheyareobservednotfrequentand
longenoughtodetectsuchweaklines.

1ninedoubleneutronstars/2000radiopulsars=4.5×10−3,i.e.0.03suchobjectsamongtheM7.

90

References

[1]D.N.Aguilera,J.A.Pons,andJ.A.Miralles.TheImpactof
MagneticFieldontheThermalEvolutionofNeutronStars.ApJ,
673:L167–L170,February2008.74,89
[2]T.Akg¨un,B.Link,andI.Wasserman.Precessionoftheisolated
neutronstarPSRB1828-11.MNRAS,365:653–672,January2006.
8476,[3]M.A.Alpar.OnDisksandMagnetars:AftertheDiscoveryofaFail-
backDisk.InESASpecialPublication,622ofESASpecialPublication,
632007.541–+,pages[4]M.A.Alpar,A.Ankay,andE.Yazgan.PulsarSpin-downbya
FallbackDiskandtheP-PDiagram.ApJ,557:L61–L65,August2001.
63[5]M.A.AlparandJ.A.Sauls.Onthedynamicalcouplingbetween
thesuperfluidinteriorandthecrustofaneutronstar.ApJ,327:723–
725,April1988.58,90
[6]D.E.BackmanandF.Paresce.Main-sequencestarswithcircum-
stellarsolidmaterial-TheVEGAphenomenon.InE.H.Levy&
J.I.Lunine,editor,ProtostarsandPlanetsIII,pages1253–1304,1993.
65[7]A.Bauswein,H.-.Janka,R.Oechslin,G.Pagliara,I.Sagert,
J.Schaffner-Bielich,M.M.Hohle,andR.Neuhaeuser.Mass
EjectionbyStrangeStarMergersandObservationalImplications.
ArXive-prints,December2008.6
[8]A.Bauswein,R.Oechslin,andH.-T.Janka.Discriminating
strangestarmergersfromneutronstarmergersbygravitational-wave
measurements.Phys.Rev.D,81(2):024012–+,January2010.6
[9]A.Baykal,M.J.Stark,andJ.Swank.DiscoveryoftheOrbitof
theTransientX-RayPulsarSAXJ2103.5+4545.ApJ,544:L129–L132,
652000.erDecemb[10]A.M.Beloborodov.GravitationalBendingofLightNearCompact
Objects.ApJ,566:L85–L88,February2002.72,73,76
[11]O.BlaesandP.Madau.Canweobserveaccreting,isolatedneutron
stars?ApJ,403:690–705,February1993.9
[12]S.Bogdanov,J.E.Grindlay,andG.B.Rybicki.ThermalX-Rays
fromMillisecondPulsars:ConstrainingtheFundamentalPropertiesof
NeutronStars.ApJ,689:407–415,December2008.76,81
[13]R.Buccheri,K.Bennett,G.F.Bignami,J.B.G.M.Bloemen,
V.Boriakoff,P.A.Caraveo,W.Hermsen,G.Kanbach,R.N.
Manchester,J.L.Masnou,H.A.Mayer-Hasselwander,M.E.
Ozel,J.A.Paul,B.Sacco,L.Scarsi,andA.W.Strong.Search
forpulsedgamma-rayemissionfromradiopulsarsintheCOS-Bdata.
A&A,128:245–251,November1983.31
[14]E.W.Burke,Jr.,W.W.Rolland,andW.R.Boy.APhotoelec-
tricStudyofMagneticVariableStars.JRASC,64:353–+,December
321970.

91

[15]V.Burwitz,F.Haberl,R.Neuh¨auser,P.Predehl,J.Tr¨umper,
andV.E.Zavlin.Thethermalradiationoftheisolatedneutronstar
RXJ1856.5-3754observedwithChandraandXMM-Newton.A&A,
399:1109–1114,March2003.10,11,45,47
[16]V.Burwitz,V.E.Zavlin,R.Neuh¨auser,P.Predehl,
J.Tr¨umper,andA.C.Brinkman.TheChandraLETGShighreso-
lutionX-rayspectrumoftheisolatedneutronstarRXJ1856.5-3754.
A&A,379:L35–L38,November2001.9,10,45,47
[17]W.Cash.Parameterestimationinastronomythroughapplicationof
thelikelihoodratio.ApJ,228:939–947,March1979.31
[18]J.Cottam,F.Paerels,andM.Mendez.Gravitationallyredshifted
absorptionlinesintheX-rayburstspectraofaneutronstar.Nature,
420:51–54,November2002.9
[19]M.Cropper,F.Haberl,S.Zane,andV.E.Zavlin.Timinganaly-
sisoftheisolatedneutronstarRXJ0720.4-3125revisited.MNRAS,
351:1099–1108,July2004.10,18,32,36,52,98
[20]M.Cropper,S.Zane,G.Ramsay,F.Haberl,andC.Motch.
ModellingthespinpulseprofileoftheisolatedneutronstarRX
J0720.4-3125observedwithXMM-Newton.A&A,365:L302–L307,
1210,2001.ryJanua[21]L.P.David,Jr.F.R.Harnden,K.E.Kearns,andM.V.Zombeck.
TheROSATHighResolutionImager(HRI),USRSDC/SAOCalibration
Report,revised,1996.17
[22]C.P.deVries,J.Vink,M.M´endez,andF.Verbunt.Long-term
variabilityintheX-rayemissionofRXJ0720.4-3125.A&A,415:L31–
L34,February2004.10,12,14,33,49,57
[23]J.W.denHerder,A.C.Brinkman,S.M.Kahn,G.Branduardi-
Raymont,K.Thomsen,H.Aarts,M.Audard,J.V.Bixler,A.J.
denBoggende,J.Cottam,T.Decker,L.Dubbeldam,C.Erd,
H.Goulooze,M.G¨udel,P.Guttridge,C.J.Hailey,K.A.
Janabi,J.S.Kaastra,P.A.J.deKorte,B.J.vanLeeuwen,
C.Mauche,A.J.McCalden,R.Mewe,A.Naber,F.B.Paerels,
J.R.Peterson,A.P.Rasmussen,K.Rees,I.Sakelliou,M.Sako,
J.Spodek,M.Stern,T.Tamura,J.Tandy,C.P.deVries,
S.Welch,andA.Zehnder.TheReflectionGratingSpectrome-
teronboardXMM-Newton.A&A,365:L7–L17,January2001.21,
41[24]D.Dewey.SubassemblyCalibration:HETG.ChandraNews,4:11–+,
25.1996erSeptemb[25]D.Dewey.HETGSpectra.ChandraNews,5:18–+,December1997.
25[26]J.J.Drake,H.L.Marshall,S.Dreizler,P.E.Freeman,A.Fr-
uscione,M.Juda,V.Kashyap,F.Nicastro,D.O.Pease,B.J.
Wargelin,andK.Werner.IsRXJ1856.5-3754aQuarkStar?ApJ,
92002.June:996–1001,572[27]M.M.Dworetsky.Aperiod-findingmethodforsparserandomly
spacedobservationsof’Howlongisapieceofstring?’.MNRAS,
203:917–924,June1983.33,34
[28]T.Eisenbeiss,C.Ginski,M.M.Hohle,V.V.Hambaryan,
R.Neuh¨auser,andT.O.B.Schmidt.Newphotometryandas-
trometryoftheisolatedneutronstarRXJ0720.4-3125usingre-
centVLT/FORSobservations.AstronomischeNachrichten,331:243–+,
6411,10,2010.[29]K.Y.Eks¸I˙andM.A.Alpar.DisksSurvivingtheRadiationPressure
ofRadioPulsars.ApJ,620:390–397,February2005.65
[30]N.R.Evans.LETGOrderSeparation.ChandraNews,5:16–+,De-
251997.ercemb

REFERENCES

[31]G.P.Garmire,M.W.Bautz,P.G.Ford,J.A.Nousek,and
G.R.Ricker,Jr.AdvancedCCDimagingspectrometer(ACIS)
instrumentontheChandraX-rayObservatory.InJ.E.Truemper
&H.D.Tananbaum,editor,SocietyofPhoto-OpticalInstrumenta-
tionEngineers(SPIE)ConferenceSeries,4851ofSocietyofPhoto-
OpticalInstrumentationEngineers(SPIE)ConferenceSeries,pages28–
252003.rchMa44,[32]U.Geppert,M.K¨uker,andD.Page.Temperaturedistributionin
magnetizedneutronstarcrusts.A&A,426:267–277,October2004.
8974,[33]U.Geppert,M.K¨uker,andD.Page.Temperaturedistribution
inmagnetizedneutronstarcrusts.II.Theeffectofastrongtoroidal
component.A&A,457:937–947,October2006.74,89
[34]K.Glampedakis,N.Andersson,andD.I.Jones.Dosuperfluidin-
stabilitiespreventneutronstarprecession?MNRAS,394:1908–1924,
1609.20rilAp[35]G.GreensteinandG.J.Hartke.Pulselikecharacterofblackbody
radiationfromneutronstars.ApJ,271:283–293,August1983.74,89
[36]H.Grigorian,D.Blaschke,andD.Voskresensky.Coolingof
neutronstarswithcolorsuperconductingquarkcores.Phys.Rev.C,
71(4):045801–+,April2005.8
[37]M.E.Gusakov,A.D.Kaminker,D.G.Yakovlev,andO.Y.
Gnedin.ThecoolingofAkmal-Pandharipande-Ravenhallneutronstar
models.MNRAS,363:555–562,October2005.6,8
[38]F.Haberl.Themagnificentseven:magneticfieldsandsurfacetem-
peraturedistributions.Ap&SS,308:181–190,April2007.2,10,12,
3421,17,15,14,[39]F.Haberl,C.Motch,D.A.H.Buckley,F.-J.Zickgraf,and
W.Pietsch.RXJ0720.4-3125:strongevidenceforanisolatedpulsat-
ingneutronstar.A&A,326:662–668,October1997.10,11
[40]F.Haberl,C.Motch,V.E.Zavlin,K.Reinsch,B.T.G¨ansicke,
M.Cropper,A.D.Schwope,R.Turolla,andS.Zane.The
isolatedneutronstarX-raypulsarsRXJ0420.0-5022andRXJ0806.4-
4123:NewX-rayandopticalobservations.a˚,424:635–645,September
112004.[41]F.Haberl,R.Turolla,C.P.deVries,S.Zane,J.Vink,
M.M´endez,andF.Verbunt.Evidenceforprecessionoftheiso-
latedneutronstar¡ASTROBJ¿RXJ0720.4-3125¡/ASTROBJ¿.A&A,
451:L17–L21,May2006.10,11,12,13,14,21,24,33,36,37,38,39,
41,44,45,47,49,57,67,68,87
[42]F.HaberlandV.E.Zavlin.XMM-Newtonobservationsofthe
isolatedneutronstarRXJ0806.4-4123.A&A,391:571–576,August
112002.[43]F.Haberl,V.E.Zavlin,J.Tr¨umper,andV.Burwitz.Aphase-
dependentabsorptionlineinthespectrumoftheX-raypulsarRX
J0720.4-3125.A&A,419:1077–1085,June2004.10,11,12,13,21,
24,33,36,37,39,41,44,45,47,48,57
[44]V.Hambaryan,R.Neuh¨auser,F.Haberl,M.M.Hohle,and
A.D.Schwope.XMM-NewtonRGSspectrumofRXJ0720.4-3125:
anabsorptionfeatureat0.57keV.A&A,497:L9–L12,April2009.41,
42,44,45,46,63,64,65,87
[45]C.O.Heinke,G.B.Rybicki,R.Narayan,andJ.E.Grindlay.
AHydrogenAtmosphereSpectralModelAppliedtotheNeutronStar
X7intheGlobularCluster47Tucanae.ApJ,644:1090–1103,June
372006.[46]A.Hewish,S.J.Bell,J.D.H.Pilkington,P.F.Scott,and
R.A.Collins.ObservationofaRapidlyPulsatingRadioSource.
Nature,217:709–713,February1968.1

92

[47]R.HirataandT.Horaguchi.Atomicspectrallineslist.Department
ofAstronomy,FacultyofScience,KyotoUniversityandNationalScience
641995.,Museum[48]W.C.G.Ho.ConstrainingthegeometryoftheneutronstarRX
J1856.5-3754.MNRAS,380:71–77,September2007.65
[49]M.Hohle.RXJ0720evolution:precession,glitching,orthelastflut-
teringsofamagnetar.InXMM-NewtonProposalID#06011701,pages
242008.erOctob26–+,[50]M.Hohle.RXJ0720.4-3125-afreeprecessingX-raypulsar?In
XMM-NewtonProposalID#06509201,pages28–+,October2009.24
[51]M.M.Hohle,F.Haberl,J.Vink,R.Turolla,V.Hambaryan,
S.Zane,C.P.deVries,andM.M´endez.Spectralandtemporal
variationsoftheisolatedneutronstarRXJ0720.4-3125:newXMM-
Newtonobservations.A&A,498:811–820,May2009.10,11,33,34,
36,37,39,41,44,45,47,57,68,87
[52]M.M.Hohle,F.Haberl,J.Vink,R.Turolla,S.Zane,C.P.de
Vries,andM.M´endez.Updatedphasecoherenttimingsolutionof
theisolatedneutronstarRXJ0720.4-3125usingrecentXMM-Newton
andChandraobservations.ArXive-prints,July2010.49,68,87
[53]R.A.HulseandJ.H.Taylor.Discoveryofapulsarinabinary
system.ApJ,195:L51–L53,January1975.1
[54]F.Jansen,D.Lumb,B.Altieri,J.Clavel,M.Ehle,C.Erd,
C.Gabriel,M.Guainazzi,P.Gondoin,R.Much,R.Munoz,
M.Santos,N.Schartel,D.Texier,andG.Vacanti.XMM-
Newtonobservatory.I.Thespacecraftandoperations.A&A,365:L1–
182001.ryJanuaL6,[55]G.H.JanssenandB.W.Stappers.30glitchesinslowpulsars.
A&A,457:611–618,October2006.15
[56]S.Johnston.Radioobservationsoftwoisolatedneutronstars:RX
J0720.4-3125andRXJ0806.4-4132.MNRAS,340:L43–L46,April
82003.[57]D.I.JonesandN.Andersson.Gravitationalwavesfromfreelypre-
cessingneutronstars.MNRAS,331:203–220,March2002.58,61
[58]J.Juda.LETGSpectra.ChandraNews,5:20–+,December1997.25
[59]M.Juda.SubassemblyCalibration:LETG.ChandraNews,4:9–+,
September1996.25
[60]J.S.Kaastra,C.P.deVries,E.Costantini,andJ.W.A.den
Herder.Effectiveareacalibrationofthereflectiongratingspectrome-
tersofXMM-Newton.I.X-rayspectroscopyoftheCrabnebula.A&A,
497:291–310,April2009.45,65
[61]D.L.Kaplan,S.R.Kulkarni,andM.H.vanKerkwijk.
AProbableOpticalCounterparttotheIsolatedNeutronStarRX
J1308.6+2127.ApJ,579:L29–L32,November2002.11
[62]D.L.Kaplan,S.R.Kulkarni,andM.H.vanKerkwijk.The
OpticalCounterpartoftheIsolatedNeutronStarRXJ1605.3+3249.
ApJ,588:L33–L36,May2003.11
[63]D.L.KaplanandM.H.vanKerkwijk.ACoherentTimingSo-
lutionfortheNearbyIsolatedNeutronStarRXJ0720.4-3125.ApJ,
628:L45–L48,July2005.10,11,15,30,31,33,36,48,49,50,67,68,
98[64]D.L.KaplanandM.H.vanKerkwijk.ACoherentTimingSo-
lutionfortheNearbyIsolatedNeutronStarRXJ1308.6+2127/RBS
1223.ApJ,635:L65–L68,December2005.11
[65]D.L.KaplanandM.H.vanKerkwijk.ConstrainingtheSpin-down
oftheNearbyIsolatedNeutronStarRXJ0806.4-4123,andImplica-
tionsforthePopulationofNearbyNeutronStars.ApJ,705:798–808,
November2009.2,11

[66]D.L.KaplanandM.H.vanKerkwijk.ConstrainingtheSpin-
downoftheNearbyIsolatedNeutronStarRXJ0806.4-4123,andIm-
plicationsforthePopulationofNearbyNeutronStars.ArXive-prints,
September2009.2
[67]D.L.KaplanandM.H.vanKerkwijk.ConstrainingtheSpin-
DownoftheNearbyIsolatedNeutronStarRXJ2143.0+0654.ApJ,
692:L62–L66,February2009.2,11
[68]D.L.Kaplan,M.H.vanKerkwijk,andJ.Anderson.TheParallax
andProperMotionofRXJ1856.5-3754Revisited.ApJ,571:447–457,
May2002.9,11
[69]D.L.Kaplan,M.H.vanKerkwijk,andJ.Anderson.TheDis-
tancetotheIsolatedNeutronStarRXJ0720.4-3125.ApJ,660:1428–
1443,May2007.9,10,11
[70]D.L.Kaplan,M.H.vanKerkwijk,H.L.Marshall,B.A.Ja-
coby,S.R.Kulkarni,andD.A.Frail.TheNearbyNeutronStar
RXJ0720.4-3125fromRadiotoX-Rays.ApJ,590:1008–1019,June
109,2003.[71]V.I.Kondratiev,M.A.McLaughlin,D.R.Lorimer,M.Burgay,
A.Possenti,R.Turolla,S.B.Popov,andS.Zane.NewLim-
itsonRadioEmissionfromX-rayDimIsolatedNeutronStars.ApJ,
702:692–706,September2009.8
[72]G.Kovacs.FrequencyshiftinFourieranalysis.Ap&SS,78:175–188,
4932,30,1981.August[73]R.P.Kraft,J.H.Chappell,A.T.Kenter,K.Kobayashi,
G.R.Meehan,S.S.Murray,M.V.Zombeck,G.W.Fraser,
J.F.Pearson,J.E.Lees,A.N.Brunton,M.Barbera,A.Col-
lura,andS.Serio.PerformanceandcalibrationoftheAXAFHigh-
ResolutionCameraII:thespectroscopicdetector.InO.H.Siegmund
&M.A.Gummin,editor,SocietyofPhoto-OpticalInstrumentation
Engineers(SPIE)ConferenceSeries,3114ofSocietyofPhoto-Optical
InstrumentationEngineers(SPIE)ConferenceSeries,pages53–73,Oc-
tober1997.25
[74]S.R.KulkarniandM.H.vanKerkwijk.OpticalObservations
oftheIsolatedNeutronStarRXJ0720.4-3125.ApJ,507:L49–L53,
November1998.10,64
[75]J.M.Lattimer.ConstraintsontheDenseMatterEquationofState
fromObservations.InS.Kubono,W.Aoki,T.Kajino,T.Mo-
tobayashi,&K.Nomoto,editor,OriginofMatterandEvolutionof
Galaxies,847ofAmericanInstituteofPhysicsConferenceSeries,pages
52006.July155–162,[76]J.M.LattimerandM.Prakash.Neutronstarobservations:Prog-
nosisforequationofstateconstraints.Phys.Rep.,442:109–165,
April2007.6,8
[77]B.Link.PrecessionofIsolatedNeutronStars.InM.Bailes,
D.J.Nice,&S.E.Thorsett,editor,RadioPulsars,302ofAs-
tronomicalSocietyofthePacificConferenceSeries,pages241–+,2003.
75[78]B.Link.Incompatibilityoflong-periodneutronstarprecessionwith
creepingneutronvortices.A&A,458:881–884,November2006.16,
90[79]B.LinkandR.I.Epstein.PrecessionInterpretationoftheIsolated
PulsarPSRB1828-11.ApJ,556:392–398,July2001.61,90
[80]K.Liu,Y.L.Yue,andR.X.Xu.PSRB1828-11:aprecessionpulsar
torquedbyaquarkplanet?MNRAS,381:L1–L5,October2007.59
[81]A.G.Lyne.Themagneticfieldsofneutronstars.InAstronomy,physics
andchemistryofH3+,358ofRoyalSocietyofLondonPhilosophical
TransactionsSeriesA,pages831–840,February2000.4
[82]W.W.Macy,Jr.PulsarMagneticAxisAlignmentandCounteralign-
ment.ApJ,190:153–164,May1974.4

93

REFERENCES

[83]V.M.Malofeev,O.I.Malov,andD.A.Teplykh.PulsedRadio
EmissionFromTwoXDINS.InIAUJointDiscussion,2ofIAUJoint
82006.August,Discussion[84]V.M.Malofeev,O.I.Malov,D.A.Teplykh,S.V.Logvinenko,
I.I.Litvinov,andS.B.Popov.Discoveryofradioemissionfrom
X-raypulsarXDINS1RXSJ214303.7+065419+06.TheAstronomer’s
Telegram,798:1–+,April2006.8
[85]R.N.Manchester,G.B.Hobbs,A.Teoh,andM.Hobbs.ATNF
PulsarCatalog(Manchester+,2005).VizieROnlineDataCatalog,
22005.August:0–+,7245[86]R.P.Mignani,C.Motch,F.Haberl,S.Zane,R.Turolla,and
A.Schwope.VLTopticalobservationsoftheisolatedneutronstar
RXJ0420.0-5022.A&A,505:707–713,October2009.11
[87]K.MoriandW.C.G.Ho.Modellingmid-Zelementatmospheres
forstronglymagnetizedneutronstars.MNRAS,377:905–919,May
105,2007.[88]C.MotchandF.Haberl.Constraintsonopticalemissionfromthe
isolatedneutronstarcandidateRXJ0720.4-3125.A&A,333:L59–L62,
May1998.10
[89]C.Motch,A.M.Pires,F.Haberl,A.Schwope,andV.E.Za-
vlin.PropermotionsofROSATdiscoveredisolatedneutronstars
measuredwithChandra:FirstX-raymeasurementofthelargeproper
motionofRXJ1308.6+2127/RBS1223.InC.Bassa,Z.Wang,
A.Cumming,&V.M.Kaspi,editor,40YearsofPulsars:Millisec-
ondPulsars,MagnetarsandMore,983ofAmericanInstituteofPhysics
ConferenceSeries,pages354–356,February2008.8,9,11
[90]C.Motch,K.Sekiguchi,F.Haberl,V.E.Zavlin,A.Schwope,
andM.W.Pakull.Thepropermotionoftheisolatedneutron
star¡ASTROBJ¿RXJ1605.3+3249¡/ASTROBJ¿.A&A,429:257–
112005.ryJanua265,[91]C.Motch,V.E.Zavlin,andF.Haberl.Thepropermotionanden-
ergydistributionoftheisolatedneutronstarRXJ0720.4-3125.A&A,
408:323–330,September2003.9,64
[92]R.W.Nelson,L.S.Finn,andI.Wasserman.TrompeL’Oeil’bi-
nary’pulsars.ApJ,348:226–231,January1990.12,57,75,76
[93]J.NoronhaandA.Sedrakian.Tkachenkomodesassourcesof
quasiperiodicpulsarspinvariations.Phys.Rev.D,77(2):023008–+,
632008.ryJanua[94]J.R.OppenheimerandG.M.Volkoff.OnMassiveNeutronCores.
PhysicalReview,55:374–381,February1939.5
[95]J.P.OstrikerandJ.E.Gunn.OntheNatureofPulsars.I.Theory.
ApJ,157:1395–+,September1969.3
[96]F.Paerels.PressureBroadeningofAbsorptionLinesinNeutronStar
AtmospheresandProspectsforMeasuringNeutronStarMassesand
Radii.ApJ,476:L47+,February1997.63
[97]C.Palomba.Simulationofapopulationofisolatedneutronstars
evolvingthroughtheemissionofgravitationalwaves.MNRAS,
359:1150–1164,May2005.4
[98]G.G.Pavlov,Y.A.Shibanov,V.E.Zavlin,andR.D.Meyer.
NeutronStarAtmospheres.InM.A.Alpar,U.Kiziloglu,&J.van
Paradijs,editor,TheLivesoftheNeutronStars,pages71–+,1995.37
[99]A.M.Pires,C.Motch,R.Turolla,A.Treves,andS.B.Popov.
Theisolatedneutronstarcandidate2XMMJ104608.7-594306.A&A,
498:233–240,April2009.7
[100]J.A.PonsandU.Geppert.Magneticfielddissipationinneutronstar
crusts:frommagnetarstoisolatedneutronstars.A&A,470:303–315,
42007.July[101]J.A.Pons,J.A.Miralles,andU.Geppert.Magneto-thermal
evolutionofneutronstars.A&A,496:207–216,March2009.74,89

REFERENCES

[102]S.B.Popov.TheZooofneutronstars.PhysicsofParticlesandNuclei,
39:1136–1142,December2008.2
[103]S.B.Popov.Tkachenkowaves,glitchesandprecessioninneutron
stars.Ap&SS,317:175–179,October2008.61,63
[104]S.B.Popov,M.Colpi,M.E.Prokhorov,A.Treves,andR.Tur-
olla.YoungisolatedneutronstarsfromtheGouldBelt.A&A,
72003.July:111–117,406[105]B.Posselt,R.Neuh¨auser,andF.Haberl.Searchingforsubstel-
larcompanionsofyoungisolatedneutronstars.A&A,496:533–545,
March2009.8,64,66
[106]B.Posselt,G.Pavlov,andM.Hohle.Isthereafallbackdisk
aroundRXJ0720.4-3125?InSpitzerProposalID#70045,pages
70045–+,June2010.65,67,90
[107]B.Posselt,S.B.Popov,F.Haberl,J.Tr¨umper,R.Turolla,
andR.Neuh¨auser.TheMagnificentSeveninthedustyprairie.
Ap&SS,308:171–179,April2007.8,11
[108]B.Posselt,K.Schreyer,R.Perna,M.W.Sommer,B.Klein,
andP.Slane.SubmillimetreobservationsofRXJ1856.5-3754.MN-
RAS,405:1840–1844,July2010.65
[109]J.PoutanenandA.M.Beloborodov.Pulseprofilesofmillisecond
pulsarsandtheirFourieramplitudes.MNRAS,373:836–844,Decem-
ber2006.48,49,72,73
[110]S.M.Ransom,S.S.Eikenberry,andJ.Middleditch.Fourier
TechniquesforVeryLongAstrophysicalTime-SeriesAnalysis.AJ,
124:1788–1809,September2002.31,32,48,49,50,55,98
[111]S.M.Ransom,B.M.Gaensler,andP.O.Slane.ADeepSearch
forPulsationsfromtheNearbyIsolatedNeutronStarRXJ1856.5-
3754.ApJ,570:L75–L78,May2002.9
[112]M.Ruderman.LongPeriodOscillationsinRotatingNeutronStars.
Nature,225:619–620,February1970.61,63
[113]R.E.Rutledge,D.B.Fox,andA.H.Shevchuk.Discoveryofan
IsolatedCompactObjectatHighGalacticLatitude.ApJ,672:1137–
72008.ryJanua1143,[114]C.L.SarazinandJ.N.Bahcall.OntheZeemansplittingofX-ray
linesbyneutron-starmagneticfields.ApJ,216:L67–L70,September
641977.[115]A.D.Schwope,V.Hambaryan,F.Haberl,andC.Motch.The
pulsedX-raylightcurvesoftheisolatedneutronstarRBS1223.A&A,
441:597–604,October2005.11
[116]A.D.Schwope,V.Hambaryan,F.Haberl,andC.Motch.
ThecomplexX-rayspectrumoftheisolatedneutronstarRBS1223.
Ap&SS,308:619–623,April2007.11
[117]S.L.ShapiroandS.A.Teukolsky.Blackholes,whitedwarfs,and
neutronstars:Thephysicsofcompactobjects.1983.4,5,7
[118]I.H.Stairs.Massesofradiopulsars.JournalofPhysicsGNuclear
Physics,32:259–+,December2006.1,4,90
[119]I.H.Stairs.Binarypulsarsandtestsofgeneralrelativity.In
S.A.Klioner,P.K.Seidelmann,&M.H.Soffel,editor,IAU
Symposium,261ofIAUSymposium,pages218–227,January2010.1
[120]L.Str¨uder,U.Briel,K.Dennerl,R.Hartmann,E.Kendziorra,
N.Meidinger,E.Pfeffermann,C.Reppin,B.Aschenbach,
W.Bornemann,H.Br¨auninger,W.Burkert,M.Elender,
M.Freyberg,F.Haberl,G.Hartner,F.Heuschmann,H.Hipp-
mann,E.Kastelic,S.Kemmer,G.Kettenring,W.Kink,
N.Krause,S.M¨uller,A.Oppitz,W.Pietsch,M.Popp,P.Pre-
dehl,A.Read,K.H.Stephan,D.St¨otter,J.Tr¨umper,

94

P.Holl,J.Kemmer,H.Soltau,R.St¨otter,U.Weber,U.We-
ichert,C.vonZanthier,D.Carathanassis,G.Lutz,R.H.
Richter,P.Solc,H.B¨ottcher,M.Kuster,R.Staubert,
A.Abbey,A.Holland,M.Turner,M.Balasini,G.F.Bignami,
N.LaPalombara,G.Villa,W.Buttler,F.Gianini,R.Laine,´
D.Lumb,andP.Dhez.TheEuropeanPhotonImagingCameraon
XMM-Newton:Thepn-CCDcamera.A&A,365:L18–L26,January
2418,2001.[121]N.Tetzlaff,R.Neuh¨auser,andM.M.Hohle.Theoriginofthe
Guitarpulsar.MNRAS,400:L99–L102,November2009.4
[122]N.Tetzlaff,R.Neuh¨auser,M.M.Hohle,andG.Maciejewski.
Identifyingbirthplacesofyoungisolatedneutronstars.MNRAS,
402:2369–2387,March2010.4,8,9,11,58
[123]V.K.Tkachenko.StabilityofVortexLattices.SovietJournalof
ExperimentalandTheoreticalPhysics,23:1049–+,December1966.61
[124]J.Tr¨umper.TheROSATmission.Adv.SpaceRes.,2:241–249,1982.
17[125]M.J.L.Turner,A.Abbey,M.Arnaud,M.Balasini,M.Bar-
bera,E.Belsole,P.J.Bennie,J.P.Bernard,G.F.Big-
nami,M.Boer,U.Briel,I.Butler,C.Cara,C.Chabaud,
R.Cole,A.Collura,M.Conte,A.Cros,M.Denby,P.Dhez,
G.DiCoco,J.Dowson,P.Ferrando,S.Ghizzardi,F.Gian-
otti,C.V.Goodall,L.Gretton,R.G.Griffiths,O.Hainaut,
J.F.Hochedez,A.D.Holland,E.Jourdain,E.Kendziorra,
A.Lagostina,R.Laine,N.LaPalombara,M.Lortholary,
D.Lumb,P.Marty,S.Molendi,C.Pigot,E.Poindron,K.A.
Pounds,J.N.Reeves,C.Reppin,R.Rothenflug,P.Salve-
tat,J.L.Sauvageot,D.Schmitt,S.Sembay,A.D.T.Short,
J.Spragg,J.Stephen,L.Str¨uder,A.Tiengo,M.Trifoglio,
J.Tr¨umper,S.Vercellone,L.Vigroux,G.Villa,M.J.Ward,
S.Whitehead,andE.Zonca.TheEuropeanPhotonImagingCam-
eraonXMM-Newton:TheMOScameras:TheMOScameras.A&A,
365:L27–L35,January2001.18,34,39
[126]R.Turolla,S.Zane,andJ.J.Drake.BareQuarkStarsorNaked
NeutronStars?TheCaseofRXJ1856.5-3754.ApJ,603:265–282,
9.2004rchMa[127]M.H.vanKerkwijkandD.L.Kaplan.TimingtheNearbyIsolated
NeutronStarRXJ1856.5-3754.ApJ,673:L163–L166,February2008.
1110,2,[128]M.H.vanKerkwijk,D.L.Kaplan,M.Durant,S.R.Kulka-
rni,andF.Paerels.AStrong,BroadAbsorptionFeatureintheX-
RaySpectrumoftheNearbyNeutronStarRXJ1605.3+3249.ApJ,
112004.June:432–443,608[129]M.H.vanKerkwijk,D.L.Kaplan,G.G.Pavlov,andK.Mori.
SpectralandRotationalChangesintheIsolatedNeutronStarRX
J0720.4-3125.ApJ,659:L149–L152,April2007.10,11,12,15,30,
31,33,34,36,48,49,50,59,60,62,65,67,98
[130]J.Vink.RXJ0720evolution:precession,glitching,thelastflutter-
ingsofamagnetar?InXMM-NewtonProposalID#05545101,pages
222007.erOctob135–+,[131]F.M.Walter.TheProperMotion,Parallax,andOriginoftheIso-
latedNeutronStarRXJ185635-3754.ApJ,549:433–440,March2001.
9[132]F.M.Walter,T.Eisenbeiss,J.M.Lattimer,B.Kim,V.Ham-
baryan,andR.Neuhaeuser.RevisitingtheParallaxoftheIsolated
NeutronStarRXJ185635-3754UsingHST/ACSImaging.ArXive-
prints,August2010.9,11
[133]F.M.WalterandJ.M.Lattimer.ARevisedParallaxandItsImpli-
cationsforRXJ185635-3754.ApJ,576:L145–L148,September2002.
119,7,[134]F.M.WalterandL.D.Matthews.Theopticalcounterpartof
theisolatedneutronstarRXJ185635-3754.Nature,389:358–360,
117,1997.erSeptemb

[135]F.M.Walter,S.J.Wolk,andR.Neuh¨auser.Discoveryofa
nearbyisolatedneutronstar.Nature,379:233–235,January1996.7
[136]J.C.L.Wang.EvidenceforMagneticFieldDecayinRXJ0720.4-
3125.ApJ,486:L119+,September1997.9
[137]N.Wang,R.N.Manchester,R.T.Pace,M.Bailes,V.M.Kaspi,
B.W.Stappers,andA.G.Lyne.Glitchesinsouthernpulsars.MN-
RAS,317:843–860,October2000.15
[138]Z.Wang,D.Chakrabarty,andD.L.Kaplan.Adebrisdiskaround
anisolatedyoungneutronstar.Nature,440:772–775,April2006.63
[139]K.Wette,B.J.Owen,B.Allen,M.Ashley,J.Betzwieser,
N.Christensen,T.D.Creighton,V.Dergachev,I.Gholami,
E.Goetz,R.Gustafson,D.Hammer,D.I.Jones,B.Krishnan,
M.Landry,B.Machenschalk,D.E.McClelland,G.Mendell,
C.J.Messenger,M.A.Papa,P.Patel,M.Pitkin,H.J.Pletsch,
R.Prix,K.Riles,L.SanchodelaJordana,S.M.Scott,A.M.
Sintes,M.Trias,J.T.Whelan,andG.Woan.Searchingforgrav-
itationalwavesfromCassiopeiaAwithLIGO.ClassicalandQuantum
Gravity,25(23):235011–+,December2008.4
[140]A.WolszczanandD.A.Frail.Aplanetarysystemaroundthemil-
lisecondpulsarPSR1257+12.Nature,355:145–147,January1992.
651,[141]F.Wu,R.X.Xu,andJ.Gil.Thebrakingindicesinpulsaremission
models.A&A,409:641–645,October2003.4
[142]R.X.Xu.AThermalFeaturelessSpectrum:EvidenceforBare
StrangeStars?ApJ,570:L65–L68,May2002.9
[143]R.X.XuandG.J.Qiao.PulsarBrakingIndex:ATestofEmission
Models?ApJ,561:L85–L88,November2001.4
[144]Y.YaoandQ.D.Wang.X-RayAbsorptionLineSpectroscopyofthe
GalacticHotInterstellarMedium.ApJ,624:751–764,May2005.64
[145]J.P.Yuan,R.N.Manchester,N.Wang,X.Zhou,Z.Y.Liu,
andZ.F.Gao.AverylargeglitchinPSRB2334+61.ArXive-prints,
632010.July[146]J.P.Yuan,N.Wang,R.N.Manchester,andZ.Y.Liu.29glitches
detectedatUrumqiObservatory.MNRAS,404:289–304,May2010.
15

95

REFERENCES

[147]L.Zampieri,S.Campana,R.Turolla,M.Chieregato,
R.Falomo,D.Fugazza,A.Moretti,andA.Treves.1RXS
J214303.7+065419/RBS1774:AnewIsolatedNeutronStarcandi-
date.A&A,378:L5–L9,October2001.7,11
[148]S.Zane.Neutronstarsurfaceemission:Beyondthedipolemodel.
Ap&SS,308:259–265,April2007.74,89
[149]S.Zane,M.Cropper,R.Turolla,L.Zampieri,M.Chieregato,
J.J.Drake,andA.Treves.XMM-NewtonDetectionofPulsations
andaSpectralFeatureintheX-RayEmissionoftheIsolatedNeutron
Star1RXSJ214303.7+065419/RBS1774.ApJ,627:397–403,July
112005.[150]S.Zane,A.deLuca,R.P.Mignani,andR.Turolla.The
propermotionoftheisolatedneutronstarRXJ1605.3+3249.A&A,
457:619–622,October2006.11
[151]S.Zane,F.Haberl,M.Cropper,V.E.Zavlin,D.Lumb,S.Sem-
bay,andC.Motch.TiminganalysisoftheisolatedneutronstarRX
J0720.4-3125.MNRAS,334:345–354,August2002.10,32,36,52
[152]S.Zane,F.Haberl,G.L.Israel,A.Pellizzoni,M.Burgay,
R.P.Mignani,R.Turolla,A.Possenti,P.Esposito,D.Cham-
pion,R.P.Eatough,E.Barr,andM.Kramer.Discoveryof59ms
Pulsationsfrom1RXSJ141256.0+792204(Calvera).ArXive-prints,
72010.erSeptemb[153]S.Zane,R.P.Mignani,R.Turolla,A.Treves,F.Haberl,
C.Motch,L.Zampieri,andM.Cropper.AnOpticalCounterpart
CandidatefortheIsolatedNeutronStarRBS1774.ApJ,682:487–491,
6511,2008.July[154]S.ZaneandR.Turolla.Unveilingthethermalandmagneticmap
ofneutronstarsurfacesthoughtheirX-rayemission:methodand
light-curveanalysis.MNRAS,366:727–738,March2006.71
[155]S.Zane,R.Turolla,andJ.J.Drake.IsRXJ1856.5-3754anaked
neutronstar?AdvancesinSpaceResearch,33:531–536,2004.65
[156]S.Zane,R.Turolla,andD.Page,editors.IsolatedNeutronStars:
fromtheSurfacetotheInterior,2007.65
[157]V.E.Zavlin,G.G.Pavlov,andY.A.Shibanov.Modelneutron
staratmosphereswithlowmagneticfields.I.Atmospheresinradiative
equilibrium.A&A,315:141–152,November1996.37

REFERENCES

96

endixApp

Time

of

timing

A

rrivalsa

utionsol

As)(TO

and

97

of

the

individual

final

erioP

ds

A.TIMEOFARRIVALS(TOAS)OFTHEFINALTIMINGSOLUTIONAND
PERIODSINDIVIDUAL

andTROSArfo(exceptband)
eV1000−400(rdhaand)eV400−120A.1:ableTtthaNote2.3).tablealso(seeobservationsChandramergedtherkmatagsThelisted).reacountsallfromderivedsderiopthei.e.HRC,Chandrauncertain.ighlyhreaand[19]inlistedthosefromsignificantlydeviate2.1)table(seeernumbcountwloawithdataTROSAtheofdseriopthetheofsolution”atda“allther(fobandrdhatheofand4.4)tableseeband,softtheofsolutiondata”“allther(fobandsofttheofAsTOThecurves)lightfittedthefrom(derivedAsTOtheand[110]dserioptheofrserroThe129].[63;indefinitionthewfollo4.4)letabseeband,rdha1denoteandrenthesispaingivenrea
softtherfo3125−(
l.leveconfidenceσpindividualTheJ0720.4RXofdserio

)eV1000]2547298(21).6873509(35).5562812(17).9975702(20).3004729(18).6878472(21).0395693(16).
−ys400257,,198210,353,391,925,577,
AdaTO50505050504951[(6878393(11)3004644(14)9975633(27)5562791(18)6873383(25)2547153(16)0395641(21)

)eV4002547153(16).6873383(25).5562791(18).9975633(27).3004644(14).6878393(11).0395641(21).
−]257,198,210,353,391,925,577,
ATO120(ysda[49505050505051
)eV1000−400]s[(39120(44).3852(63).83443(11).84902(98).8391130(50).3921(10).839063(49).
)eV88deriopderiop120(s[
8400−]

Instrument/setupId.Obs.

44323979(69).47179286(78).4717923(13).95710803(84).9949874(27).67672069(69).
677,677,677,869,869,248,
5144324000(30).5147179274(83).5147179234(54).5195710586(60).519949836(13).526767290(15).
677,677,677,869,869,248,
515151515152

391085(35).391090(55).391033(53).39124(12).39107(32).391133(13).
39120(44).3852(63).83443(11).84902(98).8391130(50).3921(10).839063(49).
8888391113(18).88391090(45).88391113(23).88391268(58).8839122(22).88391093(13).8
111thinEPIC-MOS1/FFS1thinEPIC-MOS2/SWS2medWEPIC-MOS1/LS722
HRC-S/LETGHRC-S/LETGHRC-S/LETGCIS-CCAACIS-CC
thinEPIC-pn/FFS30078medEPIC-pn/FFS30175
PSPCrp300338n00HRIrh300508n00HRIrh180100n00HRIrh300508n01HRIrh400884n00HRIh400944n00
36974536827732774

98

–Continued.–A.1:ableT

)eV1000−]Ays400TOda([

)eV400−]ATO120(da[ys
)eV1000−derio400]sp[()eV

d400−eriop120(s[
]

Instrument/setupId.Obs.

9260530(10).9200294(15).9199325(16).00129506(97)..9952766(29)9952735(14).99514812(64).2413532(20).8668516(28).24144068(14).8669491(20).11627407(69).9900211(20).1679433(29).9900222(24).1679407(14)..6813159(12)
584,584,584,587,586,586,761,762,761,,762761,940,939,940,939,940,016,
5292605120(69).5291993465(11).5291993465(95).5200129529(39).529952779(18).5299527264(93).5299514720(82).522413478(13).528668566(19).522413439(17).528669520(11).5211635982(97).5299012307(84).521679353(12).529900070(17).521679318(13).5368131016(91).
584,584,584,587,586,586,761,762,761,762,761,940,939,940,939,940,016,
5252525252525252525252525252525253

391098(73).39088(16).39104(20).391317(63).39116(18).39137(23).391138(23).39100(20).39100(17).39126(15).39118(21).391188(82).39077(52).39059(41).39051(49).39147(26).3911216(28).
88888888888888888

391143(43).39136(12).39122(12).391225(40).39119(11).39137(13).391133(18).39130(16).39101(13).39100(15).390950(95).391082(48)..39125(31)39087(24).39169(32).39091(22).3911142(23).
88888888888888888

2277122772thinEPIC-MOS1/FFS1thinEPIC-MOS2/FFS2thinEPIC-MOS1/FFS1thinEPIC-MOS2/FFS2medEPIC-MOS1/FFS5thinEPIC-MOS1/FFS3medEPIC-MOS2/FFS6thinEPIC-MOS2/FFS4thinEPIC-MOS1/FFS3nthiWEPIC-MOS1/LS5thinEPIC-MOS2/FFS4nthiWEPIC-MOS2/LS63466634667
CIS-CCACIS-CCACIS-CCACIS-CCA
0533thinEPIC-pn/FFS3thinEPIC-pn/FFS30534thickEPIC-pn/SWU20622medEPIC-pn/SWS80711

99

)eVPERIODSINDIVIDUALANDSOLUTIONTIMINGFINAL–Continued.–A.1:ableT

THE1000−]ys400da[()ATOATO120(ysda[
eV400−])eV1000−400]s()eVeriopderiopd120([]s[
400−Instrument/setupId.Obs.

OF4157091(15).6812041(15).6883883(31).6883911(21).5756243(19).
062,147,147,147,230,
534157092(15).5368119387(43).536883801(11).5368838022(93).535756209(11).
062,147,147,147,230,
5353535353

S)391143(58).39111(15).39120(13).3911165(16).391140(30).391008(48).391018(53).391082(33)..391130(50)391163(58).
39109(25).88391010(95).391138(63).839129(25).839110(11).8
8391105(35).8391108(68).8391150(60).83911146(15).8391138(23).8391095(45).8391183(38).8391120(20).8391095(40).8391103(38).
8888888888
334thinEPIC-MOS1/FFS2thinEPIC-MOS2/FFS355556thinEPIC-MOS1/SWS1thinEPIC-MOS2/SWS278thinEPIC-MOS1/SWS1thinEPIC-MOS2/SWS29
ACIS-CCCIS-CCAHRC-S/LETGCIS-CCACIS-CCACIS-CCACIS-CCAHRC-S/LETGHRC-S/LETGHRC-S/LETGHRC-S/LETG
S10815thinEPIC-pn/FFthinEPIC-pn/FFS30986thinEPIC-pn/FFS31060
46684669530546704671467246735581558263646369

A6674775(23).67561797(84).6695969(13).6696931(14).9398385(29).0881131(20).3001616(10).2941416(13).29413962(83).2601885(15).
393,488,488,488,,522610,636,636,636,652,
536674769(19).5367561302(44).536695937(14).536696892(13).539398395(35).530881154(30).5330015746(23).5329413571(70).5329413754(96).532601916(17).
393,488,488,488,522,610,636,636,636,652,
53535353535353535353

(TO100

ALSARRIVOFTIMEA.

–Continued.–

A.1:ableT

)eV1000−]ys400da([)ATOATO120(da[ys
eV400−])eV1000−derio400]

p()s[eV400−deriop120(]s[
Instrument/setupId.Obs.

17180817(92).16588680(52).1658857(12).0243020(12).
687,687,687,720,
.5317180535(53)531657835(12).531658825(10).530243035(13).
687,,687687,720,
53535353

35091144(12).3285752(11).32255272(65).3225524(16).6053791(11).5990664(13).5990665(18).84099190(98).83457862(99).8346782(22).36989479(60).3635840(15).
775,877,877,877,,044044,044,225,225,225,421,421,
533509131(17).5332857154(71).533225489(15).533225491(11).5460537610(44).545990605(12).5459906220(62).5484098865(82).548345794(18).548346806(13).5436989356(53).543635797(17).
775,877,877,877,044,044,044,225,225,225,421,421,
535353535454545454545454

39212(88)39120(11)39101(20)39116(18)39104(11)39074(17)39096(19)391113(98)39066(27)39096(22)391085(85)39109(17)

391072(38).391085(80).390998(78).39120(11)..39101(20)39116(18).39104(11).39074(17).39096(19).391113(98).39066(27).39096(22).391085(85).39109(17).
391115(10).8839212(88).
8391125(25).88391003(63).88391200(55).88391090(70).8839137(17).8839131(13).88391075(65).8839117(16).8839099(13).88391150(65).8839107(21).839103(23).888391130(50).8839090(16).8
9thinEPIC-MOS1/SWS1thinEPIC-MOS2/SWS210101010thinEPIC-MOS1/SWS2thinEPIC-MOS2/SWS3thinEPIC-MOS1/FFS2thinEPIC-MOS2/FFS3thinEPIC-MOS1/FFS2thinEPIC-MOS2/FFS3thinEPIC-MOS1/FFS2
HRC-S/LETGHRC-S/LETGHRC-S/LETGHRC-S/LETGHRC-S/LETGHRC-S/LETGthinEPIC-pn/FFS310867243724472455584thinEPIC-pn/FFS11181thinEPIC-pn/FFS11265thinEPIC-pn/FFS11356thinEPIC-pn/FFS11454
72517177

101

A.TIMEOFARRIVALS(TOAS)OFTHEFINALTIMINGSOLUTIONAND
PERIODSINDIVIDUAL

–Continued.–A.1:ableT

)eV1000].3635849(18)7916751(12).
−400ysda421,863,
(eV400−[]543635875(20).547916775(17).
)ATOATO120(ysda[,54,54
863421)eV100039127(22)

d−78046975(81).7440479(17).7440483(15).6684187(15).3044632(11).2966943(13).2967885(11).
911,911,911,085,096,096,096,
547856154(16).547440458(30).547440524(13).556684206(14).5530446151(69).552966932(13).552967896(14).
911,911,911,085,096,096,096,
54545455555555

3912(12).39136(29).39118(35).39119(20).39101(15).39120(20).39102(24).
8888888

400]s39127(22).3912(12).39136(29).39118(35).39119(20).839101(15).39120(20).39102(24).
39129(20)()eV.8eriopderiop120([]s[839131(22).8839108(99).88839097(26).839103(25).8839102(12).8839097(20).839104(15).88
400−thinEPIC-MOS2/FFS31111thinEPIC-MOS1/FFU2thinEPIC-MOS2/FFU212thinEPIC-MOS1/SWS1thinEPIC-MOS2/SWS2
HRC-S/LETGHRC-S/LETGHRC-S/LETGInstrument/setupId.Obs.1086110700EPIC-pn/FFS31700thin10701thinEPIC-pn/FFS31792

102

BendixApp

PhDduringPublications

erspapScientificB.1

•Acatalogueofyoungrunawaystarswithin3kpcfromHipparcos;
Tetzlaff,N.;Neuh¨auser,R.;Hohle,M.M.;MNRAS;2010;inpress

•UpdatedphasecoherenttimingsolutionoftheisolatedneutronstarRXJ0720.4−3125
usingrecentXMM-NewtonandChandraobservations;
Hohle,M.M.;Haberl,F.;Vink,J.;Turolla,R.;Zane,S.;deVries,C.P.;M´endez,
M.;A&A;2010;inpress

•O,B-type&redsupergiantmassesandluminosities;
Hohle,M.M.;Neuh¨auser,R.;Schutz,B.F.;Cat;2010

•Kinematicsofyoungassociations/clusters;
Tetzlaff,N.;Neuh¨auser,R.;Hohle,M.M.;Maciejewski,G.;Cat;2010

•Identifyingbirthplacesofyoungisolatedneutronstars;
Tetzlaff,N.;Neuh¨auser,R.;Hohle,M.M.;Maciejewski,G.;MNRAS;2010;402,
2369

•MassesandluminositiesofO-andB-typestarsandredsupergiants;
Hohle,M.M.;Neuh¨auser,R.;Schutz,B.F.;AN;2010;331,349

•NewphotometryandastrometryoftheisolatedneutronstarRXJ0720.4−3125using
observations;ORST/FVLrecentEisenbeiss,T.;Ginski,C.;Hohle,M.M.;Hambaryan,V.V.;Neuh¨auser,R.;
Schmidt,T.O.B;AN;2010;331,243

•TheoriginoftheGuitarpulsar;
Tetzlaff,N.;Neuh¨auser,R.;Hohle,M.M.;MNRAS;2009;400,99

103

PHDDURINGTIONSPUBLICAB.

•PhotometricstudyoftheOBstarclustersNGC1502andNGC2169andmassesti-
mationoftheirmembersattheUniversityObservatoryJena;
Hohle,M.M.;Eisenbeiss,T.;Mugrauer,M.;Freistetter,F.;Moualla,M.;
Neuh¨auser,R.;Raetz,St.;Schmidt,T.O.B.;Tetzlaff,N.;Vaˇnko,M.;AN;2009;
511330,

•Photometricanalysisoftheeclipsingbinary2MASS19090585+4911585;
Raetz,St.;Vaˇnko,M.;Mugrauer,M.;Schmidt,T.O.B.;Roell,T.;Eisenbeiss,T.;
Hohle,M.M.;Koeltzsch,A.;Ginski,Ch.;Marka,C.;and4coauthors;AN;2009;
504330,

•PhotometricmonitoringoftheyoungstarPar1724inOrion;
Neuh¨auser,R.;Koeltzsch,A.;Raetz,St.;Schmidt,T.O.B.;Mugrauer,M.;Young,
N.;Bertoldi,F.;Roell,T.;Eisenbeiss,T.;Hohle,M.M.;and5coauthors;AN;
493330,2009;

•Variabilityofyoungstars:Determinationofrotationalperiodsofweak-lineTTauri
starsintheCepheus-Cassiopeiastar-formingregion;
Koeltzsch,A.;Mugrauer,M.;Raetz,St.;Schmidt,T.O.B.;Roell,T.;Eisenbeiss,
T.;Hohle,M.M.;Vaˇnko,M.;Ginski,Ch.;Marka,C.;and4coauthors;AN;2009;
482330,

•PlanetarytransitobservationsattheUniversityObservatoryJena:XO−1band
1;−rESTRaetz,St.;Mugrauer,M.;Schmidt,T.O.B.;Roell,T.;Eisenbeiss,T.;Hohle,M.
M.;Tetzlaff,N.;Vaˇnko,M.;Seifahrt,A.;Broeg,Ch.;and2coauthors;AN;2009;
475330,

•PlanetarytransitobservationsattheUniversityObservatoryJena:TrES−2;
Raetz,St.;Mugrauer,M.;Schmidt,T.O.B.;Roell,T.;Eisenbeiss,T.;Hohle,M.
M.;Koeltzsch,A.;Vaˇnko,M.;Ginski,Ch.;Marka,C.;and7coauthors;AN;2009;
459330,

•NewbrowndwarfcandidatesinthePleiades;
Eisenbeiss,T.;Moualla,M.;Mugrauer,M.;Schmidt,T.O.B.;Raetz,St.;Neuh¨auser,
R.;Ginski,Ch.;Hohle,M.M.;Koeltzsch,A.;Marka,C.;and4coauthors;AN;2009;
439330,

•Follow-upobservationsofComet17P/Holmesafteritsextremeoutburstinbrightness
ofend2007;erOctob

104

B.2AcceptedproposalsforobservationslistedintheADS

Mugrauer,M.;Hohle,M.M.;Ginski,C.;Vanko,M.;Freistetter,F.;AN;2009;
425330,

•SpectralandtemporalvariationsoftheisolatedneutronstarRXJ0720.4−3125:new
observations;XMM-NewtonHohle,M.M.;Haberl,F.;Vink,J.;Turolla,R.;Hambaryan,V.;Zane,S.;deVries,
C.P.;M´endez,M.;A&A;2009;498,811

•XMM-NewtonRGSspectrumofRXJ0720.4−3125:anabsorptionfeatureat
eV;k0.57Hambaryan,V.;Neuh¨auser,R.;Haberl,F.;Hohle,M.M.;Schwope,A.D.;A&A;
9497,2009;

•MassEjectionbyStrangeStarMergersandObservationalImplications;
Bauswein,A.;Janka,H.-Th.;Oechslin,R.;Pagliara,G.;Sagert,I.;Schaffner-Bielich,
J.;Hohle,M.M.;Neuh¨auser,R.;Phys.Rev.Lett.;2009;103,011101

B.2Acceptedproposalsforobservationslistedinthe
ADS

•IsthereafallbackdiskaroundRXJ0720.4−3125?;
Posselt,Bettina;Pavlov,George;Hohle,Markus;Spitzerprop.;2010;70045

•RXJ0720.4−3125-afreeprecessingX-raypulsar?;
Hohle,M.M.;Haberl,F.;Vink,J.;Turolla,R.;Zane,S.;deVries,C.P.;M´endez,
M.;XMM-Newtonprop;2009;28

•RXJ0720evolution:precession,glitching,orthelastflutteringsofamagnetar;
Hohle,M.M.;Haberl,F.;Vink,J.;Turolla,R.;Zane,S.;deVries,C.P.;M´endez,
M.;XMM-Newtonprop;2008;26

B.3Conferencecontributionsandproceedingslistedin
ADSthe

•VariablespectrumoftheX-RaypulsarRXJ0720.4−3125;
Hohle,M.;Haberl,F.;2009;hrxs.confE..21H

105

PHDDURINGTIONSPUBLICAB.

•XMM-NewtonRGSspectrumofRXJ0720.4−3125:Absorptionfeatureat0.57keV;
Hambaryan,V.;Neuh¨auser,R.;Haberl,F.;Hohle,M.M.;Schwope,A.D.;2009;
hrxs.confE..20H

•RXJ0720.4−3125-aprecessingX-raypulsar?;
Hohle,M.;Haberl,F.;2009;epsc.conf....4H

•TransitobservationattheobservatoryinGrossschwabhausen:XO−1bandTrES−1;
Vaˇnko,M.;Raetz,S.;Mugrauer,M.;Schmidt,T.O.B.;Roell,T.;Eisenbeiss,
T.;Hohle,M.;Seifahrt,A.;Koeltzsch,A.;Broeg,C.;and2coauthors;2009;
US..253..440VIA

•ObservationsofthetransitingplanetTrES-2withtheAIUJenatelescopeinGrosss-
abhausen;chwRaetz,S.;Mugrauer,M.;Schmidt,T.O.B.;Roell,T.;Eisenbeiss,T.;Hohle,
M.;Seifahrt,A.;Koeltzsch,A.;Vaˇnko,M.;Broeg,Ch.;and2coauthors;2009;
US..253..436RIA

•Usingradioactivitiestoimprovethesearchfornearbyradio-quietneutronstars;
Hohle,MarkusM.;Neuh¨auser,Ralph;Tetzlaff,Nina;NewAR;2008;52,405

•NewluminositiesforOandBstars;
Hohle,MarkusM.;Neuh¨auser,Ralph;AN;2007;328,713

•FirstplanetarytransitobservationswiththeAIUJenatelescopeinGrossschwab-
hausen;Raetz,Stefanie;Mugrauer,Markus;Schmidt,Tobias;Roell,Tristan;Eisenbeiss,
Thomas;Hohle,Markus;Seifahrt,Andreas;Koeltzsch,Alexandra;Vaˇnko,Mar-
tin;Neuhaeuser,Ralph;AN;2007;328,710

106

endixAppC

alksT

stalkScientificC.1

•AnnualMeetingandGeneralAssemblyoftheAstronomischeGesellschaft,Bonn,
16.09.2010,Germany“RXJ0720−anX-raypulsarindustyenvironment?”

•Semi-annualmeetingoftheSFB/TR-7GravitationalWaveAstronomy,Garching,
25.02.2010,Germany“Populationsynthesisofmassivestars,projectC7−Previousandplannedworkfor
C7andplannedworkforC8(newproject)”

•WorkshopondenseQCDphasesinHeavyIonCollisionsandSupernovae,Prerow,
12.10.2009,Germany“RXJ0720.4-31.25:aprecessingX-raypulsar?Spectralandtemporalvariations/
(invited)timing”coherentphase

•EuroPlanetConference,Potsdam,Germany,18.9.2009
“RXJ0720.4−3125−aprecessingneutronstar?(invited)”

•InternationalSummerSchoolonNuclearTheoryandAstrophysicalApplications,
2008Julyia,RussDubna,“SpectralbehaviouroftheM7likeneutronstarRXJ0720.4-3125”

•DPGFr¨uhjahrstagunginFreiburg/Breisg.,Germany,05.03.2008
“Neutronstarpopulationsynthesis−predictionsforGWdetection”

•Semi-annualmeetingoftheSFB/TR-7GravitationalWaveAstronomy,Pots-
dam/Golm,26.02.2008,Germany“Neutronstarpopulationsynthesis−predictionsforGWdetection(?)”

107

ALKSTC.

•InternationalWorkshopofAstronomywithRadioactivitiesatRingbergCastleofthe
Max-Planck-GesellschaftinKreuth,Germany,7−10January2008
“Usingradioactivitiestoimprovethesearchfornearbyradio-quietneutronstars”

kstalPublicC.2

•Vortragf¨ureineBesuchergruppe(talkforvisitors),Jena,Germany,19.09.2010
“EinekurzeReisedurchunserSonnensystem”(AbriefvoyagethroughourSolar
system)

•LangeNachtderWissenschaften(longnightofscience),Jena,Germany,13.11.2009
“Neutronensterne−unheimlicheSterne”(Neutronstars−spookystars)

•Einsteintag(Einsteinday,workshop),Jena,Germany,16.09.2009
“KoordinatensystemeinderAstronomie,BewegungenamHimmel”(coordinatesys-
temsinastronomyandmotionsonthesky)

•Lehrerfortbildung(teachersworkshop),Jena,Germany,26.06.2009
“Neutronensterne,QuarksterneundSchwarzeL¨ocher”(neutronstars,quarkstarsand
holes)black

•Vortragf¨urKinderderNAJU(talkforchildrenoftheGermanSocietyforthePro-
tectionofNature),Jena,Germany,06.12.2008
“EinekurzeReisedurchunserSonnensystem”(AbriefvoyagethroughourSolar
system)

•Vortragf¨ureineSlowakischeSchulklasse(talkforaslowakianschoolclass),Jena,
08.09.2008,Germany“¨Ubersicht¨uberunserInstitut”(Overviewofourinstitute)

•TagderoffenenT¨ur(openday),Jena,Germany,18.01.2008
“UnheimlicheSterne−NeutronensterneundSchwarzeL¨ocher”(spookystars−neu-
tronstarsandblackholes)

108

DendixApp

ervisingsupandeachingT

•contributedtothesupervisingofthecurrentdiplomathesis“Populationssynthese
vonmassenreichenSterneninnerhalb5kpc”(Populationsynthesisofmassivestars
within5kpc)ofJ´anosSchmidt,Jena,Germany,2010

•contributedtothesupervisingofthediplomathesis“KinematischeUntersuchungen
zujungenisoliertenNeutronensternen:DieSuchenachdenOrtenpotentiellerSu-
pernovae.”(Kinematicinvestigationsofyoungisolatedneutronstars:Thesearchfor
likelysitesofsupernovae),byNinaTetzlaff,Jena,Germany,2008/2009

•supervisingthepracticalbasiccoursesofthefacultyofphysics,Jena,Germany,
31.12.2007−01.10.2007

•supervisingthepracticalcoursesforbiophysicsofthefacultyofbiology,Jena,Ger-
31.07.2007−01.03.2007,many

•supervisingthepracticalcoursesforbiophysicsofthefacultyofbiology,Jena,Ger-
31.12.2006−01.11.2006,many

•studentassistantofthefacultyofphysicsandastronomy,Jena,Germany,
03.02.2007−16.10.2006

•supervisingthepracticalbasiccoursesofthefacultyofphysics,Jena,Germany,
21.07.2006−15.05.2006

•supervisingthepracticalcoursesforbiophysicsofthefacultyofbiology,Jena,Ger-
30.04.2006−01.03.2006,many

•studentassistantofthefacultyofphysicsandastronomy,Jena,Germany,
21.12.2006−07.11.2005

109

D.

CHINGTEA

student

AND

assistant

18.04.2005

SUPERVISING

of

the

17.07.2005−

yfacult

of

physics

110

and

astronomy,

Jena,

,Germany

AppEendix

vitaeCurriculum

12.11.1982

1993−1989

2001−1993

2001

2002−2001

2007−2002Oct

2007Aug

MatthiasrkusMaHohle,

P¨birth,Germanyoßneck/Thuringia,

primaryschoolatAlfredBrehmGrundschule
Germanyrf/Thuringia,Renthendoin

highschoolatJohannHeinrichPestalozziGymnasium
rmanyGeda/Thuringia,Stadtro

Abitur

GermanAirforceinBayreuth
andF¨urstenfeldbruck/Bavaria,Germany

physicsstudiesatFriedrichSchillerUniversit¨at
GermanyJena/Thuringia,

astrophysicsandphysicsindiploma“PopulationssynthesezurAbsch¨atzungder
SupernovaratedesGouldBelts:
Neutronensternen”jungennachSuche(Populationsynthesistoestimatethe
supernovarateoftheGouldBelt:
Searchforyoungneutronstars)

111

E.AEVITCULUMCURRI

Dec−2007Aug

2010−2008

Jena,

2007

workingforSFB/TR-7

GravitationalWaveAstronomy,projectC7

atFriedrichSchillerUniversit¨atJena/Thuringia,Germany

PhDthesisinastrophysicsandgeneralrelativity,

“Thespectralandtemporalvariabilityofthe

isolatedX-raypulsarRXJ0720.4-3125”,

attheMax-Planck-Institutf¨urextraterrestrischePhysik

Germanyria,rching/BavaGa

andFriedrichSchillerUniversit¨atJena/Thuringia,Germany

signature

112

rationDecla

IherewithdeclarethatIhaveproducedthispaperwithouttheprohibitedassistance
ofthirdpartiesandwithoutmakinguseofaidsotherthanthosespecified;notions
takenoverdirectlyorindirectlyfromothersourceshavebeenidentifiedassuch.
Thispaperhasnotpreviouslybeenpresentedinidenticalorsimilarformtoanyother
Germanorforeignexaminationboard.
ThethesisworkwasconductedfromJanuary1st2008toDecember31st2010under
thesupervisionofFrankHaberlattheMax-Planck-Institutf¨urextraterrestrische
Physik.

Jena,

Icherkl¨arehiermitehrenw¨ortlich,dassichdievorliegendeArbeitselbst¨andig,ohne
unzul¨assigeHilfeDritterundohneBenutzungandereralsderangegebenenHilfs-
mittelundLiteraturangefertigthabe.DieausanderenQuellendirektoderindirekt
bernommenenDatenundKonzeptesindunterAngabederQuellegekennzeichnet.
BeiderAuswahlundAuswertungfolgendenMaterialshabenmirdienachstehend
aufgef¨uhrtenPersoneninderjeweilsbeschriebenenWeiseunentgeltlichgeholfen:

•1.FrankHaberlhatmirseineProgrammezumanalysierenderXMM-Newton
EPIC-pnDatenzurVerf¨ugunggestellt
•2.TheodorPribullahatdiePhasenresiduenmitderOrbitl¨osungmitHilfeseines
t.gefitteProgramms

WeiterePersonenwarenanderinhaltlich-materiellenErstellungdervorliegendenAr-
beitnichtbeteiligt.Insbesonderehabeichhierf¨urnichtdieentgeltlicheHilfevon
Vermittlungs-bzw.Beratungsdiensten(PromotionsberateroderanderePersonen)
inAnspruchgenommen.Niemandhatvonmirunmittelbarodermittelbargeldw-
erteLeistungenf¨urArbeitenerhalten,dieimZusammenhangmitdemInhaltder
stehen.Dissertationrgelegtenvo

DieArbeitwurdebisherwederimIn-nochimAuslandingleicheroder¨ahnlicher

FormeineranderenPf¨ufungsbeh¨ordevorgelegt.

geltendeDierdnungPromotionso

annt.ekb

dassortlich,ehrenw¨versichereIch

undverschwiegennichts

Ort,

Datum

e.hab

derPhysikalisch-AstronomischenFakult¨at

nachichestemb

Unterschrift

d.

dieWissen

erfassersV

neire

ahrheitW

istmir

gesagt