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