Transient X-ray pulsar V0332+53: pulse phase-resolved spectroscopy and the reflection model

0.58 MB·English

by  A. A. Lutovinov

Mon.Not.R.Astron.Soc.000,1–12(2014) Printed13February2015 (MNLATEXstylefilev2.2)
+
Transient X-ray pulsar V0332 53: pulse phase-resolved
spectroscopy and the reflection model
5
1 A.A.Lutovinov,1⋆ S.S.Tsygankov,2,1 V.F.Suleimanov,3,4 A.A.Mushtukov,2,5,6
0
2 V.Doroshenko,3 D.I.Nagirner6 and J.Poutanen2

n 1SpaceResearchInstituteoftheRussianAcademyofSciences,ProfsoyuznayaStr.84/32,Moscow117997,Russia
a 2Tuorlaobservatory,DepartmentofPhysicsandAstronomy,UniversityofTurku,Va¨isa¨la¨ntie20,FI-21500Piikkio¨,Finland
J 3Institutfu¨rAstronomieundAstrophysik,KeplerCenterforAstroandParticlePhysics,Universita¨tTu¨bingen,Sand1,
0 D-72076Tu¨bingen,Germany
2 4Kazan(Volgaregion)FederalUniversity,Kremlevskajastr.,18,Kazan420008,Russia
5PulkovoObservatoryoftheRussianAcademyofSciences,SaintPetersburg196140,Russia
] 6SobolevAstronomicalInstitute,SaintPetersburgStateUniversity,SaintPetersburg,StaryjPeterhof198504,Russia
E
H
.
h 13February2015
p
-
o
r ABSTRACT
t We present the results of the pulse phase- and luminosity-resolved spectroscopy of the
s
a transient X-ray pulsar V0332+53, performed for the first time in a wide luminosity range
[ (1− 40)× 1037 erg s−1 during a giant outburst observed by the RXTE observatory in Dec

2004 – Feb 2005. We characterize the spectra quantitatively and built the detailed “three-
1
dimensional”pictureofspectralvariationswithpulsephaseandthroughouttheoutburst.We
v
3 showthatallspectralparametersarestronglyvariablewiththepulsephase,andthepatternof
8 thisvariabilitysignificantlychangeswithluminositydirectlyreflectingtheassociatedchanges
7 inthestructureofemissionregionsandtheirbeampatterns.Obtainedresultsarequalitatively
3 discussedintermsoftherecentlydevelopedreflectionmodelfortheformationofcyclotron
0 linesinthespectraofX-raypulsars.
.
2
Keywords: X-ray:binaries–(stars:)pulsars:individual–V0332+53
0
5
1
:
v
i 1 INTRODUCTION ing capabilities of the RXTE observatory with its good spectral
X characteristicsallowedalsotoperformapulsephase-resolvedanal-
TheobservedemissionofX-raypulsarsoriginatesfromoneortwo
r ysisfor anumber of X-ray pulsars(see, e.g., Kreykenbohmetal.
a hot regions, located near the neutron star magnetic poles where
2004;Klochkovetal.2008;Fu¨rstetal.2011).
the accreting matter is funneled to by the strong magnetic field
In this work we focus on the detailed pulse phase-resolved
of the neutron star. The geometry of the emission regions de-
spectroscopyfortheX-raypulsarV0332+53inawidedynamical
pends mostly on the accretion rate, magnetic field structure and
luminosityrangeL ≃1−40(hereL =L /1037ergs−1,assum-
strength, and can be described as spots, mounds or columns (see 37 37 X
ingthedistancetothesourceof7kpc,Negueruelaetal.1999).Itis
e.g.,Basko&Sunyaev1976;Burnardetal.1991;Becker&Wolff
importanttoemphasize,thatsuchsystematicanalysishasnotbeen
2007; Mushtukovetal. 2014). The geometry and the beaming
carriedoutbefore.
propertiesofthesehotregionsshapetheobservedX-rayspectrum,
itspulse-phaseandaccretion-ratedependenceswhichcanbestud- The X-ray pulsar V0332+53 was observed by the RXTE
iedobservationallyandusedtouncoverintrinsicpropertiesofthe observatory during a powerful outburst in 2004–2005, that pro-
emissionregions. vided a very good coverage of different outburst stages. An ad-
Significant progress in X-ray astronomy has been achieved ditional reason to choose V0332+53 for the study of physical
in the last decades with the Compton-GRO, RXTE, Bep- conditions and geometry of the emission regions in X-ray pul-
poSAX, INTEGRAL and Swift observatories, which allowed sars and for an examination of a recently developed reflection
to study several dozens of X-ray pulsars in details (see, model(Poutanenetal.2013)isapresenceofthecyclotronabsorp-
e.g., reviews of Bildstenetal. 1997; dalFiumeetal. 2000; tion line (so-called cyclotron resonant scattering feature, CRSF)
Coburnetal.2002;Filippovaetal.2005;Lutovinov&Tsygankov anditshigherharmonicsinthesourcespectrum(Makishimaetal.
2009a;Caballero&Wilms2012).Acombinationofexcellenttim- 1990;Pottschmidtetal.2005;Kreykenbohmetal.2005).Astudy
ofthesourcepulse-averagedspectrashowedthatthecyclotronline
energy, as well as parameters of the spectral continuum, signifi-
⋆ [email protected] cantlychange withthesourceluminosity(Tsygankovetal.2006;
2 Lutovinovetal.
Table1.LogofRXTEobservations(orderedbyluminosity)usedforthepulsephase-resolvedanalysisoftheX-raypulsarV0332+53.
# Observation Date Luminositya Phaseb
ID MJD (1037ergs−1)
1 90089-11-04-04 53360.0 36.9±0.2 m
2 90089-11-04-02G 53358.6 35.4±0.2 b
3 90089-11-04-00G 53356.5 34.3±0.3 b
4 90089-11-03-01G 53354.7 32.8±0.3 b
5 90089-11-03-03 53352.8 30.4±0.2 b
6 90089-11-03-04 53353.7 28.5±1.1 b
7 90427-01-03-01 53385.1 22.5±0.8 d
8 90427-01-03-05 53387.0 20.2±0.1 d
9 90427-01-03-06 53387.4 19.6±0.1 d
10 90427-01-03-09 53388.4 18.6±0.4 d
11 90427-01-03-12 53389.3 18.0±0.5 d
12 90014-01-02-13 53390.4 17.3±0.1 d
13 90089-11-02-03 53343.8 16.3±0.1 b
14 90089-11-02-00 53342.8 15.4±0.1 b
15 90014-01-03-020 53394.4 15.3±0.1 d
16 90014-01-03-03 53395.3 14.3±0.1 d
17 Group1: 12.7±0.2 d
90014-01-04-00 53398.5
90014-01-04-01 53399.6
90014-01-04-02 53401.4
18 90014-01-05-01 53407.6 9.7±0.1 d
19 90427-01-04-04 53413.8 7.0±0.2 d
20 Group2: 6.2±0.1 d
90427-01-04-02 53414.3
90427-01-04-03 53413.8
90427-01-04-05 53414.8
21 90427-01-04-01 53416.6 5.0±0.1 d
22 Group3: 3.2±0.1 d
90014-01-07-01 53419.4
90014-01-07-02 53420.7
90014-01-07-03 53420.7
23 90014-01-07-00 53424.4 1.7±0.1 d
a Luminosityinthe3–100keVenergybandassumingthesourcedistanceof7kpc
b Outburstphase:b–brightening,d–declining,m–nearthemaximum
Mowlavietal.2006;Tsygankovetal.2010;Nakajimaetal.2010) Note, that first results on the pulse phase-resolved spec-
along the outburst. This behaviour was interpreted as a result of troscopy for V0332+53 were obtained by Pottschmidtetal.
changesintheheightoftheaccretioncolumnwherethecyclotron (2005), however, available observations did not contain the PCA
absorptionlinewasassumed tooriginate(see,e.g.,Mihara1995; datawiththerequiredenergyandtimeresolution, sotheanalysis
Scho¨nherretal. 2007; Nishimura 2008, 2014; Beckeretal. 2012, was limited to the HEXTE data and, therefore, it was not trivial
andreferencestherein).However,alternativescenariohasrecently to constrain the parameters of the broadband spectrum. As a re-
been proposed byPoutanenetal.(2013),where thelineformsin sult,nosignificantvariationsofspectralparameterswiththepulse
the illuminated atmosphere of the neutron star. In our paper, we phase had been reported. Later, some preliminary results (using
focusonthelattermodelwhendiscussingobservedspectralvaria- only two observations of V0332+53) on the phase and luminos-
tions. itydependenceofthecontinuumandCRSFparameterswerepub-
Accordingtothemodelcalculationsthecyclotronlineparam- lishedbyLutovinov&Tsygankov(2009b)andtheresultsonvari-
eters should strongly depend on the viewing angle, pulse phase, abilityoftheironemissionlinewiththepulsephaseandluminosity
bulk velocity of the falling plasma, etc. (Isenbergetal. 1998; by Tsygankov&Lutovinov (2009). Also no attempts to interpret
Araya&Harding 1999; Araya-Go´chez&Harding 2000; Serber theobtainedresultshavebeenmade.
2000;Scho¨nherretal.2007).Parametersofthecontinuumshould
also depend on the viewing angle due to the significant angular
dependenceofthecontinuumopacityinthestrongmagneticfield
2 OBSERVATIONS,SPECTRALMODELANDDATA
neartheneutronstarsurface(see,e.g.,Kaminkeretal.1982,1983).
ANALYSIS
Thus,observationsofV0332+53 giveusanuniquepossibilityto
buildforthefirsttimeadetailed“three-dimensional”picture(pa- As already mentioned, V0332+53 has been observed with the
rametervspulsephasevsluminosity) ofthesourcespectrumbe- RXTE observatory during the so-called giant outburst, which
haviour,andultimatelyuncover thephysicalandgeometricalpic- startedintheendof2004(Swanketal.2004)andlastedforabout
tureoftheaccretionontoamagnetizedneutronstar. two months. In the current work we use the same data set as
PulsephasespectroscopyofV0332+53 3
Figure1. Representativeexamplesofthepulsephase-resolvedspectraofV0332+53fortwodifferentluminositiesL37 =36.9(obs.1,left)and20.2(obs.
8,right).Blacksymbolscorrespondtothespectraatphases0.5625–0.625(left)and0.75–0.8125(right),redsymbolscorrespondtothespectraatphases
0.9375–1.0(left)and0.5–0.5625(right),thebluesymbolsareforthephases0.5–0.5625(left)and0.375–0.4325(right).Valuesofχ2andthecyclotronline
energyarealsoshownforreference.Residualsfromthebest-fittingmodels(summarisedinTable2)areshowninlowerpanels.
Table2.Best-fittingparametersforthreepulsephase-resolvedspectrafortwodifferentluminositiesofV0332+53.
Phase Γ Ecut E0 σ0 τ0 E1 σ1 τ1 χ2(d.o.f.)
keV keV keV keV keV
Obs.1,L37=36.9
0.5625–0.625 0.35±0.07 7.3+0.7 23.72±0.15 6.57+0.72 1.47±0.08 51.6+2.6 8.2±3.8 1.83+0.64 91.9(90)
−0.5 −0.16 −1.5 −0.34
0.9375–1.0 0.42±0.05 7.6+0.5 23.93±0.11 6.68+0.47 1.93±0.08 51.6+1.2 5.9+2.4 2.56+0.92 97.5(90)
−0.4 −0.18 −0.8 −1.8 −0.45
0.5–0.5625 0.18+0.08 8.95+1.24 23.20+0.18 7.15+0.85 1.38±0.08 50.7+1.8 10.5±2.8 2.62+0.68 94.1(90)
−0.04 −0.44 −0.08 −0.38 −1.1 −0.30
Obs.8,L37=20.2
0.75–0.8125 0.34±0.07 8.5+0.5 25.54+0.15 6.00+0.24 1.81±0.07 52.2+1.2 9.0+2.1 2.37±0.32 111.9(107)
−0.7 −0.17 −0.55 −0.9 −1.3
0.5–0.5625 0.28±0.08 8.6+1.0 26.17±0.27 7.15+0.58 1.88±0.13 53.4+1.4 5.5+2.7 4.0+5.4 90.1(107)
−0.9 −0.92 −1.1 −2.6 −1.2
0.375–0.4325 0.38±0.08 7.7±0.7 26.60+0.22 5.41+0.53 1.76±0.09 54.4+1.7 6.4±2.5 2.38+0.83 99.5(107)
−0.19 −0.79 −0.9 −0.47
in Tsygankovetal. (2010) apart from a number of observations HEXTE instruments onboard RXTE we used standard programs
(ObsIDs. 90014-01-01-XX, 90089-11-05-XX, 90089-22-01-XX, of the ftools/lheasoft v. 6.14 package and methods described in
90427-01-01-XX,90427-01-02-XX),performedwithtimeresolu- theRXTEcookbook1.Dependingonthespectrumqualityphotons
tioninsufficientforthepulse-phaseresolvedanalysis(typically16 were folded into 16, 8 or 4 phase bins, using individually deter-
s,whilethesourcepulseperiodisaboutof4.35s).Theuseddataset mined (per observation) and barycentrically corrected pulse peri-
coversbothbrighteninganddecliningphasesoftheoutburstmore ods.
orlessuniformly.Thereisonlyasmallgapbetweenluminosities Theobtainedspectrawereapproximatedbyapowerlawmodel
of L = 22.5and L = 28.5duetotheabsenceof observations withanexponentialcutoff(cutoffplinthexspecpackage)
37 37
of the required timing quality. To improve the statisticfor obser-
AE−Γexp(−E/E ), (1)
vationsatlowerluminositiesorwithsmallexposureswegrouped cut
closelyspacedobservationswithapproximatelythesameaveraged whereΓisthephoton index, E isthecutoffenergy, Aisanor-
cut
sourceintensityintothreegroupswiththeaveragedluminositiesof malization.Thespectrumwasmodifiedbyoneorseveralcyclotron
L37≃3.2,6.2and12.7.Thelistofanalysedobservationswithcor- absorptionlinesintheform
respondingaveragedluminositiesinthe3–100keVenergyrangeis
−τ (E/E )2σ2
presentedinTable1.Theseluminosityvaluesmayberegardedas exp N N N , (2)
closetothebolometriconesundertheassumptionthatthebulkof (E−EN)2+σ2N!
theenergyisreleasedintheX-rays.
To extract pulse phase-resolved spectra from the PCA and 1 http://heasarc.nasa.gov/docs/xte/recipes/cook book.html
4 Lutovinovetal.
1.2 1.02
1 1
0.8
0.98
0.6
-0.2
0
-0.3
-0.2
-0.4
-0.4
-0.5
12 10
10 9
8 8
24.5
27.5
24
23.5
27
23
56
54
52 54
50 52
2.3 2.1
2.2 2
2.1 1.9
2
2
1.8
1.6
1.8
1.4
9 7
8 6
7
5
6
3 4
2.5
3
2
1.5
2
20 12
15 10
10 8
5 6
0 0.5 1 1.5 2 0 0.5 1 1.5 2
Figure2.DependenceofspectralparametersofV0332+53onthepulsephaseforluminositiesofL37 =36.9(obs.1,left)andL37 =12.7(obs.17,right).
Correspondingpulseprofilesareshownbyblack(upperpanels)andgrey(otherpanels)lines.Uncertaintiescorrespondtothe1σconfidencelevel.Twoperiods
areshownforclarity.
where E , σ and τ are the energy, widthand depth of the cy- clusionofhigherharmonicsinthemodelinsuchcasesonthepa-
N N N
clotron line (N = 0) and harmonics (N > 0), respectively (cy- rametersof thecyclotron lineand of thecontinuum. Similarlyto
clabsinthexspec package; Miharaetal. 1990). Thesame model theanalysisofthepulse-averagedspectra(Tsygankovetal.2006),
was used earlier for the analysis of pulse-phase averaged spectra theenergyofthefirstharmonicE wasassumedeithertobeafree
1
andreasonsforthechoiceofthecontinuumandlinemodelswere parameterorfixedequaltothedoubledenergyofthefundamental
discussedbyTsygankovetal.(2006,2010).Note,thatinclusionof E .Wehavefoundthattheparametersofthecontinuumwithinthe
0
thephotoelectricabsorptioninthemodeldoesnotaffecttheresults uncertaintiesdo not depend on whether thehigher harmonics are
offittinginthe3–100keVenergyrangeandthusitwasnottaken includedinthemodel.Theenergyandwidthofthecyclotronline
intoaccount. werefoundtoslightlyvarywiththesystematicuncertaintyofabout
0.1and0.2keV, respectively. Inthefollowinganalysistheseval-
The first harmonic of the cyclotron absorption line was not uesweretakenintoaccountwhencalculatinguncertaintiesofthese
confidentlyobservedanditsparameterswerenotwellconstrained parameters.Finally,totakeintoaccounttheironfluorescentlineat
inalldatasets.Therefore,weexaminedpossibleeffectsofthein-
PulsephasespectroscopyofV0332+53 5
∼6.4keVaGaussianlineatthisenergywithafixedwidth0.1keV
wasincludedinthemodelaswell.
The total number of spectra which were analysed in the pa-
perexceedstwohundredsand,therefore,itisnotpossibletofully
discusstheresultsoffittingoftheindividualspectrahere.Wethus
presentinFig.1severalexamplesofpulse-phaseresolvedspectra
for two luminosity levels to give some impression on the quality 1
ofthedataandtypicalvariationofspectralparameterswithpulse
phase.Thebest-fittingparametersaresummarisedinTable2.Itcan
beseenfromFig.1thatthemodel adequately describesobserva-
tionsinawideenergyrange3–100keV.Pottschmidtetal.(2005) 2
andNakajimaetal.(2010)havediscussed acomplex structureof
theV0332+53 spectrumnear thecyclotron line.Thisisalsovis-
ibleintheresidualsofourspectra.Thesearelikelyrelatedtothe
oversimplifieddescriptionof theCRSF(i.e.withaGaussian ora 1
Lorentzianabsorptionprofiles),whereasinrealityithasprobably
amorecomplexshape(asdiscussede.g.byScho¨nherretal.2007 5 10 50
andMukherjee&Bhattacharya2012). Energy, keV
Figure3.(a)EnergyspectraofV0332+53obtainedforthe4th(i.e.phase
0.1875-0.25;redpoints)and7thbins(i.e.phase0.375-0.4375;bluecrosses)
3 RESULTS ofthepulseprofile(seeFig.2)inthehighluminositystate(L37=36.9,obs.
1,Table1),and(b)theirratio.Thesolidlinesrepresentbest-fittingmodels
The analysis had been carried out uniformly for all observations forbothspectra.
andastrongvariationofboththecontinuumandthecyclotronline
parameterswiththepulsephasehadbeenfoundatallluminosities.
An example of such variability for two luminosities (L = 36.9 with an absorbed power law with exponential cutoff at high
37
and L = 12.7) is presented in Fig. 2 together with the source energies. The study of the pulse-averaged spectra showed that
37
pulseprofileinthe3–20keVenergyband.Toalignthephasesof the spectrum becomes softer and the cutoff energy increases
individualobservationsweusethepulseprofilesin3–20keVen- whenluminositydrops(Lutovinov&Tsygankov2011).Moreover,
ergyrange.Duetosignificantvariationofthespinperiodandthe the cutoff and cyclotron line energies were found to correlate
pulse profileshape withluminosity, finding a robust timing solu- (Lutovinov&Tsygankov2011),althoughthephysicalreasonsbe-
tioncoherentlydefiningpulsephaseatallluminositiesisproblem- sidesthiscorrelationarenot fullyclear.Inthispaper, weusethe
atic (Raichur&Paul 2010). Therefore, we roughly aligned pulse samemodelasitisthesimplestmodelwhichseemstocaptureall
profilesobtainedforindividualobservationstohavethezerophase relevantfeaturesofthespectrum.
coincidewiththemainminimumofthepulse,andfurtherononly
discussvariationsofthespectralparametersoverthepulseprofile.
Thisapproachdoesnotrequireprecisephaseconnectionoverthe 3.2 Variationsofthecyclotronfundamentallineparameters
wholeoutburst. withphaseandluminosity
As can be seen from Fig. 2, the spectrum of the source is
As is evident from Fig.2, the cyclotron line parameters signif-
stronglyvariablewithpulsephase.Moreover,thepulse-phasede-
icantly vary with the pulse phase and the shape of these varia-
pendence of most parameters appears to be different at different tions (below we refer to them as ‘cyclotron energy/width/depth
luminosities (see detailed descriptions in following sections). We
profiles’forsimplicity)dependsonthesourceluminosity.Theob-
notethatourspectralmodelhasmanyparameters,someofwhich
served changes of these profiles should directly reflect changes
can be correlated (e.g., photon index versus cutoff energy, cut-
in the structure of emission regions and their beam patterns with
off energy versus cyclotron line energy, see Coburnetal. 2002;
luminosity. To trace this variability we constructed the cyclotron
Lutovinov&Tsygankov 2011 for results and discussion). There- energy/width/depth profiles for all observations from Table1 and
fore,achangeinoneparametermightinprinciplebecompensated
comparedthemwiththecorrespondingpulseprofiles.InFig.4,the
by a change in another parameter with no change in the overall
pulse-phasedependenciesofthecyclotronlineparametersarepre-
spectral shape. Todemonstrate that thisisnot generally thecase, sentedforeightlevelsofthesourceluminosityL =36.9(a),32.8
37
and that the spectrum does indeed significantly change its shape,
(b),20.2(c),16.3(d),12.7(e),9.7(f),6.2(g),and1.7(h).
wepresent(asanexample)inFig.3twospectraobtainedatdiffer- AthighluminositiesL ≃32–37thecyclotronenergyprofile
37
ent pulsephases aswellastheirratio.Thevariabilitybothinthe
has a double-peaked shape with the maxima roughly coinciding
continuum andnearthecyclotronlineenergyisapparent. Below,
withthemaximaofthepulseprofile.Withdecreasingofthelumi-
wediscussindetailsthesevariations. nositytoL ≃30theprofilebecomessinglepeaked.Suchashape
37
remainsthenmoreorlessstabledowntoluminosityof L ≃ 14.
37
Atevenlowerluminosities,themaximumofthecyclotronenergy
3.1 Continuum
profilemovestothe inter-peakminimumof thepulseprofileand
Currently there are no commonly accepted theoretical models canbeclearlyseenforluminositiesbelowL ≃10.
37
to describe the spectra of accreting pulsars in details provided The evolution of the cyclotron depth profile with the lumi-
by observations, so empirical models are typically used instead. nositydiffersfromthedescribedabovebehaviourofthecyclotron
As it was noted above, the broadband spectra of V0332+53 energyprofile.Inparticular,practicallyforallluminositiesitsmax-
(both the pulse-averaged and the phase-resolved) were described imumroughlycorrespondstotheinter-peakminimumofthepulse
6 Lutovinovetal.
25
1.2 1.2
24 8
0.8 7 0.8
23
25.2
1 8 1
24.8
24.4 0.8 7 0.8
1.04 8 1.04
27
26 0.96 6 0.96
25
4
28 1.04 8 1.04
26 0.96 6 0.96
27.5 1.02 7 1.02
1 6 1
27
0.98 5 0.98
29 1.04 7 1.04
28 1 6 1
27 0.96 5 0.96
29 1.04 6 1.04
1 1
28 0.96 5 0.96
32 1.04 1.04
1 6 1
30 0.96 0.96
0 0.5 1 1.5 2 0 0.5 1 1.5 2
2 1.2
1.5 0.8
1
1.8
0.8
1.6
2 1.04
0.96
1.6
1.04
2
0.96
1.6
1.02
2
1
1.8 0.98
1.04
2 1
1.5 0.96
2.5 1.04
1
2 0.96
1.04
4
1
2 0.96
0 0.5 1 1.5 2
Figure4.Variationsofthecyclotronlineenergy(topleft),width(topright)anddepth(bottom)withthepulsephasefordifferentluminosities:L37=36.9(a),
32.8(b),20.2(c),16.3(d),12.7(e),9.7(f),6.2(g),1.7(h)(blackhistograms).Therelativecolumnsheightsaccordingthereflectionmodel(Poutanenetal.
2013)are:h/R=0.97(a),0.84(b),0.57(c),0.48(d),0.4(e),0.32(f),0.22(g),and0.07(h).Greylinesrepresentthecorrespondingnormalizedpulseprofiles
(rightaxis).Thelinewidthwasfixedat6keVfortheobservationwiththelowestluminosityL37=1.7(obs.23).
PulsephasespectroscopyofV0332+53 7
1.2
52
2.2
51
0.8
50 2.1
1.04
54 2.05
1
2
52
0.96
1.04
54 2
1
52
1.9
0.96
2.1
56 1.02
54 2 1
52 1.9 0.98
1.04
53
1
1.9
52
0.96
2
55 1.95 1.04
54 1.9 1
53 1.85 0.96
0 0.5 1 1.5 2 0 0.5 1 1.5 2
Figure5.Dependenceofthefirstharmonicenergy(left)andtheratioofthelineenergiesE1/E0(right)onthepulsephasefordifferentluminosities:L37=36.9
(a),18.6(b),15.3(c),12.7(d),9.7(e),6.2(f)(blackhistograms).Greylinesrepresentcorrespondingpulseprofiles.
profile,andonlyattheverylowluminositiescoveredbyobserva- observations, covering aluminosityrange from L ≃ 5to≃ 37,
37
tions(L =1.7)themaximumofthecyclotrondepthprofileshifts whereacombinationofthesourceintensityandexposureallowed
37
tooneofpulseprofilepeaks. ustodetermineandconstraintheparametersofthefirstharmonic.
Thecyclotronlinewidthtendstoanti-correlatewiththeflux ProfilesofitscentroidenergyandcorrespondingratioE /E asa
1 0
at high luminosities (Fig.4a, b, d) and to correlate with it at low functionofthepulsephasearepresentedinFig.5.
luminosities(Fig.4e,f,g).Suchabehaviourisindeedexpectedin It is difficult to make a detailed comparison of the E be-
1
the reflection model. Generally speaking, although the width de- haviourwithE ,however,itcanbeseenthattheirprofilesarenot
0
pends on several factors, it is expected to be broader in the case coincident(seeFigs.4and5).Thisisprobablyduetothefactthat
when we see the illuminated neutron star surface from aside and different parts of emission regions are responsible for the forma-
narrowerwhentheilluminatedsurfaceisseenfromthepoles(see tionofthecyclotronlineandfirstharmonicoftheCRSF.Theratio
anextendeddiscussioninSection4.2). E /E is also strongly variable (up to ∼ 10%) during the pulse.
1 0
Ontheaverage,itdemonstratesalsoadecreasewiththeluminos-
ity, similarthat found for pulse-average spectra (Tsygankovetal.
2006;Nakajimaetal.2010).
3.3 Variationsoftheenergyofthefirstharmonic
Tsygankovetal.(2006)showedthatthecentroidenergyE ofthe
1
first harmonic roughly follows the luminosity dependence of the
4 DISCUSSION
cyclotronlineE .However,theratiooftheenergiesofthefirsthar-
0
monictothefundamentalonedoeschangeslightlywithluminos- Wenowwilltrytodescribequalitativelytheobservedpulse-phase
ity,fromabout∼2.2athighestluminositiesto∼1.9atthelowest changes of the cyclotron line parameters using the recently pro-
(Tsygankovetal.2006;Nakajimaetal.2010).Takingintoaccount posed reflection model (Poutanenetal. 2013). According to the
thatduringthepulsedifferentpartsoftheemissionregionsareob- widelyacceptedparadigm(Basko&Sunyaev1976),brightX-ray
served at different viewing angles and that thecyclotron line and pulsars have relatively tall (comparable with the neutron star ra-
thefirstharmoniccouldpotentiallybeformedinslightlydifferent dius)accretioncolumns atbothmagneticpoles. Thecolumnsare
regions,itwouldbeinterestingandimportanttotracethebehaviour supportedbytheradiativepressureoftheX-raystrappedwithinthe
ofthefirstharmonicenergyE andoftheratioE /E bothwiththe opticallythickaccretionflowandslowlydiffusingthroughthesides
1 1 0
pulsephaseandluminosity. ofthecolumns, sotheplasmaismosteffectivelysloweddownin
Notethattheparametersofthefirstharmonicarereasonably thecoreofthecolumn,whereastheoutershellfallsalmostfreely
constrained only in a subset of all observations even for pulse- (Lyubarskii&Syunyaev1988).Asaresult,theemergingemission
averagedspectra(seedetaileddiscussioninTsygankovetal.2006). isexpectedtobestronglybeamedtowardstheneutronstarsurface
The situation is even worse for the phase resolved analysis due duetothescatteringonfastfree-fallingelectrons(Kaminkeretal.
tolowernumber ofphotons. Nevertheless,wefoundanumberof 1976;Lyubarskii&Syunyaev1988).Theformationofacyclotron
8 Lutovinovetal.
0.4
0.3
0.2
0.1
0
10 20 30 40
Figure 6. Sketch of the angular distribution of different components for Figure7.Dependenceofthephaseshiftbetweenmaximaofthepulsepro-
high(a)andlow (b)luminosities. Reddiagram corresponds tothedirect fileandthecyclotronlineenergy∆φontheX-raypulsarluminosity.The
component,blueone–tothereflectedone.Onlyoneaccretioncolumnis errorbarscorrespondtophasebins.
drawnforclarity.
theneutronstarsurface.Neverthelesssomeobservationalfeatures
describedabovecouldbeunderstoodqualitatively.
feature in the directly observed column spectrum is rather prob- Ifreflectionofftheneutronstarsurfaceisindeedresponsible
lematic due to a strong gradient of the magnetic field along the fortheformationoftheCRSF,theobservedlineparameterssuch
column and scattering onfree-falling electrons (seediscussion in as its energy, width and depth will depend on the size of illumi-
Nishimura2008,2014).Ontheother hand, suchafeaturecanbe natedspot(s).This,inturn,dependsonmanyfactorsincludingthe
formed in the spectrum reflected from a neutron star atmosphere accretioncolumnsheight,beaming oftheemergingradiation,the
wherethemagneticfieldchangeissmaller(Poutanenetal.2013). neutronstarcompactness,etc.Moreover,theobservablepartofthe
Thesizeofthespotontheneutronstarsurfaceilluminatedbythe illuminated hot spots also depends on the relative position of the
accretioncolumndependsonthecolumnheight,which,inturn,de- observer,beingafunctionofthepulsephase.Thus,thecyclotron
pendsontheX-raypulsarluminosity.Thefractionofthecolumn lineparametersshouldbevariablewiththepulsephase.
emissionwhichisinterceptedbytheneutronstarremains,however, Fromgeometricconsiderations,thelineenergyisexpectedto
largeatallluminosities,soonedoesexpectthatalargefractionof bemaximalwhenoneofmagneticpolesisdirectedtotheobserver,
theobservedemissionisreflectedoffthesurfaceoftheneutronstar. sothatthepolar regions withthestrongest fieldareobserved. At
Itisnotunlikely,therefore,thattheobservedcyclotronfeaturesalso other angles large fraction of reflected radiation will be scattered
formintheatmosphereoftheneutronstar.Thisscenarioallowsto furtherfromthepoles,wherethefieldislower,andaslightdecrease
explain many important observational features of the CRSFsthat intheobservedCRSFenergyisexpected.
otherwise are difficult to explain. For instance, the luminosity of It is interesting to note that the observed line energy maxi-
V0332+53 in the considered outburst (and, therefore, the height mumtends tocoincide withone of thetotal fluxmaxima athigh
of the accretion columns) changes by factor of twenty, whereas luminosities (see Figs 4a-e) and it tends to be between two flux
thelineenergy variesbyjust∼ 30per cent, whichishard toex- maximaatlowluminosities(Figs4f-h).Aquantitativeanalysisthis
plain if thelineis formed withinthecolumn. Onthe other hand, behaviour isnot simple. Pulseprofilesaswellasthe dependence
the dipole magnetic field over the neutron star surface decreases of the line energy on the phase are very different and variable.
only by factor of two from the magnetic pole to the equator, so Thismakesthestandardcorrelationanalysisproblematic.Instead,
smallervariationsoftheCRSFenergyareeasiertoaccommodate. aphaseshiftbetweenthemaximaoftheconsideredcurvescanbe
Infact, Poutanenetal. (2013) showed that theexpected variation usedtoquantifythepotentialcorrelation.Toaccountfortheappar-
of the CRSFenergy inthiscase iscompatible withobservations. ent asymmetry of theprofiles, weused thecentreof thesegment
Moreover,thereflectionmodelwasalsocapableofexplainingthe connecting rising and declining parts of the pulsed maximum at
observedcorrelationofthelineenergywithluminosity.Belowwe halfofthemaximumfluxasareferencephase.Resultsofsuchan
willdiscussqualitativelyhowtheobservedvariationofCRSFpa- analysisarepresentedinFig.7andtheyareinagreementwithour
rameterswithpulsephaseandluminositycanbequalitativelyex- expectations–thephaseshiftisarelativelysmall(<∼0.1)athigh
plainedwithinthismodel. luminositiesandincreasesatlowluminosities.
In the framework of the reflection model, the cyclotron line
only contributes to the reflected spectrum, whereas total flux at
agiven pulsephase includes bothreflected anddirectly observed
4.1 Phasedependenceofthecyclotronlineenergyas
emission. Therefore, the observed change in the pulse phase be-
functionofluminosity
haviour of thecyclotron lineenergy can be explained if theratio
Thequantitativecomparisonofresultsofthephase-resolvedspec- betweenthesetwocomponentschangeswithluminosity.Theratio
troscopywiththepredictionsofanytheoreticalmodels,including ofthereflectedemissiontothatobserveddirectlyfromthecolumn
the reflection model, will be possible only after a self-consistent dependsontotalfractionofinterceptedemissionandonthebeam-
model emerges that describes the accretion column structure and ing characteristics of the two components. The reflected compo-
theradiationfieldaround thepulsar including thereflectionfrom nentisexpectedtohaveabroadpencil-likebeampatterndirected
PulsephasespectroscopyofV0332+53 9
alongthemagneticdipoleaxis.Thebeampatternoftheemission theobtained spectra withthe model described above (cutoffpl +
observeddirectlyismorecomplicatedanddependsonluminosity. cyclabs).Theobservations where cyclotron lineparameters were
Athighluminosities,bothcolumnsareexpectedtocontribute notreasonablyconstrainedduetoinsufficientstatistics(effectively
totheobservedfluxatallpulsephaseswiththecombinedbeampat- limitingthe number of phase bins to four or less) were excluded
ternsimilartothatofthereflectedcomponent(seeFig.6a).There- from further analysis. Obtained results are presented in Fig.8. In
fore,thepulseprofileisexpectedtohavetwomaximacorrespond- general, its left panel issimilar to the figure 5 from the paper of
ingtothetwoilluminatedspotsaroundthetwomagneticpoles.In Tsygankovetal. (2006), where the dependence of the cyclotron
suchasituation,themaximumofthecyclotronlineenergyprofile linewidthonitsenergywasshownforpulsephaseaveragedspec-
willcoincidewithoneofthepulseprofilemaxima,whichinturn tra.Noteafairlystrongscatterofthedatapointsforlargecyclotron
corresponds to thepole with thesmallest inclination angle tothe energies,whichisprobablycausedbylowerstatisticsatlowlumi-
lineofsight. nosities.
Atlowerluminosities,theheightofthecolumndecreases,and Note that we used the cyclabs model to describe the cy-
the illuminatedspot around the second pole becomes lessvisible clotron absorption line as opposed to many other authors (e.g.,
or even fullyobscured by theneutron star. Asaresult,a fan-like Coburnetal. 2002; Kreykenbohmetal. 2004; Klochkovetal.
beampatternfromthetwocolumnsisexpectedinthiscasetohave 2008), who used thegaussian absorption line profile(gabs in the
twomaximawhenbothcolumnsareobservedsideways(seeFig.6). xspecpackage):
Thereflectedcomponentretainsthepencil-likebeamingand,there-
1 E−E 2
fore,isexpectedtobeinanti-phasewiththedirectemission.Even exp −τ exp − N , (3)
tchroeausgehatthelotwotearllfuramcitnioonsiotifetsh,eornelflyeccotendtriebmuitsiosinonfriosmexopneectpeodletociann- where EN,σ,a2nd τσaNret!heenergy, widthandoptical depth of
N N N
be observed at a time. On the other hand, both columns are ex- the cyclotron line (N = 0) and harmonics (N > 0), respectively.
pectedtobevisiblewhenthecontributionofthedirectlyobserved Bothmodelsadequatelyapproximatecyclotronabsorptionlineand
componentismaximal,sotheoverallmaximumofthepulseprofile itsharmonics (see Table3, where best-fitting parameters for both
shallbedefinedbythecomponent observeddirectly.Still,thecy- cyclabsand gabs models are presented). Note, that the cyclotron
clotronlineisonlypresentinthereflectedcomponent,whichisin lineenergyderivedfromthecyclabsmodelissystematicallylower
anti-phasewiththedirectlyobservedemission.Therefore,themax- (by∼1–3keV)thantheenergyderivedfromthegabsmodel (see
imumofthecyclotronlineenergyprofileisexpectedtomoveaway e.g.Mihara1995;Nakajimaetal.2010;Tsygankovetal.2012).
fromthepulse-profilemaximumatlowerluminositiesinagreement Inthispaper,weattemptnotonlytofindspectralparameters
withobservations. ofV0332+53,butalsotosearchfortheirdependenceonthepulse
We can find a relative column height in the framework of phase and luminosity and possible physical correlations between
thereflectionmodel (Poutanenetal.2013).Weusedequation(2) them.Therefore,acorrelationanalysiswascarriedout toinvesti-
in that paper and substituted model parameters which give the gatepotentialintrinsiccorrelationsofCRSFparametersforcyclabs
best fit to the observed dependence Ecyc versus L (see Fig. 5 in andgabsmodels.Toillustrateobtainedresults,weplotinFig.9the
Poutanenetal.2013).Wefindthattherelativecolumnheighth/R confidencecontoursofthecyclotronlinewidthσ versuscyclotron
0
decreasesfrom0.89forthebrighteststateto0.07forthedimmest lineenergyE obtainedwithcyclabsandgabsmodelsforluminos-
0
one(therelativecolumnheightsforalltheluminositiesaregiven ityL ≃15.3(obs.15)(resultsforotherluminositiesaresimilar).
37
inthecaptiontoFig.4).Inframeworkofthismodel, thefirstde- Severalconclusions canbemadefromthisanalysis:theline
scribedscenariowiththepencil-likereflectioncomponentdomina- energydepends ontheCRSFmodels(seeabove); anaccuracy of
tionisrealisedduringthehigh-luminositystatesandrelativelytall thelineenergymeasurementsisbetterforthecyclabsmodel,while
columnswithh/R>0.5.Thesecondscenario,withthedirectfan- theaccuracyofthelinewidthmeasurementsisbetterforthegabs
likecomponent,islikelyrealisedforshortcolumnswithh/R≤0.2. model;thereisanintrinsiccorrelationbetweenσ and E forthe
0 0
Finally,wenotethatthelightbendingisanimportantfactor gabsmodel,whilenocorrelationandfairlysignificantscatterofthe
influencingthevisibilityofilluminatedspots(seee.g.Beloborodov datapointsorevenanti-correlationareseenforthecyclabsmodel.
2002;Annala&Poutanen1999)whichwedidnotaccount inout A linear regression fit to the data shown in both panels of
qualitativediscussion.However,estimationsofh/Raredoneonthe Fig.8givesahintthatthereisindeedsomeweakanti-correlation:
baseofthemodelbyPoutanenetal.(2013)whoaccountedforlight σ = (12.7±1.6)−(0.24±0.06)E andσ /E =(0.30±0.03)−
0 0 0 0
bending. (0.030±0.015)τ . Thus, we confirm here the previous result by
0
Tsygankovetal. (2010) that there is no positive correlation be-
tweenthecyclotronlineparametersforV0332+53ifthecyclabs
4.2 Correlationsbetweentheparametersofthecyclotronline
model is used for the cyclotron line. Finally, we note that if the
Based on the spectral analysis of several X-ray pulsars, faintest observation is excluded from Fig.8 (black squares), the
Coburnetal. (2002) found that there are two types of correla- significance of the anti-correlation is increased and in this case
tionsbetweencyclotronlineparameters:betweenitswidthσ and σ = (17.0±1.2)−(0.41±0.05)E andσ /E =(0.42±0.03)−
0 0 0 0 0
energy E , and between the relative cyclotron line width σ /E (0.095±0.016)τ .
0 0 0 0
andthelinedepthτ .Later,similarcorrelationswerereportedby Formation of the CRSF in the framework of the reflection
0
Kreykenbohmetal.(2004)forpulsephase-resolvedspectraofthe model is still pretty much work in progress, so here we restrict
X-raypulsarGX301–2.Atthesametimenoobviouscorrelations ourselvestoqualitativediscussionoftheresults.Thecyclotronline
werefoundbyTsygankovetal.(2010)fromtheanalysisofpulse- widthσ ismainlydeterminedbytwofactors.Firstofall,thelineis
0
averagespectraofV0332+53inawideenergyband. thermallybroadenedbyafactorwhichdependsontheplasmatem-
To obtain the relations σ − E and (σ /E )− τ we have peratureinthelineformingregionandtheanglebetweenphoton
0 0 0 0 0
reanalyseduniformlyalldatasetsfromTable1,dividingthecor- momentum direction and themagnetic field. Themaximum ther-
respondingpulseprofilesintoeightphasebinsandapproximating mal linewidth is realised for the radiation propagating along the
10 Lutovinovet al.
0.4
10
0.3
8
6
0.2
4
0.1
23 24 25 26 27 28 29 30 1.5 2 2.5 3
Figure8.(a)Cyclotronlinewidthσ0versuscentroidenergyE0.(b)Relativecyclotronlinewidthσ0/E0versusitsdepthτ0.Differentcoloursandsymbols
correspondtoobservationswithdifferentluminosities(seeTable1):obs.1–redsquares,4–blacktriangles,5–greencircles,8–bluesquares,13–magenta
circles,15–greentriangles,17–cyancircles,18–blackcircles,19–cyantriangles,20–redcircles,21–blacksquares.
0 0
E,keV E,keV
0 0
Figure 9. Cyclotron line width σ0 vs. cyclotron line energy E0,obtained using spectral fits with cyclabs (left panel) and gabs (right panel) models for
phase-resolvedspectraofV0332+53inobservation15(Table1).Contours(solid,dashed,dottedlines)correspondtothe1,2,3σlevels,respectively.
Table3.Parametersofthebestfitswithcyclabsandgabsmodelstothesamepulsephase-resolvedspectraofV0332+53(Obs.15,L37=15.3).
Model Γ Ecut E0 σ0 τ0 E1 σ1 τ1 χ2(d.o.f.)
keV keV keV keV keV
1stbin(phase0.0–0.125)
gabs 0.38±0.02 7.49+0.20 29.02+0.21 5.31+0.18 1.67+0.07 52.2+0.7 6.7+0.5 2.45±0.11 105.9(107)
−0.11 −0.14 −0.08 −0.03 −0.2 −0.2
cyclabs 0.32±0.03 8.36+0.33 26.65±0.10 6.50+0.36 1.73±0.04 51.6±0.6 4.6+0.8 4.0+2.3 109.2(107)
−0.16 −0.12 −0.7 −0.7
7thbin(phase0.75–0.875)
gabs 0.36±0.04 8.56±0.15 27.90±0.15 5.04±0.09 1.93±0.07 54.8±1.0 10.5±0.2 2.8±0.3 108.3(107)
cyclabs 0.30±0.04 10.14±0.25 25.85±0.08 6.35+0.21 2.09±0.04 52.2±0.7 10.5±1.1 3.2±0.3 107.2(107)
−0.06