J/A+A/700/A70ivo://CDS.VizieR/J/A+A/700/A70doi:10.26093/cds/vizier.37000070CDSManiadakis D.K.Sokolova-Lapa E.D'Ai A.Ambrosi E.Ferrigno C.,Cusumano G.Anitra A.Burderi L.Del Santo M.Di Salvo T.Fuerst F.,Iaria R.La Parola V.Malacaria C.Kretschmar P.Pintore F.Pinto C.,Rodriguez Castillo G.A.2025-08-27T20:01:23Z2025-08-05T09:23:42ZCDS support team

CDS, Observatoire de Strasbourg, 11 rue de l'Universite, F-67000 Strasbourg, France

cds-question@unistra.frx-ray-binary-starsspectroscopyWe aim to study the energy-dependent pulse profile of the X-ray accreting pulsar 4U 1538-52 and its phase-dependent spectral variability, with particular emphasis on the behavior around the cyclotron resonant scattering feature at Ecyc~21keV. We analyze all available NuSTAR observations of 4U 1538-52. We decompose energy-resolved pulse profiles into Fourier harmonics to study their energy dependence. Specifically, we compute pulsed fraction spectra, cross-correlation, and lag spectra, identifying discontinuities and linking them to features in the phase-averaged spectra. We perform both phase-averaged and phase- resolved spectral analyses to probe spectral variability and its relation to pulse profile changes. Finally, we interpret our findings via physical modeling of energy- and angle-dependent pulse profile emission, performing radiative transfer in a homogeneous slab-like atmosphere under conditions relevant to 4U 1538-52. The emission is projected onto the observer's sky plane to derive expected observables. In contrast to the dips in pulsed fraction spectra observed in other sources (e.g., Her X-1), we find a broad bump near the cyclotron resonance energy in 4U 1538-52. This increase is driven primarily by phase-dependent spectral variability, especially by strong variations in cyclotron line depth across different phase intervals. We interpret the observed contrast between dips and bumps in various sources as arising from phase-dependent variations of cyclotron line depth relative to the phase-modulated flux. We model the X-ray emission from an accreting neutron star and find that our simulations indicate high values of both the observer's inclination and the magnetic obliquity, along with a ~10-15{deg} asymmetry between the locations of the magnetic poles. Assuming this geometry, we satisfactorily reproduce the observed pulse profiles and introduce general trends in the observables resulting from the system's geometry.2025A&A...700A..70Mhttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/700/A70CatalogResearchIsServedByTAP VizieR generic servicehttps://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/A+A/700/A70https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/A+A/700/A70http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/A+A/700/A70https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/A+A/700/A70https://vizier.iucaa.in/viz-bin/votable?-source=J/A+A/700/A70http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/A+A/700/A70GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapX-raydefaultJ/A+A/700/A70/table1Observation logrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintObsIDObservation IDmeta.id;obscharExpExposure timekstime.duration;obs.exposurefloatCtsTotal number of counts in units of 1E+04 counts10000countphot.count;em.X-rayfloatFluxAbsorbed 4-50 keV flux in 10^-10^erg/cm^2^/s1e-13W.m**-2phot.flux;em.X-rayfloatLumBolometric luminosity (assumed D = 6.6 kpc)1e+36solLumphys.luminosityfloatFreqPulse frequencymHzem.freq;src.varfloatTrefReference time since 2010-01-01 UTCstime;arith.diffdoubleJ/A+A/700/A70/table2Best-fit PFS modeling parametersrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintObsIDObservation IDmeta.id;obscharEbumpEnergy of broad bumpkeVem.energyfloate_Ebump1-sigma uncertainty on EbumpkeVstat.errorfloatSbumpSigma bumpkeVstat.stdevfloate_SbumpUncertainty on SbumpkeVstat.errorfloatAbumpAmplitude of the bumpsrc.var.amplitude;spect.linefloate_Abump1-sigma uncertainty on Abumpstat.errorfloatEFe? Iron line centroid (if present)keVphys.energy;spect.linefloatnullablee_EFe? 1-sigma uncertainty on EFekeVstat.errorfloatnullableSFe? sigma of Fe linekeVstat.errorfloatnullablee_SFe? Uncertainty on sigma of Fe linekeVstat.errorfloatnullableAFe? Amplitude of Fe linesrc.var.amplitude;spect.linefloatnullableE_AFe? Upper uncertainty on AFestat.error;stat.maxfloatnullablee_AFe? Lower uncertainty on AFestat.errorfloatnullableEsplitEnergy at which polynomial split occurskeVem.energyfloatnpolLowPolynomial order below Esplitinstr.orderintnpolHighPolynomial order above Esplitinstr.orderintchi2LowReduced chi^2^ for low-energy bandstat.fit.chi2floatdofLowDegrees of freedom (low band)stat.fit.dofintchi2HighReduced chi^2^ for high-energy bandstat.fit.chi2floatdofHighDegrees of freedom (high band)stat.fit.dofintJ/A+A/700/A70/table3Phase-averaged spectral fit (NuSTAR/XMM)e_EcycLower uncertainty on EcyckeVstat.errorfloatrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintObsIDObservation IDmeta.id;obscharEcutCutoff energykeVem.energyfloate_EcutLower uncertainty on EcutkeVstat.errorfloatE_EcutUpper uncertainty on EcutkeVstat.error;stat.maxfloatEfoldFolding energykeVem.energyfloate_EfoldLower uncertainty on EfoldkeVstat.errorfloatE_EfoldUpper uncertainty on EfoldkeVstat.error;stat.maxfloatGammaPower-law photon indexmeta.code;spect.indexfloate_GammaLower uncertainty on Gammastat.errorfloatE_GammaUpper uncertainty on Gammastat.error;stat.maxfloatNnewhcutNormalization of the cutoff modelstat.fit.paramfloate_NnewhcutLower uncertainty on Nnewhcutstat.errorfloatE_NnewhcutUpper uncertainty on Nnewhcutstat.error;stat.maxfloatNbbodyBlackbody normalization (in units of 1E-04)stat.fit.paramfloate_NbbodyLower uncertainty on Nbbodystat.errorfloatE_NbbodyUpper uncertainty on Nbbodystat.error;stat.maxfloatEcycCyclotron line energykeVphys.energy;spect.linefloatE_EcycUpper uncertainty on EcyckeVstat.error;stat.maxfloatScycWidth of cyclotron linekeVspect.line.widthfloate_ScycLower uncertainty on ScyckeVstat.errorfloatE_ScycUpper uncertainty on ScyckeVstat.error;stat.maxfloatDcycDepth of cyclotron absorptionphot.flux.density;arith.ratiofloate_DcycLower uncertainty on Dcycstat.errorfloatE_DcycUpper uncertainty on Dcycstat.error;stat.maxfloatSFeFe line widthkeVspect.line.widthfloate_SFeLower uncertainty on SFekeVstat.errorfloatE_SFeUpper uncertainty on SFekeVstat.error;stat.maxfloatAFeFe line amplitude (in units of 1E-04)src.var.amplitude;spect.linefloate_AFeLower uncertainty on AFestat.errorfloatE_AFeUpper uncertainty on AFestat.error;stat.maxfloatCfpmbCross-normalization FPMBstat.fit.paramfloate_CfpmbLower uncertainty on Cfpmbstat.errorfloatE_CfpmbUpper uncertainty on Cfpmbstat.error;stat.maxfloatFluxAbsorbed 4-50 keV fluxphot.flux;em.X-rayfloatWstatW-statisticstat.fit.paramfloatdofDegrees of freedomstat.fit.dofintJ/A+A/700/A70/tablec1Phase-resolved spectroscopy of ObsID 304e_AFeLower uncertainty on AFestat.errorfloatrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintPhaseSpin phase bintime.phasecharEcutCutoff energykeVem.energyfloate_EcutLower uncertainty on EcutkeVstat.errorfloatE_EcutUpper uncertainty on EcutkeVstat.error;stat.maxfloatEfoldFolding energykeVem.energyfloate_EfoldLower uncertainty on EfoldkeVstat.errorfloatE_EfoldUpper uncertainty on EfoldkeVstat.error;stat.maxfloatGammaPhoton indexmeta.code;spect.indexfloate_GammaLower uncertainty on Gammastat.errorfloatE_GammaUpper uncertainty on Gammastat.error;stat.maxfloatNnewhcutNormalization of the cutoff modelstat.fit.paramfloate_NnewhcutLower uncertainty on Nnewhcutstat.errorfloatE_NnewhcutUpper uncertainty on Nnewhcutstat.error;stat.maxfloatNbbodyBlackbody normalization (in units of 1E-04)stat.fit.paramfloate_NbbodyLower uncertainty on Nbbodystat.errorfloatE_NbbodyUpper uncertainty on Nbbodystat.error;stat.maxfloatEcycCyclotron line energykeVphys.energy;spect.linefloate_EcycLower uncertainty on EcyckeVstat.errorfloatE_EcycUpper uncertainty on EcyckeVstat.error;stat.maxfloatScyc? Width of cyclotron line (if fit)keVspect.line.widthfloatnullablee_Scyc? Lower uncertainty on ScyckeVstat.errorfloatnullableE_Scyc? Upper uncertainty on ScyckeVstat.error;stat.maxfloatnullableDcycCyclotron line depthphot.flux.density;arith.ratiofloate_DcycLower uncertainty on Dcycstat.errorfloatE_DcycUpper uncertainty on Dcycstat.error;stat.maxfloatSFeFe line width (if fit)keVspect.line.widthfloate_SFeLower uncertainty on SFekeVstat.errorfloatE_SFeUpper uncertainty on SFekeVstat.error;stat.maxfloatAFeFe line amplitude (in units of 1E-04)src.var.amplitude;spect.linefloatE_AFeUpper uncertainty on AFestat.error;stat.maxfloatCfpmbFPMB cross-normalizationstat.fit.paramfloate_CfpmbLower uncertainty on Cfpmbstat.errorfloatE_CfpmbUpper uncertainty on Cfpmbstat.error;stat.maxfloatWstatW-statistic from fitstat.fit.paramfloatdofDegrees of freedomstat.fit.dofintJ/A+A/700/A70/tablec2Phase-resolved spectroscopy of ObsID 306-2E_GammaUpper uncertainty on Gammastat.error;stat.maxfloatNnewhcutNormalization of the cutoff modelstat.fit.paramfloatEcycCyclotron line energykeVphys.energy;spect.linefloatrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintEcutCutoff energykeVem.energyfloate_EcutLower uncertainty on EcutkeVstat.errorfloatE_EcutUpper uncertainty on EcutkeVstat.error;stat.maxfloatEfoldFolding energykeVem.energyfloate_EfoldLower uncertainty on EfoldkeVstat.errorfloatE_EfoldUpper uncertainty on EfoldkeVstat.error;stat.maxfloatGammaPhoton indexmeta.code;spect.indexfloate_GammaLower uncertainty on Gammastat.errorfloate_NnewhcutLower uncertainty on Nnewhcutstat.errorfloatE_NnewhcutUpper uncertainty on Nnewhcutstat.error;stat.maxfloatNbbody? Blackbody normalization (in units of 1E-04)stat.fit.paramfloatnullablee_Nbbody? Lower uncertainty on Nbbodystat.errorfloatnullableE_Nbbody? Upper uncertainty on Nbbodystat.error;stat.maxfloatnullablee_EcycLower uncertainty on EcyckeVstat.errorfloatE_EcycUpper uncertainty on EcyckeVstat.error;stat.maxfloatScyc? Width of cyclotron line (if fit)keVspect.line.widthfloatnullablee_Scyc? Lower uncertainty on ScyckeVstat.errorfloatnullableE_Scyc? Upper uncertainty on ScyckeVstat.error;stat.maxfloatnullableTauOptical depth (CompTT)phys.absorption.opticalDepthfloate_TauLower uncertainty on Taustat.errorfloatE_TauUpper uncertainty on Taustat.error;stat.maxfloatSFeFe line widthkeVspect.line.widthfloate_SFeLower uncertainty on SFekeVstat.errorfloatE_SFeUpper uncertainty on SFekeVstat.error;stat.maxfloatAFeFe line amplitude (in units of 1E-04)src.var.amplitude;spect.linefloate_AFe? Lower uncertainty on AFestat.errorfloatnullableE_AFe? Upper uncertainty on AFestat.error;stat.maxfloatnullableCfpmbFPMB cross-normalizationstat.fit.paramfloate_CfpmbLower uncertainty on Cfpmbstat.errorfloatE_CfpmbUpper uncertainty on Cfpmbstat.error;stat.maxfloatWstatW-statistic from fitstat.fit.paramfloatdofDegrees of freedomstat.fit.dofintPhaseSpin phase bintime.phasecharJ/A+A/700/A70/listList of filesrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintFileNameName of the filemeta.id;meta.filecharTitleTitle of the filemeta.title;meta.filechar