A re-analysis of the NuSTAR and XMM-Newton broad-band spectrum of Ser~X-1
M. Matranga, T. Di Salvo, R. Iaria, A. F. Gambino, L. Burderi, A. Riggio, A. Sanna
aa r X i v : . [ a s t r o - ph . H E ] J a n Astronomy & Astrophysicsmanuscript no. serx1_ref_mod_2 c (cid:13)
ESO 2018November 12, 2018
A re-analysis of the NuSTAR and XMM-Newton broad-bandspectrum of Ser X-1
M. Matranga , T. Di Salvo , R. Iaria , A. F. Gambino , L. Burderi , A. Riggio , and A. Sanna Universitá degli Studi di Palermo, Dipartimento di Fisica e Chimica, via Archirafi 36, 90123 Palermo, Italye-mail: [email protected] Universitá degli Studi di Cagliari, Dipartimento di Fisica, SP Monserrato-Sestu KM 0.7, 09042 Monserrato, ItalyNovember 12, 2018
ABSTRACT
Context.
High resolution X-ray spectra of neutron star Low Mass X-ray Binaries (LMXBs) in the energy range 6.4-6.97 keV, are oftencharacterized by the presence of K α transition features of iron at di ff erent ionization stages. Since these lines are thought to originateby reflection of the primary Comptonization spectrum over the accretion disk, the study of these features allows us to investigate thestructure of the accretion flow close to the central source. Thus, the study of these features gives us important physical information onthe system parameters and geometry. Ser X-1 is a well studied LMXB which clearly shows a broad iron line. Several attempts to fitthis feature as a smeared reflection feature have been performed on XMM-Newton , Suzaku , NuSTAR , and, more recently, on
Chandra data, finding di ff erent results for the inner radius of the disk and other reflection or smearing parameters. For instance, Miller et al.(2013) have presented broad-band, high quality NuSTAR data of Ser X-1. Using relativistically smeared self-consistent reflectionmodels, they find a value of R in close to 1.0 R ISCO (corresponding to 6 R g , where R g is the Gravitational radius, defined as usualR g = GM / c ), and a low inclination angle of less than ∼ ◦ . Aims.
The aim of this paper is to probe to what extent the choice of reflection and continuum models (and uncertainties therein) cana ff ect the conclusions about the disk parameters inferred from the reflection component. To this aim we re-analyze all the availablepublic NuSTAR and XMM-Newton which have the best sensitivity at the iron line energy observations of Ser X-1. Ser X-1 is a wellstudied source, its spectrum has been observed by several instruments, and is therefore one of the best sources for this study. Methods.
We use slightly di ff erent continuum and reflection models with respect to those adopted in literature for this source. Inparticular we fit the iron line and other reflection features with self-consistent reflection models as reflionx (with a power-law illumi-nating continuum modified with a high energy cuto ff to mimic the shape of the incident Comptonization spectrum) and rfxconv. Withthese models we fit NuSTAR and
XMM-Newton spectra yielding consistent spectral results.
Results.
Our results are in line with those already found by Miller et al. (2013) but less extreme. In particular, we find the inner diskradius at ∼ R g and an inclination angle with respect to the line of sight of ∼ ◦ . We conclude that, while the choice of the reflectionmodel has little impact on the disk parameters, as soon as a self-consistent model is used, the choice of the continuum model canbe important in the precise determination of the disk parameters from the reflection component. Hence broad-band X-ray spectra arehighly preferable to constrain the continuum and disk parameters. Key words. line: formation, line: identification, stars: individual: Serpens X-1, stars: neutron, X-rays: binaries, X-rays: general
1. Introduction
X-ray spectra emitted by Low Mass X-Ray Binaries (LMXBs)of the atoll class (Hasinger & van der Klis 1989) are usuallycharacterized by two states of emission: the soft and the hardstate. During soft states the spectrum can be well described by asoft thermal component, usually a blackbody or a disk multi-color blackbody, possibly originated from the accretion disk,and a harder component, usually a saturated Comptonizationspectrum. In some cases, a hard power-law tail has been de-tected in the spectra of these sources during soft states bothin Z sources (Di Salvo et al. 2000), and in atoll sources (e.g.,Piraino et al. 2007), usually interpreted as Comptonization o ff a non-thermal population of electrons. On the other hand, dur-ing hard states the hard component of the spectrum can be de-scribed by a power law with high energy cuto ff , interpreted asunsaturated Comptonization, and a weaker soft blackbody com-ponent (e.g., Di Salvo et al. 2015). The hard component is gen-erally explained in terms of inverse Compton scattering of soft photons, coming from the neutron star surface and / or the inneraccretion disk, by hot electrons present in a corona possibly lo-cated in the inner part of the system, surrounding the compactobject (D’Aì et al. 2010).In addition to the continuum, broad emission lines in therange 6.4-6.97 keV are often observed in the spectra of LMXBs(see e.g. Cackett et al. 2008; Pandel et al. 2008; D’Aì et al. 2009,2010; Iaria et al. 2009; Di Salvo et al. 2005, 2009; Egron et al.2013; Di Salvo et al. 2015). These lines are identified as K α tran-sitions of iron at di ff erent ionization states and are thought tooriginate from reflection of the primary Comptonization spec-trum over the accretion disk. These features are powerful toolsto investigate the structure of the accretion flow close to the cen-tral source. In particular, important information can be inferredfrom the line width and profile, since the detailed profile shape isdetermined by the ionization state, geometry and velocity field ofthe emitting plasma (see e.g. Fabian et al. 1989). Indeed, whenthe primary Comptonization spectrum illuminates a colder ac-cretion disk, other low-energy discrete features (such as emis- Article number, page 1 of 13 & Aproofs: manuscript no. serx1_ref_mod_2 sion lines and absorption edges) are expected to be created byphotoionization and successive recombination of abundant ele-ments in di ff erent ionizations states as well as a continuum emis-sion caused by direct Compton scattering of the primary spec-trum o ff the accretion disk. All these features together form theso-called reflection spectrum, and the whole reflection spectrumis smeared by the velocity-field of the matter in the accretiondisk.Ser X-1 is a persistent accreting LMXB classified as an atollsource, that shows type I X-ray bursts. The source was discov-ered in 1965 by Friedman et al. (1967). Li et al. (1976) firstlydiscovered type-I X-ray bursts from this source that was there-fore identified as an accreting neutron star. Besides type-I burstswith typical duration of few seconds (Balucinska & Czerny1985), a super-burst of the duration of about 2 hours has alsobeen reported (Cornelisse et al. 2002). Recently Cornelisse et al.(2013), analyzing spectra collected by GTC, detected a two-hours periodicity. They tentatively identified this periodicity asthe orbital period of the binary and hence proposed that the sec-ondary star might be a main sequence K-dwarf.Church & Baluci´nska-Church (2001) have performed a sur-vey of LMXBs carried out with the ASCA satellite. The best-fitmodel used by these authors to fit the spectrum of Ser X-1 wasa blackbody plus a cuto ff power-law with a Gaussian iron line.Oosterbroek et al. (2001) have analyzed two simultaneous obser-vations of this source collected with BeppoSAX and RXTE. Theauthors fitted the broad-band (0.1-200 keV) BeppoSAX spec-trum with a model consisting of a disk blackbody, a reflectioncomponent described by the XSPEC model p exrav, and a Gaus-sian line. However, in that case the improvement in χ with re-spect to a model consisting of a blackbody, a Comptonizationspectrum modeled by compST, and a Gaussian was not signif-icant, and therefore it was not possible to draw any definitiveconclusion about the presence of a reflection continuum.Bhattacharyya & Strohmayer (2007) carried out the analysisof three XMM-Newton observations of this system. They man-aged to fit the EPIC / pn spectrum with a model consisting of diskblackbody, a Comptonization continuum modeled with c ompTTand a d iskline, i.e. a Gaussian line distorted and smeared by theKeplerian velocity field in the accretion disk (Fabian et al. 1989).They found strong evidence that the Fe line has an asymmetricprofile and therefore that the line originates from reflection in theinner rim of the accretion disk. Fitted with a Laor profile (Laor1991), the line shape gave an inner disk radius of 4 − R g or16 R g (depending from the observation) and an inclination an-gle to the binary system of 40 − ◦ . Cackett et al. (2008), fromdata collected by SUZAKU , performed a study of the iron lineprofiles in a sample of three LMXBs including Ser X-1. Fromthe analysis of XIS and PIN spectra, they found a good fit of thebroad-band continuum using a blackbody, a disk blackbody anda power-law. Two years later Cackett et al. (2010) re-analyzed
XMM-Newton and
SUZAKU data of a sample of 10 LMXBs thatincludes Ser X-1, focusing on the iron line - reflection emis-sion. In particular, for Ser X-1, they analyzed 4 spectra: threeEpic-PN spectra obtained with
XMM-Newton and one obtainedwith the XIS and the PIN instruments on board of
SUZAKU .Initially, they fitted the spectra of the continuum emission us-ing a phenomenological model, consisting of a blackbody, adisk-blackbody and a power-law. Then, they started the study ofthe Fe line adding first a diskline component and after a reflec-tion component convolved with rdblur (that takes into accountsmearing e ff ects due to the motion of the emitting plasma in aKeplerian disk). They obtained di ff erent results for the smearingparameters both for di ff erent observations and for di ff erent mod- els used on the same observation. For sake of clarity these resultsare summarized in Table 1.Miller et al. (2013) analyzed two NuSTAR observations car-ried out on July 2013. They fitted the continuum emission us-ing a model consisting of a blackbody, a disk blackbody and apower-law. With respect to this continuum model, evident resid-uals were present around 6.40-6.97 keV, suggesting the pres-ence of a Fe line. Therefore they added a kerrdisk componentto the continuum to fit the emission line, taking into account apossible non-null spin parameter for the neutron star. They alsotried to fit the reflection spectrum (i.e. the iron line and otherexpected reflection features) with the self-consistent reflectionmodel reflionx , a modified version of reflionx calculated for ablackbody illuminating spectrum, convolved with the kerrconv component. The addition of the reflection component gave a sig-nificant improvement of the fit. In most cases the best fit gave lowinclination angles (less than ∼ ◦ ), in agreement with recent op-tical observations (Cornelisse et al. 2013), inner disk radii com-patible with the Innermost Stable Circular Orbit (ISCO), corre-sponding to about 6 Rg for small values of the spin parameter, aionization parameter log ξ ∼ . − .
6, and a slight preference foran enhanced iron abundance. The fit resulted quite insensitive tothe value of the adimensional spin parameter, a, of the neutronstar.More recently, Chiang et al. (2016) analysed a recent 300ks Chandra / HETGS observation of the source performed in the"continuous clocking" mode and thus free of photon pile-up ef-fects. They fitted the continuum with a combination of multi-color disk blackbody, blackbody and power-law. The iron linewas found significantly broader than the instrumental energyresolution and fitting this feature with a diskline instead of abroad Gaussian gave a significant improvement of the fit. Theyalso tried self-consistent reflection models, namely the reflionxmodel with a power-law continuum as illuminating source andxillver (see e.g. García et al. 2013), to describe the iron line andother reflection features, yielding consistent results. In particular,this analysis gave a inner radius of ∼ − g and an inclinationangle of about 30 deg.As described above, di ff erent continuum models were usedto fit the spectrum of Ser X-1 observed with various instrumentsat di ff erent times. In Table 1 we summarize the results of thespectral analysis of this source obtained from previous studies,and in particular the results obtained for the iron line and the re-flection model. Quite di ff erent values have been reported for theinclination angle (from less than 10 deg to about 40 deg), for theinner disk radius (from 4 to more than 100 R g ) and for the ironline centroid energy and / or the ionization parameter log ξ indi-cating that the disk is formed by neutral or very highly ionizedplasma.In this paper we re-analyzed all the available public NuSTAR observations of Ser X-1, fitting the iron line and other reflectionfeatures with both phenomenological and self-consistent reflec-tion models. These data were already analysed by Miller et al.(2013) using a di ff erent choice of the continuum and reflec-tion models. We compare these results with those obtainedfrom three XMM-Newton observations (already analyzed byBhattacharyya & Strohmayer 2007) fitted with the same mod-els. We choose to re-analyse
NuSTAR and
XMM-Newton spec-tra because these instruments provide the largest e ff ective areaavailable to date, coupled with a moderately good energy res-olution, at the iron line energy, and a good broad-band cover-age. Moreover, the source showed similar fluxes during the NuS-TAR and
XMM-Newton observations. Note also that
NuSTAR isnot a ff ected by pile-up problems in the whole energy range. The Article number, page 2 of 13. Matranga et al.: A re-analysis of the NuSTAR and XMM-Newton broad-band spectrum of Ser X-1 spectral results obtained for
NuSTAR and
XMM-Newton are verysimilar to each other and the smearing parameters of the reflec-tion component are less extreme than those found by Miller et al.(2013), and in good agreement with the results obtained from theChandra observation (Chiang et al. 2016). In particular we findan inner disk radius in the range 10 − R g and an inclinationangle with respect to the line of sight of 25 − ◦ .
2. Observations and Data Reduction
In this paper we analyze data collected by the
NuSTAR satel-lite. Ser X-1 has been observed twice with
NuSTAR , obsID:30001013002 (12-JUL-2013) and obsID: 30001013004 (13-JUL-2013). The exposure time of each observation is about40 ksec. The data were extracted using NuSTARDAS (NuSTARData Analysis Software) v1.3.0. Source data have been extractedfrom a circular region with 120" radius whereas the backgroundhas been extracted from a circular region with 90" radius in aregion far from the source. First, we run the "nupipeline" withdefault values of the parameters as we aim to get "STAGE 2"events clean. Then spectra for both detectors, FPMA and FPMB,were extracted using the "nuproducts" command. Correspond-ing response files were also created as output of nuproducts. Acomparison of the FPMA and FPMB spectra, indicated a goodagreement between them. To check this agreement, we have fit-ted the two separate spectra with all parameters tied to each otherbut with a constant multiplication factor left free to vary. Sincethe value of this parameter is 1 . ± . NuSTAR observations and the two
NuSTAR modules. We fitted this spec-trum in the 3-40 keV energy range, where the emission from thesource dominates over the background.We have also used non-simultaneous data collected withXMM-Newton satellite on March 2004. The considered obsIDare 0084020401, 0084020501 and 0084020601. All observa-tions are in Timing Mode and each of them has a duration of ∼
22 ksec. We extracted source spectra, background spectra andresponse matrices using the SAS (Science Analysis Software)v.14 setting the parameters of the tools accordingly. We pro-duced a calibrated photon event file using reprocessing tools "ep-proc" and "rgsproc" for PN and RGS data respectively. We alsoextracted the MOS data; these were operated in uncompressedtiming mode. However, the count rate registered by the MOSwas in the range 290 −
340 c / s, which is above the threshold foravoiding deteriorated response due to photon pile-up. The MOSspectra indeed show clear signs of pile-up and we preferred notto include them in our analysis, since these detectors cover thesame energy range of the PN.Before extracting the spectra, we filtered out contaminationsdue to background solar flares detected in the 10-12 keV EpicPN light-curve. In particular we have cut out about 600 sec forobsID 0084020401, about 800 sec for obsID 0084020501 and fi-nally about 1600 sec for obsID 0084020601. In order to removethe flares, we applied time filters by creating a GTI file with thetask "tabgtigen". In order to check for the presence of pile-upwe have run the task "epatplot" and we have found significantcontamination in each observation. The count-rate registered inthe PN observations was in the range 860-1000 c / s that is justabove the limit for avoiding contamination by pile-up. There- fore, we extracted the source spectra from a rectangular region(RAW X ≥
26) and (RAW X ≤
46) including all the pixels in they direction but excluding the brightest columns at RAW X = =
36. This reduced significantly the pile up (pile upfraction below a few percent in the considered energy range).We selected only events with PATTERN ≤ = ≥
1) and (RAWX ≤ + RGS2, the relativeadded background spectrum along with the relative response ma-trices. We have fitted RGS spectrum in the 0.35-1.8 keV energyrange, whereas the Epic-PN in the 2.4-10 keV energy range.Spectral analysis has been performed using XSPEC v.12.8.1(Arnaud 1996). For each fit we have used the phabs model inXSPEC to describe the neutral photoelectric absorption due tothe interstellar medium with photoelectric cross sections fromVerner et al. (1996) and element abundances from Wilms et al.(2000). For the
NuSTAR spectrum, which lacks of low- energycoverage up to 3 keV, we fixed the value of the equivalent hy-drogen column, N H , to the same value adopted by Miller et al.(2013), namely N H = × cm − (Dickey & Lockman 1990),while for the XMM-Newton spectrum we left this parameter freeto vary in the fit, finding a slightly higher value (see Tab. 2 and3). As a further check, we have fitted the NuSTAR spectrum fix-ing N H to the same value found for the XMM spectrum, but thefit parameters did not change significantly.
3. Spectral Analysis
The
NuSTAR observations caught the source in a high-luminosity ( ∼ erg / s, Miller et al. (2013)) state, thereforemost probably in a soft state. As seen in other similar atollsources, the spectrum of Ser X-1 is characterized by a soft com-ponent (i.e. blackbody), interpreted as thermal emission fromthe accretion disk, a hard component (i.e. a Comptonizationspectrum), interpreted as saturated Comptonization from a hotcorona, and often by the presence of a broad iron emission lineat 6 . − .
97 keV depending on the iron ionization state. Weused the Comptonization model nthComp ( ˙Zycki et al. 1999) inXSPEC, with a blackbody input seed photon spectrum, to fit thehard component. We used a simple blackbody to describe thesoft component. Substituting the blackbody with a multicolordisk blackbody, diskbb in XSPEC, gives a similar quality fitand the best-fit parameters do not change significantly.To fit the iron line we first tried simple models such as aGaussian profile or a diskline (Fabian et al. 1989). The best-fitparameters, obtained using alternatively a Gaussian or disklineprofile, are in good agreement with each other (see Tab. 2). Usinga diskline instead of a Gaussian profile we get an improvementof the fit corresponding to ∆ χ =
54 for the addition of twoparameters. Spectra, along with the best-fit model and residualsare shown in Fig.1. In both cases, the fit results are poor (therelative null hypothesis probability is 2 . × − ; the reduced χ are still relatively large, and evident residuals are present,especially above 10 keV, see Fig.1).In order to fit the residuals at high energy, we added a powerlaw component (a hard tail) to all the models describedabove. A hard power-law tail is often required to fit high-energyresiduals of atoll sources in the soft state (see e.g. Pintore et al. Article number, page 3 of 13 & Aproofs: manuscript no. serx1_ref_mod_2 gauss-pl and diskline-pl , respectively. The new best fit parame-ters are reported in Tab 2. While the best-fit parameters do notchange significantly with the addition of this component, we getan improvement of the fit corresponding to a reduction of the χ by ∆ χ =
123 (for the model with a Gaussian line profile) and ∆ χ =
113 (for the model with a diskline profile) for the additionof one parameter, respectively. The probabilities of chance im-provement of the fit are 8 . × − and 8 . × − , respectively.Some residuals are still present between 10 and 20 keV probablycaused by the presence of an unmodeled Compton hump. Notethat the soft blackbody component remains significant even af-ter the addition of the power-law component. If we eliminatethis component from the fitting model we get a worse fit, cor-responding to a decrease by ∆ χ =
245 for the addition of twoparameters when the soft component is included in the fit and aprobability of chance improvement of the fit of ∼ × − . We have also tried to fit the
NuSTAR spectrum of Ser X-1 withmore sophisticated reflection models, performing a grid of fitwith self-consistent models such as reflionx or rfxconv . Re-flionx and rfxconv models both include the reflection continuum,the so called Compton hump caused by direct Compton scat-tering of the reflected spectrum, and discrete features (emissionlines and absorption edges) for many species of atoms at di ff er-ent ionization stages (Ross & Fabian 2005; Kolehmainen et al.2011).The reflionx model depends on 5 parameters, that are theabundance of iron relative to the solar value, the photon indexof the illuminating power-law spectrum ( Γ , ranging between 1.0to 3.0), the normalization of reflected spectrum, the redshift ofthe source, and the ionization parameter ξ = L X / ( n e r ) where L X is the X-ray luminosity of the illuminating source, n e is theelectron density in the illuminated region and r is the distanceof the illuminating source to the reflecting medium. When using reflionx , which uses a power-law as illuminating spectrum, inorder to take into account the high-energy roll over of the Comp-tonization spectrum, we have multiplied it by a high-energy cut-o ff , highecut , with the folding energy E fold set to 2.7 timesthe electrons temperature kT e and the cuto ff energy E cuto f f tiedto 0.1 keV. In this way we introduce a cuto ff in the reflectioncontinuum, which otherwise resembles a power-law. The cut-o ff energy fixed at 2.7 times the electron temperature of the Comp-tonization spectrum (assumed to be similar to a blackbody spec-trum), is appropriate for a saturated Comptonization (see e.g.Egron et al. 2013). To fit the Comptonization continuum we usedthe nthComp model. Moreover we fixed the photon index of theilluminating spectrum, Γ , to that of the nthComp component. Westress that in our analysis we use a di ff erent reflionx reflec-tion model with respect to that used by Miller et al. (2013). Infact we used a model that assumes an input power-law spectrumas the source of the irradiating flux modified, in order to mimicthe nthcomp continuum, by introducing the model component highecut . Miller et al. (2013) instead used a modified versionof reflionx calculated for a blackbody input spectrum, since thatcomponent dominates their phenomenological continuum. rfxconv is an updated version of the code inDone & Gierli´nski (2006), using Ross & Fabian (2005) re- flection tables. This is a convolution model that can be used withany input continuum and has therefore the advantage to take asilluminating spectrum the given Comptonization continuum. Itdepends on 5 parameters: the relative reflection fraction (rel-refldefined as Ω / π , namely as the solid angle subtended by thereflecting disk as seen from the illuminating corona in unitsof 2 π ), the cosine of the inclination angle, the iron abundancerelative to the Solar value, the ionization parameter Log ξ of theaccretion disk surface, and the redshift of the source.Due to its high velocities, the radiation re-emitted from theplasma located in the inner accretion disk undergoes to Dopplerand relativistic e ff ects (which smears the whole reflection spec-trum). In order to take these e ff ects into account we have con-volved the reflection models with the rdblur component (thekernel of the diskline model), which depends on the values ofthe inner and outer disk radii, in units of the Gravitational ra-dius ( R g = GM / c ), the inclination angle of the disk (that waskept tied to the same value used for the reflection model), andthe emissivity index, Betor, that is the index of the power-lawdependence of the emissivity of the illuminated disk (whichscales as r Betor ). Finally, we have also considered the possi-bility that neutron star has a spin. In this case, the reflectioncomponent has been convolved with the
Kerrconv component(Brenneman & Reynolds 2006) that through its adimensionalspin parameter ’a’ allowed us to implement a grid of models ex-ploring di ff erent values of ’a’ (see Appendix A). For this modelthere is also the possibility to fit the emissivity index of the innerand outer part of the disk independently, although in our fits weused the same emissivity index for the whole disk. For all the fitswe have fixed the values of R out to 2400 R g , the iron abundanceto solar value, Fe / solar =
1, and the redshift of the source to 0.The best fit parameters are reported in Tab 2–A.2.We started to fit the data adding a reflection component, reflionx or rfxconv , convolved with the blurring component rdblur , to the continuum model given by the blackbody andthe nthcomp components (models are called rdb-reflio and rdb-rfxconv , respectively). Fit results for both models are acceptable,with χ red close to 1.09. There are a few di ff erences between thebest-fit parameters of the rdb-reflio model with respect to thoseof the rdb-rfxconv model. In particular the rdb-rfxconv modelgives a lower value of R in , while the rdb-reflio model gives ahigher ionization parameter (although with a large uncertainty).Spectra, along with the best-fit model and residuals are reportedin Fig.1. The residuals that are very similar for the two mod-els, apart for the 8-10 keV energy range where rdb-reflio modelshows flatter residuals than rdb-rfxconv model (see Fig. 1).As before, we also tried to add a power-law component tothe models obtained by the convolution of the blurring compo-nent (rdblur) with the two di ff erent reflection components (rfx-conv or reflionx). The two new models are called rdb-rfxconv-pl and rdb-reflion-pl , respectively. In both cases we get a signif-icant improvement of the fit, with ∆ χ =
90 for the additionof two parameters and ∆ χ =
66 for the addition of one pa-rameter, respectively. In these cases, an F-test yields a probabil-ity of chance improvement of 3 . × − for rdb-reflion-pl and6 . × − for rdb-rfxconv-pl model, respectively. Spectra, alongwith best-fit model and residuals are reported in Fig. 2, whereasvalues of the best-fit parameters are listed in Tab. 3. Residualsare now flat (see plots reported in upper panels of Fig. 2). Notealso that in this way we get more reasonable values of the best-fitparameters, especially for the ionization parameter, log ξ , whichis around 2.7 for both models, in agreement with the centroidenergy of the iron line at about 6.5 keV, and well below 3.7 (a Article number, page 4 of 13. Matranga et al.: A re-analysis of the NuSTAR and XMM-Newton broad-band spectrum of Ser X-1 ionization parameter log ξ ∼ . NuSTAR spectrum of Ser X-1is obtained fitting the continuum with a soft blackbody compo-nent, a Comptonization spectrum, and a hard power-law tail andfitting the reflection features with the rfxconv model smearedby the rdblur component, since the fitting results are quite in-sensitive to the value of the spin parameter a (see Appendix A).This fit, corresponding to a χ ( do f ) = . ≃ .
54 keV, a temperature of the seed pho-tons for the Comptonization of ≃ .
93 keV, an electron tempera-ture of the Comptonizing corona of ≃ .
70 keV and a photon in-dex of the primary Comptonized component of ≃ .
17, whereasthe photon index of the hard power-law tail is steeper, around3.2. The reflection component gives a reflection amplitude (thatis the solid angle subtended by the accretion disk as seen fromthe Comptonizing corona) of ≃ .
24 and a ionization parameterof log ξ ≃ .
7. The smearing of the reflection component givesan inner disk radius of R in ranging between 10 and 16 R g , andinclination angle of the disk with respect to the line of sight of i ≃ ◦ , and the emissivity of the disk scaling as ∝ r − . ± . .Note that the Compton hump is highly significant. To evaluateits statistical significance we can compare the best fit obtainedwith the model diskline-pl with the best fit given by the modelrdb-rfxconv-pl (the main di ff erence between the two models is infact that rfxconv contains the reflection continuum and disklinedoes not). Using rfxconv instead of diskline we get a decreasesof the χ by ∆ χ =
87 for the addition of 1 parameter and anF-test probability of chance improvement of 8 × − , which isstatistically significant. We have also carried out the analysis of
XMM-Newton obser-vations of Ser X-1. A previous study, based only on the PNdata analysis, has been reported by Bhattacharyya & Strohmayer(2007). We updated the analysis by performing the fit of the RGSspectra in the 0.35–1.8 keV energy range and the PN spectrain the 2.4–10 keV energy range. Following the same approachused for the analysis on
NuSTAR data, we assumed a contin-uum model composed of a blackbody, a hard power-law andthe nthComp component. In addition to the continuum compo-nents described above, we have also detected several discretefeatures present in all RGS spectra, both in absorption and inemission that were supposed to be of instrumental origin byBhattacharyya & Strohmayer (2007). The energies of the mostintense features detected in our spectra lie between 0.5 keV and0.75 keV. To fit these features we have therefore added three ad-ditional gaussians to our model: two absorption lines at 0.528keV and at 0.714 keV, respectively, and one in emission at 0.541keV. The identification of these lines is not straightforward. The0.528 keV energy is close to the neutral O K α line, expected ata rest frame energy of 0.524 keV, while the 0.541 keV emissionline is close to the expected energy of the O I edge at 0.538 keV.These two lines may be therefore instrumental features causedby a miscalibration of the neutral O edge in the RGS. The otherabsorption line at 0.714 keV is close to the O VII absorptionedge expected at a rest-frame energy of 0.739 keV. Given that theidentification of these lines is uncertain, we will not discuss themfurther in the paper. To this continuum we first added a diskline(model called diskline-pl-xmm , see Table 2) to fit the iron lineprofile. Then we fitted the spectra substituting the diskline withthe self-consistent reflection model that gave the best fit to the NuSTAR data, that is ’rfxconv’, convolved with the smearing component ’rdblur’ (model called rdb-rfxconv-pl-xmm , resultsare reported in Table 3).We have performed the fit of the spectrum obtained fromthese three observations simultaneously, tying parameters of theRGS with the all parameters of the PN from the same observa-tion. The spectra of the three XMM observations are very similarwith each other, except for the soft black body temperature thatwas left free to vary in di ff erent datasets. Values of the best-fitparameters of the model diskline-pl-xmm result to be in goodagreement with what we have found from the fit of the NuSTAR spectra with the same model.We have also performed the fit with a model including thereflection component rfxconv , called rdb-rfxconv-pl-xmm . Asbefore, in order to take into account structures visible in the RGSspectra, we have added three gaussians to the model. As beforewe have tied parameters of the RGS to the corresponding param-eters of the PN from the same observation except for the param-eter kT bb that was left free to vary among the three observations.Note also that for the these fits the inclination angle is fixed tothe corresponding values we found from the NuSTAR spectra.Results are reported in Table 3, and are in good agreement withthose obtained for the
NuSTAR spectrum.
4. Discussion
Ser X-1 is a well studied LMXB showing a broad emission lineat 6 . − .
97 keV interpreted as emission from iron at di ff er-ent ionization states and smeared by Doppler and relativistic ef-fects caused by the fast motion of matter in the inner accretiondisk. Moderately high energy resolution spectra of this sourcehave been obtained from XMM-Newton , Suzaku , NuSTAR , and
Chandra . However, as described in Sec. 1, spectral results forthe reflection component are quite di ff erent for di ff erent obser-vations or for di ff erent models used to fit the continuum and / orthe reflection component. While spectral di ff erences in di ff erentobservations may be in principle justified by intrinsic spectralvariations of the source, di ff erences caused by di ff erent contin-uum or reflection models should be investigated in detail in orderto give a reliable estimate of the parameters of the system. For in-stance, in a recent NuSTAR observation analyzed by Miller et al.(2013), assuming a modified version of reflionx calculated fora black-body input spectrum, the authors report a significant de-tection of a smeared reflection component in this source, fromwhich they derive an inner radius of the disk broadly compat-ible with the disk extending to the ISCO (corresponding to 6Rg in the case a =
0) and an inclination angle with respect tothe line of sight < ◦ . On the other hand, Chiang et al. (2016),analysing a recent 300 ks Chandra / HETGS observation of thesource obtained a high-resolution X-ray spectrum which gave ainner radius of R in ∼ − R g and an inclination angle of ∼ ◦ .In this paper we analyzed all the available NuSTAR and
XMM-Newton observations of Ser X-1. These observa-tions have been already analyzed by Miller et al. (2013) andBhattacharyya & Strohmayer (2007), respectively, who used dif-ferent continuum and reflection models and report di ff erent re-sults for the reflection component. The same XMM-Newton ob-servations have also been analyzed by Cackett et al. (2010) whoalso report di ff erent results for the reflection component, withhigher inner disk radii (between 15 and more than 45 R g ) andquite low inclinations angles ( < ◦ ) when using a blurred re-flection model, and inclination angle between 10 and 35 ◦ whenusing a diskline component to fit the iron line profile (see Tab.1 for more details). We have shown that we can fit the NuSTAR and
XMM-Newton spectra independently with the same contin-
Article number, page 5 of 13 & Aproofs: manuscript no. serx1_ref_mod_2 uum model and with a phenomenological model (i.e. diskline)or a self-consistent reflection model (i.e. reflionx or rfxconv) forthe reflection component, finding in all our fit similar (compati-ble within the associated uncertainties) smearing parameters forthe reflection component.To fit these spectra we have used a continuum model com-posed by a blackbody component (bbody) and a comptoniza-tion continuum (nthcomp), which has been widely used in liter-ature to fit the spectra of neutron star LMXBs both in the softand in the hard state (see e.g. Egron et al. 2013). With respect tothe continuum model used by Miller et al. (2013) we have sub-stituted one of the two blackbody components, the hottest one,with a Comptonization spectrum. Since this component gives themost important contribution to the source flux, especially above5 keV, we have subsequently used this component as the sourceof the reflection spectrum. In all our fit the addition of a hardpower-law component, with a photon index ∼ ff a non-thermalpopulation of electrons (see e.g. Di Salvo et al. 2000).To fit the reflection component, which is dominated by aprominent iron line, we have first used a phenomenologicalmodel consisting of a Gaussian line or a diskline, with a disklineproviding a better fit than a Gaussian profile (cf. fitting resultsreported in Table 2). All the diskline parameters obtained fromthe fitting of the NuSTAR and
XMM-Newton spectra are compat-ible with each other, except for the line flux which appears to belower during the
XMM-Newton observations.In order to fit the reflection spectrum with self-consistentmodels, which take into account not only the iron line butalso other reflection features, we have used both reflionx and rfxconv reflection models. In both these models, emission andabsorption discrete features from the most abundant elementsare included, as well as the reflected continuum. We have con-volved the reflection spectrum with the relativistic smearingmodel rdblur , taking into account Doppler and relativistic ef-fects caused by the fast motion of the reflecting material in theinner accretion disk. We have also investigated the possibilitythat the neutron star has a significant spin parameter. We havetherefore performed a grid of fits using the kerrconv smearingmodel, instead of rdblur, freezing the spin parameter ’a’ at di ff er-ent values: 0, 0.12, 0.14 and letting it free to vary in an additionalcase (see Appendix A for more details). In agreement with theresults reported by Miller et al. (2013) we find that the fit is al-most insensitive to the spin parameter but prefers low values ofthe spin parameter ( a < . reflionx or rfxconv aresomewhat di ff erent in the fits not including the hard power-lawcomponent. However, the reflection and smearing parametersbecome very similar when we add this component to the contin-uum model (cf. results in Tabs. 3, A.1, A.2). The addition of thiscomponent also significantly improves all the fits. We consideras our best fit model the one including the hard power-lawcomponent, rfxconv as reflection component smeared by the rbdblur component (model named rdb-rfxconv-pl in Tab.3). The fit of the XMM-Newton spectra with the same modelgave values of the parameters that overall agree with thoseobtained fitting the
NuSTAR spectra. In this case, we have foundvalues of the ionization parameter log( ξ ) ranging between 2.58and 2.71 (a bit higher, around 3, for the XMM-Newton spectra)and reflection amplitudes between 0.2 and 0.3, indicating arelatively low superposition between the source of the primary Comptonization continuum and the disk (a value of 0.3 wouldbe compatible with a spherical geometry of a compact coronainside an outer accretion disk). For the smearing parametersof the reflection component we find values of the emissivityindex of the disk ranging from -2.8 to -2.48, an inner radiusof the disk from 10.6 to 16 . R g , and an inclination angle ofthe system with respect to the line of sight of 25 − ◦ . Inour results the inclination angle is higher than that found byMiller et al. (2013) (who report an inclination angle less than10 ◦ ), but is very similar to that estimated from Chandra spectra(25 − ◦ , see Chiang et al. (2016). Moreover, the inner diskradius we find is not compatible with the ISCO. Assuming a1 . M ⊙ for the neutron star, the inner radius of the disk is locatedat 22 −
34 km from the neutron star center. Note that this valueis compatible to the estimated radius of the emission region ofthe soft blackbody component, which is in the range 19 −
5. Conclusions
The main aim of this paper is to test the robustness of disk pa-rameters inferred from the reflection component in the case ofneutron star LMXBs; to this aim we used broad-band, mod-erately high resolution spectra of Serpens X-1, a neutron starLMXB of the atoll type with a very clear reflection spectrum thathas been studied with several instruments. In particular, we havecarried out a broad-band spectral analysis of this source usingdata collected by
NuSTAR and
XMM-Newton satellites, whichhave the best sensitivity at the iron-line energy. These data havebeen already analyzed in literature. In particular Miller et al.(2013) have analyzed the
NuSTAR spectra and have obtained alow inclination angle of about 8 ◦ , an inner disk radius compati-ble with the ISCO, a ionization parameter log ξ between 2.3 and2.6 along with an iron abundance of about 3.In the following we summarize the results presented in thispaper: – We have performed the fitting using slightly di ff erent con-tinuum and reflection models with respect to that used byother authors to fit the X-ray spectrum of this source. Our thebest fit of the NuSTAR spectrum of Ser X-1 is obtained fit-ting the continuum with a soft blackbody, a Comptonizationspectrum, a hard power-law tail in addition to the reflectionfeatures. To fit the reflection features present in the spectrumwe used both empirical models and self-consistent reflectioncomponents as reflionx and rfxconv , as well as two dif-ferent blurring components that are rdblur and kerrconv .From the analysis carried out using kerrcov we have obtainedthat our fit is insensitive to the value assumed by the adimen-sional spin parameter ’a’, in agreement with what is foundby Miller et al. (2013) in their analysis. – With regard the reflection features, we obtain consistent re-sults using phenomenological models (such as diskline) orself-consistent models to fit the
NuSTAR spectrum of thesource. In particular, the reflection component gives a re-flection amplitude of Ω / π ∼ . − . Ω is thesolid angle of the disk as seen from the corona in units of2 π ) and a ionization parameter of log( ξ ) ∼ . − .
7. Thesmearing of the reflection component gives an inner disk ra-dius of R in ∼ . − . R g , an emissivity index of the disk Article number, page 6 of 13. Matranga et al.: A re-analysis of the NuSTAR and XMM-Newton broad-band spectrum of Ser X-1 in the range − (2 . − . − ◦ . We note that the inner disk radius derived from thereflection component results compatible with the radius in-ferred from the soft blackbody component, which results inthe range 19 −
31 km. – The analysis of
XMM-Newton spectra, carried out using thesame models adopted to fit the
NuSTAR spectra, gave valuesof the parameters compatible to those described above, al-though the two observations are not simultaneous. The onlydi ff erences are the reflection amplitude, Ω / π ∼ . − . ξ ) ∼ . − .
1, which results somewhat higher with respect to thenon-simultaneous
NuSTAR observations.In conclusion, in this paper we performed an investigationof to which extent the disk parameters inferred from reflectionfitting depend on the chosen spectral models for both the contin-uum and the reflection component. Despite the fact that severalauthors in previous work have used basically the same contin-uum model, the resulting reflection parameters, such as the in-ner disk radius, R in , and the inclination angle are scattered overa large range of values. In this paper we have re-analyzed allthe available public NuSTAR and
XMM-Newton observations ofSer X-1, fitting the continuum with a slightly di ff erent, physi-cally motivated model and the iron line with di ff erent reflectionmodels. By performing a detailed spectral analysis of NuSTAR and
XMM-Newton data of the LMXB Ser X-1 using both phe-nomenological and self-consistent reflection models, and usinga continuum model somewhat di ff erent from that used in litera-ture for this source, the best fit parameters derived from the twospectra are in good agreement between each other. These arealso broad agreement with the findings of Miller et al. (2013) al-though we find values of the inner disk and the inclination anglethat are less extreme. Hence, the use of broad-band spectra andof self-consistent reflection models, together with an investiga-tion of the continuum model, are highly desirable to infer reliableparameters from the reflection component. Acknowledgements.
We thank the anonymous referee for useful suggestionswhich helped to improve the manuscript. The High-Energy Astrophysics Groupof Palermo acknowledges support from the Fondo Finalizzato alla Ricerca (FFR)2012 /
13, project N. 2012-ATE-0390, founded by the University of Palermo. Thiswork was partially supported by the Regione Autonoma della Sardegna throughPOR-FSE Sardegna 2007-2013, L.R. 7 / / / / References
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Article number, page 7 of 13 & A p r oo f s : m a nu s c r i p t no . s e r x1_ r e f _ m od_2 Table 1.
Results of Spectral Analysis of Ser X-1 from Previous Studies
Instrument Continuum Model Reflection Model Line Model Line Energy (keV) Equivalent width R in (R g ) Incl (deg) Emissivity index log ( ξ ) Flux (ergs / cm / sec) Reference ASCA bbody + cutpowerlaw — gaussian 6 . ± .
17 81 eV — — — — Ref(1)
RXTE bbody pexrav gaussian – – — — — — Ref(2)
BeppoSAX bbody + compTT — gaussian 6.46 + . − . − eV — — — — Ref(2) XMM-Newton diskbb + compTT — laor 6.40 + . − . × − Ref(3)
SUZAKU bbody + diskbb + powerlaw — diskline 6.83 + . − . ±
12 eV 7.7 ± ± ± × − a Ref(4)
SUZAKU bbody + diskbb + powerlaw — diskline 6.97 + . − .
98 eV 8.0 ± ± ± × − Ref(5)
SUZAKU bbody + diskbb + powerlaw reflionx — — — 6 ± ± ± ± × − Ref(5)
XMM-Newton bbody + diskbb + powerlaw — diskline 6.66 - 6.97 38 - 50 eV 14 - 26 13 - 32 — 0.5-25 keV: (0.6-0.7) × − Ref(5)
XMM-Newton bbody + diskbb + powerlaw reflionx — — — 15 - 107 3 - 9 2.6 - 2.8 0.5-25 keV: (0.6-0.7) × − Ref(5)
NuSTAR bbody + diskbb + powerlaw — kerrdisk 6.97 ± ± ± ± × − Ref(6)
NuSTAR bbody + diskbb + powerlaw reflionx — — — 6 - 8.3 <
10 2.30 - 2.60 — Ref(6)
Chandra bbody + diskbb + powerlaw — diskline 6.97 ± ±
15 eV 7.7 ± ± Chandra bbody + diskbb + powerlaw reflionx — — — 7.1 + . − . ± + . − . — Ref(7) Chandra bbody + diskbb + powerlaw xillver — — — 8.4 + . − . ± + . − . — Ref(7) Notes.
Ref(1): Church & Baluci´nska-Church (2001) - Ref(2): Oosterbroek et al. (2001) - Ref(3): Bhattacharyya & Strohmayer (2007)- Ref(4): Cackett et al. (2008) - Ref(5): Cackett et al. (2010) -Ref(6): Miller et al. (2013) - Ref(7): Chiang et al. (2016) a Estimated only for the continuum component A r ti c l e nu m b e r , p a g e f . Matranga et al.: A re-analysis of the NuSTAR and XMM-Newton broad-band spectrum of Ser X-1 Table 2.
Results of the fit of NuSTAR and XMM-Newton spectra of Ser X-1 using Gaussian and Diskline models
Component Parameter gauss diskline gauss-pl diskline-pl diskline-pl-xmmphabs N H ( × cm − ) 0.4 (f) 0.4 (f) 0.4 (f) 0.4 (f) 0.863 ± kT bb (keV) 0.47 ± ± ± ± ± BB (km) 46.1 ± ± ± ± ± × − ) 22.6 ± ± ± ± ± ± ± ± ± × − ) 4.03 ± ± ± ± ± ± ± ± in ( R g ) — 18.6 ± ± + . − . diskline R out ( R g ) — 2400(f) — 2400(f) 2400(f)diskline Incl (deg) — 40.1 ± ± ± × − ) — 4.38 ± ± ± ± ± ± ± + . − . nthComp kT e (keV) 2.95 ± ± ± ± ± kT bb (keV) 0.96 ± ± ± ± ± ± ± × − ) 219 ±
11 200 ±
15 229 ±
12 217 ±
18 160 ± ± ± ± × − keV) — — — — 2.19 (f)gau-rgs Norm ( × − ) — — — — -18.4 (f)gau-rgs E (keV) — — — — 0.541 (f)gau-rgs Sigma ( × − keV) — — — — 1.36 (f)gau-rgs Norm ( × − ) — — — — 57.1 (f)gau-rgs E (keV) — — — — 0.714 ± × − keV) — — — — 5.8 ± × − ) — — — — -12.1 ± ± ± ± ± ±
16 ; 93 ±
18 ; 79 ±
16- Obs. Flux 5.25 ± ± ± ± ± ± ± ± ± ± χ red (d.o.f.) - 1.2750(915) 1.2186(913) 1.14134(914) 1.0961(912) 1.3521(4546) Notes.
Flux and luminosity are obtained for the 3–40 keV energy band. Fluxes units are 10 − (ergs / cm / sec), whereas luminosities units are 10 (ergs / sec) . The seed-photon temperature was left free to vary among the three di ff erent XMM-Newton observations, this is why we report threevalues for this parameters in the XMM-Newton fitting results (see text for more details). The values of the parameter Eq. W. refers to the equivalentwidth of the the iron line at 6.48 keV detected in each observation. Errors are reported with a 90% confidence. R BB and luminosities are estimatedassuming a distance of 7.7 kpc (Galloway et al. 2008) Appendix A: Models including kerrconv
From the spectral analysis described in Sec. 3.1, we find that ourbest fit obtained using rdblur as smearing component gives asoft blackbody temperature of 0.54 ± ± ± ± ± ± ξ ) = + . − . . Finally, the smearing of the reflection component givesan inner disk radius of R in = ± g , compatible with theradius inferred from the blackbody component, and an emissiv-ity index of the disk equal to -2.64 ± ± ◦ . The analysis of XMM-Newton spectra, car-ried out using the same models adopted to fit the
NuSTAR spec-tra, gave values of the parameters compatible to those describedabove, although the two observations are not simultaneous. Inparticular in this case we find R in + . − . R g , a reflection am-plitude of 0.183 ± ξ ) = ± . − .
85 keV, a photon index of the primary Comptonizedcomponent of 2.45 ± XMM-Newton spectra independently confirm the results obtained for the
NuS-TAR spectra.In order to check the presence of a non-null spin parameterof the neutron star, we fitted the
NuSTAR spectra using reflection components convolved with kerrconv instead of rdblur . Ker-rconv convolves the spectrum with the smearing produced by akerr disk model. It features the dimensionless ’a’ parameter thatcharacterize the spin of the system. We have performed our fitfirst leaving ’a’ as a free parameter and then fixing it to the fol-lowing three values, 0, 0.12, 0.14. The model with reflionx and’a’ treated as free parameter is called ker-reflio-af , whereas for a = a = .
12 and a = .
14 the models are called ker-reflio-a0 , ker-reflio-a012 , and ker-reflio-a014 , respectively. In the sameway, the model with rfxconv and ’a’ treated as free parameter iscalled ker-rfxconv-af , whereas for a = a = .
12 and a = . ker-rfxconv-a0 , ker-rfxconv-a012 , and ker-rfxconv-a014 , respectively. All the models fit the data well; re-duced χ are between 1.08 and 1.18 and residuals are basicallyidentical . Moreover the best-fit values of all parameters are verysimilar to the case with a = rdblur instead of kerrconv . The fit is therefore insensitive tothe spin parameter, although there is a slight preference of the fittowards low values ( a < . kerrconv with the two di ff erent reflection components (reflionx or rfx-conv). we considered ’a’ free to vary or fixed it to three di ff erentvalues (0, 0.12, 0.14). In all the cases the fits are quite good withvalues of the reduced χ from 1.0 to 1.01. Again the addition of Article number, page 9 of 13 & Aproofs: manuscript no. serx1_ref_mod_2
Table 3.
Results of the fit of NuSTAR and XMM-Newton spectra of Ser X-1 using rdblur combined with rfxconv or reflionx
Component Parameter rdb-rfxconv rdb-reflio rdb-rfxconv-pl rdb-reflio-pl rdb-rfxconv-pl-xmmphabs N H ( × cm − ) 0.4 (f) 0.4 (f) 0.4 (f) 0.4 (f) 0.896 ± kT bb (keV) 0.71 ± ± + . − . ± ± BB (km) 23.6 ± ± ± ± ± × − ) 30.9 ± ± + . − . ± ± cut (keV) — 0.1 (f) — 0.1 (f) —highecut E fold (keV) — 8.61 ± ± ± ± ± ± + . − . rdblur R in ( R g ) 7.7 ± ± ± ± + . − . rdblur R out ( R g ) 2400(f) 2400(f) 2400(f) 2400(f) 2400(f)rdblur Incl (deg) 29.2 ± ± ± ± ± ± ξ — 4990 + − — 490 + − —reflionx Norm ( × − ) — 1.97 ± ± ± ± ± ξ ) 2.68 ± + . − . — 3.04 ± ± ± ± ± ± kT e (keV) 4.36 + . − . ± ± ± + . − . nthComp kT bb (keV) 1.51 ± ± ± ± ± ± ± × − ) 71.2 ± ± ±
24 286 + − ± ± ± + . − . ± ± ± ± ± ± ± ± ± ± ± ± χ red (d.o.f.) - 1.0983(913) 1.0838(913) 1.0017(911) 1.0123(912) 1.33762(4546) Notes.
For each fit, the abundance of iron in the reflection models was kept frozen: Fe / solar =
1. Flux and luminosity are obtained for the 3–40keV energy band. Fluxes units are 10 − (ergs / cm / sec), whereas luminosities units are 10 (ergs / sec) . The seed-photon temperature was left freeto vary among the three di ff erent XMM-Newton observations, this is why we report three values for this parameters in the XMM-Newton fittingresults (see text for more details). Errors are reported with a 90% confidence. R BB and luminosities are estimated assuming a distance of 7.7 kpc(Galloway et al. 2008) −3 no r m a li ze d c oun t s s − k e V − data and folded model
105 20−202 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −3 no r m a li ze d c oun t s s − k e V − data and folded model
105 20−2024 ( d a t a − m od e l ) / e rr o r Energy (keV)10 −3 no r m a li ze d c oun t s s − k e V − data and folded model
105 20−202 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −3 no r m a li ze d c oun t s s − k e V − data and folded model
105 20−2024 ( d a t a − m od e l ) / e rr o r Energy (keV)
Fig. 1.
NuSTAR spectra of Ser X-1 and best-fitting model together with residuals in units of sigma for the corresponding model. These are:
Topleft : ’gauss’ —
Top right : ’diskline’ —
Bottom left : ’rdb-reflio’ —
Bottom right : ’rdb-rfxconv’. Dashed lines indicate the black-body component,dotted lines indicate the reflection components (i.e. the Gaussian or Diskline profile for the iron line, top panels, or the self-consistent reflectioncomponent, bottom panels, respectively), and the dashed-dotted lines indicate the comptonized component.Article number, page 10 of 13. Matranga et al.: A re-analysis of the NuSTAR and XMM-Newton broad-band spectrum of Ser X-1 −3 no r m a li ze d c oun t s s − k e V − data and folded model
105 20−202 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −3 no r m a li ze d c oun t s s − k e V − data and folded model
105 20−202 ( d a t a − m od e l ) / e rr o r Energy (keV)10 −3 k e V ( P ho t on s c m − s − k e V − ) Unfolded Spectrum1 2 5−4−202 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −3 k e V ( P ho t on s c m − s − k e V − ) Unfolded Spectrum1 2 5−4−202 ( d a t a − m od e l ) / e rr o r Energy (keV)
Fig. 2.
Top panels : NuSTAR spectra of Ser X-1 and best-fitting model together with residuals in units of sigma for the corresponding model. Theseare:
Top left : ’rdb-reflio-pl’ —
Top right : ’rdb-rfxconv-pl’. Bottom panels: XMM-Newton spectra and best-fitting model together with residualsin units of sigma for the corresponding model. These are:
Bottom left : ’diskline-pl-xmm’ —
Bottom right : ’rdb-rfxconv-pl-xmm’. For clarity onlythe first XMM-Newton observation is shown. Dashed lines indicate the black-body component, dotted lines indicate the reflection components(i.e. the Diskline profile for the iron line or the self-consistent reflection component), the solid line indicates the power-law component, and thedashed-dotted lines indicate the comptonized component. the power-law proved to be highly statistically significant. TheF-test probability of chance improvement for the addition of twoparameters is, for instance, 7 . × − and 9 × − for the ad-dition of a power-law to the model ker-reflio-af and ker-rfxconv-af , respectively. As before, the fit is quite insensitive to the valueassumed by the spin parameter ’a’. Values of the best-fit param-eters are listed in Tab A.1 and A.2. Article number, page 11 of 13 & A p r oo f s : m a nu s c r i p t no . s e r x1_ r e f _ m od_2 Table A.1.
Results of the fit of the NuSTAR spectra using kerrconv combined with rfxconv or reflionx components
Component Parameter ker-reflio-af ker-reflio-a0 ker-reflio-a012 ker-reflio-a014 ker-rfxconv-af ker-rfxconv-a0 ker-rfxconv-a012 ker-rfxconv-a014bbody kT bb (keV) 0.79 ± ± ± ± ± ± ± ± × − ) 22.4 ± ± ± ± ± ± ± ± cut (keV) 0.1 (f) 0.1 (f) 0.1 (f) 0.1 (f) — — — —highecut E fold (keV) 8.54 ± ± ± ± ± ± ± ± ± ± ± ± + . − . ± ± ± ± ± ± ± ± ± in ( R g ) 14.5 ± ± ± ± ± < . ± out ( R g ) 2400(f) 2400(f) 2400(f) 2400(f) 2400(f) 2400(f) 2400(f) 2400(f)reflionx Gamma 2.85 ± ± ± ± ξ ±
61 3784 + − + − + − — — — —reflionx Norm ( × − ) 2.38 ± ± ± + . − . — — — —rfxconv rel_refl — — — — 0.58 ± ± ± ± ξ ) — — — — 2.71 ± ± ± ± ± ± ± ± ± ± ± ± kT e (keV) 3.16 ± ± ± + . − . ± ± ± + . − . nthComp kT bb (keV) 1.42 ± ± ± ± ± ± ± ± × − ) 70.9 ± ± + . − . + . − . + . − . + . − . + . − . + . − . - R BB (km) 14.9 ± ± ± ± ± ± ± ± χ red (d.o.f.) - 1.0876(912) 1.0876(913) 1.0859(913) 1.0835(914) 1.1797(914) 1.0981(913) 1.1111(913) 1.0849(913) Notes.
For each fit, the following parameters were kept frozen: N H = × cm − , Fe / solar = br = R g . The parameter r br in the kerrconv model is break radius separating the inner andouter portions of the disk, having emissivity index Index1 and Index2, respectively, which in our fit are constrained to assume the same value, Index. Errors are reported with a 90% confidence. R BB are estimated assuming a distance of 7.7 kpc (Galloway et al. 2008) A r ti c l e nu m b e r , p a g e f . M a t r a ng ae t a l . : A r e - a n a l y s i s o f t h e N u S T A R a nd X MM - N e w t onb r o a d - b a nd s p ec t r u m o f S e r X - Table A.2.
Fitting results adding a power-law to the models of Table
Component Parameter ker-reflio-af-pl ker-reflio-a0-pl ker-reflio-a012-pl ker-reflio-a014-pl ker-rfxconv-af-pl ker-rfxconv-a0-pl ker-rfxconv-a012-pl ker-rfxconv-a014-plbbody kT bb (keV) 0.54 ± ± ± ± ± ± ± ± × − ) 6.8 ± ± ± ± ± ± ± ± cut (keV) 0.1 (f) 0.1 (f) 0.1 (f) 0.1 (f) — — — —highecut E fold (keV) 5.05 ± ± ± ± ± ± ± ± ± ± ± ± < .
019 0.0 (f) 0.12 (f) 0.14(f) 0.06 + . − . ± ± ± ± ± ± ± ± in ( R g ) 13.6 ± ± ± ± ± ± ± ± out ( R g ) 2400(f) 2400(f) 2400(f) 2400(f) 2400(f) 2400(f) 2400(f) 2400(f)reflionx Gamma 1.51 ± ± ± ± ξ + − ±
17 501 ±
19 497 + − — — — —reflionx Norm ( × − ) 10.5 ± ± ± + . − . — — — —rfxconv rel_refl — — — — 0.24 ± ± ± ± ξ ) — — — — 2.71 ± ± ± ± ± ± ± ± ± ± ± ± kT e (keV) 5.04 ± ± ± ± ± ± + . − . + . − . nthComp kT bb (keV) 1.04 ± ± ± ± ± ± ± ± × − ) 287 ±
19 289 ±
77 501 ±
15 289 ±
38 187 + − + − + − + − powerlaw Index_pl 3.20 + . − . + . − . ± ± ± + . − . ± ± ± ± BB (km) 17.6 ± ± ± ± ± ± ± ± χ red (d.o.f.) - 1.0148(910) f 1.0123(912) 1.0083(912) 1.0138(911) 1.0016(911) 1.0023(912) 1.0008(912) 1.0006(912) Notes.
For each fit, the following parameters were kept frozen: N H = × cm − , Fe / solar = br = R g . The parameter r br in the kerrconv model is break radius separating the inner andouter portions of the disk, having emissivity index Index1 and Index2, respectively, which in our fit are constrained to assume the same value, Index. Errors are reported with a 90% confidence. R BB are estimated assuming a distance of 7.7 kpc (Galloway et al. 2008) A r ti c l e nu m b e r , p a g e ff