Comprehensive broadband study of accreting neutron stars with Suzaku: Is there a bi-modality in the X-ray spectrum?
Pragati Pradhan, Biswajit Paul, Enrico Bozzo, Chandreyee Maitra, B.C. Paul
aa r X i v : . [ a s t r o - ph . H E ] J a n Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 7 January 2021 (MN L A TEX style file v2.2)
Comprehensive broadband study of accreting neutronstars with
Suzaku : Is there a bi-modality in the X-rayspectrum?
Pragati Pradhan , ⋆ Biswajit Paul Enrico Bozzo Chandreyee Maitra B.C. Paul Massachusetts Institute of Technology, Kavli Institute for Astrophysics and Space Research, Cambridge, MA, 02139, USA St. Joseph’s College, Singamari, Darjeeling-734104, West Bengal, India Raman Research Institute, Sadashivnagar, Bangalore-560080, India ISDC, University of Geneva, Chemin d’Ecogia 16, Versoix, 1290, Switzerland Max Planck Institute For Extraterrestrial Physics, 85748 Garching, Germany North Bengal University, Raja Rammohanpur, District Darjeeling-734013, West Bengal, India
ABSTRACT
We present a broadband spectral analysis of accreting neutron stars usingdata from XIS and PIN onboard
Suzaku . From spectral fits of these sourceswith a single continuum model including a powerlaw and high energy cut-off,cyclotron lines (where required), we studied the correlation between variousspectral parameters. Among 39 sources we studied, 16 are those where theexistence of a cyclotron line is known in literature, and 29 need a cutoff energy.Among these 29 sources, 18 have cutoff energy bunched in a range of 3-10 keVwhile for 11 sources, it spreads over 12-25 keV. This bi-modal behaviour isnot based on the specific nature of the systems being a Be XRB or supergiantHMXB, nor on different beaming patterns characterizing their X-ray emission(as inferred from simultaneous study of their pulse profiles). The broadbandcoverage of
Suzaku also shows that the cutoff energies saturate for highervalues of cyclotron line energies - consistent with previous works in literature -for both the groups and the width of the cyclotron line show a weak correlationwith the cyclotron line energy. We also find an anticorrelation with luminosityfor both spectral index and folding energy, respectively. Unlike previous works,we did not detect any anticorrelation between X-ray luminosity and EW of K α lines. Finally, we show that the EW and flux of the iron K α line are smaller © P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul in SFXTs than classical NS-HMXBs. We discuss these findings in terms ofdifferent properties of stellar winds and accretion mechanisms.
Key words:
X-rays: binaries–pulsars: general
High-mass X-ray binaries (HMXBs) are binary systems comprising a compact object and amassive star orbiting around a common centre of mass. The compact object can be eithera neutron star or a black hole. In this work, we mainly deal with HMXBs that harbour aneutron star as the compact object accreting from the powerful wind of the massive com-panion (White, Swank & Holt 1983; Nagase 1989; Bildsten et al. 1997). These neutron starsin HMXBs have magnetic fields of the order of & G. The accreted material is thusexpected to be channelled along the magnetic field lines at relatively large distances fromthe compact object, leading to the formation of extended accretion columns. The exactdetails of how the magnetic field affects the accretion flow is still a topic of investigation(Becker & Wolff 2007). It is generally expected that the inflowing material is directed to-wards the the magnetic poles of the neutron star where two hot spots are formed. Thegravitational potential energy of the inflowing material is first converted into kinetic energyand then released as X-rays due to shocks and dissipations into the accretion column andon the hot spots (Basko & Sunyaev 1975). If the rotation axis and the magnetic axis of theneutron star are not completely aligned, the X-ray emission from the source appears pulsedto any distant observer whose line of sight to the object intersects the beam periodically.The high magnetic fields of neutron stars can be measured from the cyclotron resonancescattering features (CRSFs). These features are known to be produced as a consequence ofcyclotron resonant scattering of X-ray photons in the presence of an intense magnetic field.Their centroid energy is related to the NS magnetic field intensity by the equation: E C = 11 . B G (1 + z ) − keV , (1)where z is the gravitational redshift.Classical HMXBs can be classified as either Be/X-ray binaries (BeXBs; Reig 2011) or Su-pergiant X-ray binaries (SGXBs; Walter et al. 2015). Relatively recently discovered HMXBswith supergiant companions, called Supergiant Fast X-ray Transients (SFXTs), are charac- ⋆ E-mail:[email protected] © , 000–000 omprehensive analysis ∼ tens of minutes) and typical durations of afew hours (Sguera et al. 2006). For this study, along with both classical HMXBs and SFXTsobserved with Suzaku (Mitsuda et al. 2007), we have also included a few sources which havea low mass companion star but are known to harbour neutron star with strong magneticfields. These four sources are Her X-1, 4U 1626-67, GX 1+4, and 4U 1822-37 and have beenclassified here as Low Mass X-ray Binaries, LMXBs (although strictly speaking, Her X-1 isan intermediate mass X-ray binary).
Suzaku (Mitsuda et al. 2007) is a broad-band X-ray observatory covering the energy range0.2-600 keV. There are two main instruments on-board
Suzaku : the X-ray Imaging Spec-trometer XIS (Koyama et al. 2007), covering the 0.2-12 keV energy range, and the HardX-ray Detector (HXD). The XIS consists of four CCD detectors of which three (XIS 0, 2and 3) are front illuminated (FI) and one (XIS 1) is back illuminated (BI). The HXD com-prises PIN diodes (Takahashi et al. 2007) that cover the 10-70 keV energy range and GSOcrystal scintillator detectors that cover the 70-600 keV energy range.For the XIS and the HXD data, we used the filtered cleaned event files which are obtainedusing the pre-determined screening criteria as suggested in the Suzaku ABC guide . The datareduction for both instruments was carried out following the reduction technique mentionedin the same Suzaku ABC guide. We applied the barycentric correction to all event files us-ing aepipeline . For the XIS data reduction we applied the following procedure: for sourcesthat showed jitters in the image, the event files were corrected by using the aeattcorr and xiscoord tools to update the attitude information; for those sources affected by pile-up,we discarded photons collected within the portion of the PSF where the estimated pile-upfraction was greater than 4 %. This was done by using the FTOOLS task pileest . XIS spec-tra were then extracted by choosing circular regions of 2 ′ , 3 ′ , or 4 ′ radius from the sourceposition depending on whether the observation was made in 1/8, 1/4, or 0 window mode,respectively. Background spectra for the XIS were extracted by selecting regions of the samesize as mentioned above in a portion of the CCD that was not significantly contaminated bythe source X-ray emission. For relatively fainter objects observed in window ‘Off’ mode (likeIGR J16493-4348, IGR J16465-4507, IGR J16479-4514, and IGR J08408-4503) choosing the http://heasarc.gsfc.nasa.gov/docs/suzaku/analysis/abc/ © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul same radius for the source and background extraction region gave rise to a dip-like artefactin the spectra visible around 6 keV. Hence, for these sources, a larger background region waschosen by adopting an annulus with inner (outer) radius of 5 ′ (7 ′ ) centered on the sourcebest known position.The PIN source spectra were additionally corrected for dead-time effects by using the FTOOLS task hxddtcor . For the HXD/PIN, simulated ‘tuned’ non X-ray background event files(NXB) corresponding to the month and year of the respective observations were used toestimate the non X-ray background (Fukazawa et al. 2009).The XIS spectra were extracted with 2048 channels and the PIN spectra with 255 chan-nels. Response files for the XIS were created using the CALDB version ‘20150312’. For theHXD/PIN spectrum, response files corresponding to the epoch of the observation were ob-tained from the Suzaku guest observer facility .The sources considered for the present study and all the OBSID corresponding to the ob-servations used are listed in Table 1. For the spectral analysis of the selected sources, we have used the spectra from all the avail-able XIS units (0, 1, 2 and 3) and the PIN. In some cases we noticed systematic differencesbetween the spectra obtained from the BI XIS 1 and the rest of the XIS units. In all thesecases, we did not make use of the BI XIS 1 data in the spectral fitting as they gave no addi-tional information and led to a poorer fit with larger χ . Spectral fitting was performed byusing XSPEC v12.9.0. Artificial residuals are known to arise in the XIS spectra around the Siedge and the Au edge. We have thus discarded the energy range ∼ ∼ ∼ https://heasarc.gsfc.nasa.gov/docs/suzaku/analysis/pinbgd.html https://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/suzaku/ © , 000–000 omprehensive analysis at the knownorbital period of the source. Except for Cen X-3, IGR J16479-4514, and 4U 1822-37, all theother sources were not observed during an X-ray eclipse. For Cen X-3 and IGR J16479-4514,we have extracted the time filtered spectrum corresponding to the times when the source wasnot in eclipse. For Cen X-3 we extracted spectra only for ‘Segment E’ of Naik, Paul & Ali(2011) while for IGR J16479-4514, we extracted the spectrum starting 143 ks after the be-ginning of the observation (as is done in Sidoli et al. 2013). For 4U 1822-37, the full Suzaku observation spanned nearly four times the orbital period of the neutron star. Hence for 4U1822-37, we extracted a spectrum only for that phase interval during which the source wasoutside the dips and eclipse (0.1-0.6 when Phase 0 is at MJD 54010.48). In the cases of VelaX-1 and 4U 1538-522, spectra were extracted only for that part of the observation duringwhich the hardness ratio remained relatively stable as done in Maitra & Paul (2013b) andHemphill et al. (2014).We fitted the spectra of all sources by using all available instruments simultaneously. We https://heasarc.gsfc.nasa.gov/docs/xte/ASM/sources.html © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul kept all spectral parameters of the different instruments tied together during the fit. Onlythe inter-calibration constants were left free to vary. We have used the most commonlyadopted models to describe the high energy emission of HMXBs and LMXBs consistingof a power law component with a high energy cutoff (HIGHECUT; White, Swank & Holt1983; Coburn et al. 2002). This model gave formally acceptable fits ( χ =0.89-1.45) to alldata, the only exceptions being A0535+026, LMC X-4, and GX 1+4. In these three cases,the NPEX (Mihara 1995; Makishima et al. 1999), FDCUT (Tanaka 1986) and NEWHCUT(Burderi et al. 2000) models respectively provided a better description of the data. We no-ticed that no formal acceptable fit could be obtained with the selected models to the dataof GX 1+4 ( χ = 1.66) and thus we decided not to include this source for the discussion onthe spectral parameters’ correlations. Such a high value of χ for GX 1+4 has also beenreported in a recent analysis of the same data set to which refer the readers for furtherdetails (Yoshida et al. 2017).Furthermore, although we fit Her X-1 and 4U 0115+63 with the HIGHECUT model, wedid not include their CRSF parameters for correlation studies. The reason being that theformer is known to show a complicated cyclotron energy variation (Staubert et al. 2014) andfor latter, the CRSF lie at ∼
11 keV, which is outside the usable PIN band (K¨uhnel et al.2020).The analytical form of the main model considered in this work: HIGHECUT is:HIGHECUT( E ) = A E − Γ × E E cut )e − ( E − E cut ) /E fold ( E > E cut ) (2)(where Γ is the photon index, E cut the cutoff energy, and E fold the folding energy),For other sources where the cutoff energy was not required (IGR J16195-4945, IGRJ16493-4348, IGR J16465-4507, IGR J16479-4514, IGR J17391-3021, IGR J08408-4503, andIGR J00370+6122), we fitted the spectrum with a simple powerlaw corrected for photo-electric absorption. In many of the analysed sources, CRSFs were clearly detected as broadabsorption features in the X-ray spectra. Where required, those features have been fit withpseudo Lorentzian optical depth profiles (CYCLABS in Xspec). We used additional Gaus-sian components to take into account the presence of emission lines, mostly due to theflourescence of neutral iron. In addition to the above components, in some cases, a partialcovering model and/or blackbody component was used to account for fractional local ab- © , 000–000 omprehensive analysis all our sources while at the same time having the leastdegeneracy between model parameters. Since HIGHECUT has shown to have the least de-generacy while describing the X-ray spectra of accreting neutron stars (Coburn et al. 2002),we use this model throughout our analysis. To minimize degeneracy in fitting though, wehave cross-checked the fitting parameters at each step to literature values (where available),and if it is physical. We are therefore confident that the correlation presented in this paperis real within the limits to what a phenomenological model can provide. The main purpose of this work is to carry out a correlation study among the various spectralparameters that are measured from known HMXBs and a few strong magnetic field LMXBsobserved by
Suzaku . We have also investigated the variation of the spectral parameterswith luminosity, L X . The distances used for L X calculations are reported in Table 1. L X is calculated over the energy range for which the individual spectra were fitted. For most For sources where distance errors are not determined, we assumed an error of 1 kpc. © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul sources, it is 0.8-70.0 keV. In other cases, as mentioned in Section 3, we have discardedspectral data below 3 keV. Due to the relatively high absorption, we verified that in thesecases the difference in the luminosity estimated in the 0.8-70 keV and 3.0-70.0 keV bands arenegligible. We also verified that for those sources where the PIN spectrum is truncated priorto 70 keV due to the poor S/N (mentioned in Section 3), the X-ray luminosity evaluatedin the energy range of the fit or in the full 0.8-70.0 keV energy range would not changesignificantly. All the fainter sources for which only the XIS spectrum is used, are markedin grey in all relevant figures. We discuss in the following sub-sections all the correlationsbetween the different parameters that we could find from the analysis of the
Suzaku data ofthe considered sources. E cut versus L X When the measured values of the E cut are plotted against L X , we note a bimodality inthe E cut distribution (see Fig. 1). For clarity, we have used different colour schemes todistinguish the two groups. The upper branch where the cutoff energy range from ∼ , theyappear clearly distinguished on the E cut - L X plane. The sources in Branch 1 are: Her X-1,4U 0115+63, Cen X-3, 4U 1626-67, 4U 1907+09, 4U 1538-522, GX 301-2, Cep X-4, IGRJ16393-4643, IGR J16318-4848, and V0332+54. The sources in Branch 2 are: Vela X-1, XTEJ1946+274, 1A 1118-61, 4U 0114+65, GX 304-1, OAO 1657-415, 4U 1700-37, GRO J1008-57, 4U 1909+07, 4U 2206+54, SW J2000.6+3210, SMC X-1, EXO 2030+375, 4U 1822-37,KS 1947+300, IGR J16207-5129, IGR J17544-2619, and IGR J18410-0535. Given that thenature of companion stars among the two lists is mixed (see Table. 1 of Sidoli & Paizis 2019),we see that this bi-modal behaviour cannot be distinguished on the basis of their companion(Be XRBs or supergiants) as illustrated in the Corbet diagram for the X-ray pulsars in ourstudy in Fig.2. Note that we did not use A 0535+026, LMC X-4, and GX 1+4 in this plot, as E cut for these three sources is obtained fromthe NPEX, FDCUT, and NEWHCUT models, respectively. All these models are mathematically different from HIGHECUTand thus the measured value of E cut has a different meaning. © , 000–000 omprehensive analysis
10 100 1000 10 E c u t ( k e V ) L X (in units of 10 erg s −1 ) LMXBsBe XRBssg HMXBsSFXTs
Figure 1.
Plot of cutoff energy versus the X-ray luminosity. To identify the apparent dichotomy, we mark the two groups inblue and magenta with SFXTs marked in grey.
Since we find only three sources with E cut within the range of 7-14 keV, there appears tobe a paucity of sources with E cut around 10 keV, which is the same energy range where thereis a gap between the XIS and PIN energy band. We therefore checked if this distribution is anartifact of the energy ranges considered here by simulating several fake spectra with varyingcutoff energies distribute from 4-20 keV and fitting them. For all these fake spectra, werecovered the same spectral parameters as the input model thereby validating the robustnessof our results.Additionally, since the cutoff energies in the second group are spread around 6 keV, andmost of the sources exhibit an iron emission line around 6.4 keV, there may be concerns abouta possible mix-up between the iron line and cutoff energies for these sources. However, itshould be noted that since the iron line emission in these sources are narrow features and © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul P s p i n ( s ) P orb (d) LMXBsBe XRBssg HMXBsSFXTs
Figure 2.
Corbet diagram of the pulsars in our study. Sources marked in blue and magenta are for the sources with cutoffenergy greater than and less than 10 keV respectively. As seen in the plot, the distinction is not on the basis of the companionstar being a Be X-ray binary or and OB star. prominently stand out in the X-ray emission, we can easily disentangle between iron lineand continuum parameters for a CCD spectrum. We also cross-checked this by simulatingseveral fake spectra with varying cutoff energies (3-7 keV) and narrow iron lines of differentequivalent width and were able to fully recover the input parameters, hence supportingour claim. Furthermore, there is no correlation between the cutoff energy and the iron lineparameters as seen in the confidence plots for the iron line energy versus the cutoff energy,and the iron line normalization versus the cutoff energy for this group in Fig. A1 and FigA2 in the Appendix.In order to test the bi-modality against reported values in literature, we also checkedthe cutoff energy in literature (with RXTE) obtained using the same model as in this work.These values are tabulated in Table 5. We make a histogram of these literature values andthe ones we obtain from our work and find that although for some sources, the cut offenergy is different in these two instruments, an apparent bi-modality is visible in both thecut-off energy distribution as seen in top panel of Fig. 3. It should be pointed out that we If the equivalent width of the iron line is smaller, it only gives large uncertainty for the line flux but does not affect thecontinuum parameters © , 000–000, 000–000
Corbet diagram of the pulsars in our study. Sources marked in blue and magenta are for the sources with cutoffenergy greater than and less than 10 keV respectively. As seen in the plot, the distinction is not on the basis of the companionstar being a Be X-ray binary or and OB star. prominently stand out in the X-ray emission, we can easily disentangle between iron lineand continuum parameters for a CCD spectrum. We also cross-checked this by simulatingseveral fake spectra with varying cutoff energies (3-7 keV) and narrow iron lines of differentequivalent width and were able to fully recover the input parameters, hence supportingour claim. Furthermore, there is no correlation between the cutoff energy and the iron lineparameters as seen in the confidence plots for the iron line energy versus the cutoff energy,and the iron line normalization versus the cutoff energy for this group in Fig. A1 and FigA2 in the Appendix.In order to test the bi-modality against reported values in literature, we also checkedthe cutoff energy in literature (with RXTE) obtained using the same model as in this work.These values are tabulated in Table 5. We make a histogram of these literature values andthe ones we obtain from our work and find that although for some sources, the cut offenergy is different in these two instruments, an apparent bi-modality is visible in both thecut-off energy distribution as seen in top panel of Fig. 3. It should be pointed out that we If the equivalent width of the iron line is smaller, it only gives large uncertainty for the line flux but does not affect thecontinuum parameters © , 000–000, 000–000 omprehensive analysis one-to-one correspondence on the values of cutoff energies from these twoinstruments since they cover different energy ranges and also because for some sources, theX-ray spectrum evolve with flux (see Reig & Nespoli 2013). The interesting finding here isthe apparent bi-modal distribution of cut-off energy for sources even within the same class.We also carried out a number of statistical tests to quantify the bi-modality in thedistribution of cut-off energy so obtained. We first performed a 2D KS test for these twobranches. The 2D test allow us to compare how different the two distributions are from eachother. For the L X versus E cut variation for red and green groups, the p value is low ( ∼ × − ) indicating that these two distributions are different.However, since our main finding is the bi-modality in the distribution of cut-off energy,we next focus on this. We performed a Dip test (Hartigan & Hartigan 1985) and obtained a p -value of 0.15. The rule of thumb for interpretation of this test is that p -values less than 0.05indicate significant bimodality and values in the range of 0.05-0.10 suggest bimodality withmarginal significance. Therefore, while the Dip test do not favor multimodality in the cut-offenergy, it should be remarked that this Hartigan’s Dip test work best for small samples butwith large bumps . The alternative approach is therefore to search for modes in the datadistribution by generating the probability densities of the cut-off energies. In order to dothis, we first calculate the best value of band-width based on Silverman’s band-width testand then look for points of inflexion in the Kernel (probability) Density Estimates (KDE)using this band-width as the smoothing function. As seen in the middle of Fig. 3, we findtwo points of inflexion at ∼ χ ∼ >
30) values of χ .Next, we extracted the PIN pulse profiles (15.0-70.0 keV) for the pulsating sources ineach branch to check if a different beaming mechanism (fan or pencil; Davidson & Ostriker https://github.com/syrte/ndtest/blob/master/ndtest.py https://github.com/BenjaminDoran/unidip https://towardsdatascience.com/modality-tests-and-kernel-density-estimations-3f349bb9e595 © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul . Asshown in Fig. 4, the single and double peaked pulse profiles indicating pencil and fan beamrespectively are spread out in both groups at random. We therefore also conclude that thecurrent bi-modality in the distribution between E cut and L X is not based on the beamingpattern of X-rays. As the beaming pattern depends on the accretion rate, ˙ M , the bi-modalityis independent of beaming pattern and the accretion rate as well. That the bi-modality in E cut is independent of the X-ray luminosity (and hence the accretion rate), can also be seefrom Fig. 1. We maintained the same colour scheme for the different sources in all otherfigures that we describe in the following sections to investigate alternative possibilities thatcould give rise to the observed behavior.We inspected the ratio of the source spectra to Crab to see if the E cut values measuredare also evident in the Crab spectral ratio. We however found that since CRSF is ratherstrong for many sources, the spectral curvature is affected by this absorption feature inthe X-ray spectrum for many sources and bi-modality therefore is not straightforward tointerpret from this exercise.Furthermore, in order to check the robustness of our results, with another model, wealso tried fitting the 29 sources (that required a cutoff energy) with another phenomologicalmodel ‘FDCUT’ in XSPEC . We could reasonably fit 26 sources with FDCUT, albeit withmuch higher reduced chi-square than HIGHECUT for each source. We find that even whenfitting with FDCUT, there are two branches distinguished in the L X versus E cut plane –similar to what we see with HIGHECUT. Note, however that since the cutoff energies forboth these models are mathematically different from each other, their numerical values donot match.All these factors indicate that the bi-modality in the X-ray spectral shape of these groupsare possibly real and further investigations with physical models will allow us to furtherunderstand the cause for this. Such detailed studies is however beyond the scope of thiscurrent work. We did not extract the pulse profiles of the two sources 4U 1822-37, due to the very low pulse fraction (see Sasano et al.2014), and V 0332+53, due to the limited statistics of the available
Suzaku data. © , 000–000 omprehensive analysis Figure 3.
Top: Histogram of cutoff energies from RXTE in red and the current work in gray. The RXTE measurementsare indicative of the bi-modality as found in the
Suzaku measurements. Middle: The KDE plotted (with a chosen Silvermanbandwidth of 3) demonstrate that there are two peaks in the data at ∼ ∼ Suzaku data with finer binning compared to top and middle figure. The histogramfits well with a bi-modal function plotted in green as compared to single Gaussian fits shown by red line (the trailing edge ofGaussian). © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul4.1.2 Γ versus L X We report the dependence of Γ as a function of L X in the case of neutron star HMXBs(including Be XRBs, SGXBs, SFXTs and a few LMXBs), accreting high magnetic field NSin LMXBs spanning over five orders of magnitude in X-ray luminosity. As we show in topof Fig. 5, we find that for all these sources Γ and L X are marginally anticorrelated with thebest-fit to all our data as: Γ = a log L X + b, where a = -0.25 ± ± L X in the case of Be XRBs have been previously investigatedby Reig & Nespoli (2013) who found that Γ and L X anticorrelate with the X-ray flux duringthe low X-ray intensity (sub-critical) states of these sources, while a positive correlation ismeasured during the high intensity (super-critical) states. Their study spanned two ordersof magnitude variation in L X .It should be noted that most of the sources in our sample are in the sub-critical luminosityregime (see section 5) and our findings are therefore consistent with the anti-correlation seenby Reig & Nespoli (2013) for individual sources.The luminosity span in the current work is however much larger than the RXTE obser-vation of Reig & Nespoli (2013) and while the RXTE observations focused on the evolutionof spectra for individual sources (using multiple observations of same Be XRB pulsars atdifferent luminosities), we focus on the overall ‘class’ behaviour of the sources as a functionof luminosity. Another improvement with the previous paper is that for the RXTE observa-tions, the authors froze the N H values for most of the sources while in our analysis - giventhe better low energy coverage of XIS - we were able to constrain both the photon indexand the N H independently (see contour plots, Fig. A3 and Fig. A4 in Appendix) in mostcases . E fold versus L X In models of the X-ray spectrum, E fold is a measure of the electron temperature of theinfalling plasma. An anti-correlation between luminosity and E fold has been reported earlierfor individual sources like A 0535+26, RX J0440.9+4431, for example (M¨uller et al. 2013;Ferrigno et al. 2013). It is for the first time that we present here a comprehensive behaviourof the E fold dependence on L X using a wider sample. In the bottom panel of Fig. 5, we except some systems where the line of sight absorption is very low, like LMC X-4, Her X-1, SMC X-1 etc; see Table 2 © , 000–000 omprehensive analysis E fold value show a weak anti-correlation with thePearson co-efficient for these two quantities being -0.19. E fold versus E cut We find that the sources in Branch 2 (magenta) have a somewhat larger median of E fold thanthose in Branch 1 (blue). A plot of their variation is shown in Fig. 6. We remark here thatwe could independently constrain both the E cut and E fold as seen in the confidence plots inAppendix (Fig. A5 and Fig. A6) and there is no degeneracy between these two quantitiesfor both groups.A similar correlation between these two quantities has also been reported earlier byMakishima et al. 1999 where the cutoff energies seem to be divided into two groups (theirFig. 12 b) less than and above 10 keV. The authors however do not comment about this intheir paper. E cut versus E cyc The variation of E cut with E cyc for HMXBs has been investigated in earlier works. Coburn et al.(2002) and Makishima et al. (1999) used RXTE and
Ginga data respectively to obtain therelationship E cut ∝ E . cyc for E cyc below 35 keV. Thanks to the broadband spectral capabilityof Suzaku , in our analysis, we show that the correlation between these two quantities (con-tour plots in Fig. A7 in Appendix) is not unique but rather have a complex behaviour (leftof Fig. 7). The sources in blue branch can be fitted to a functional form of E cut ∝ E . ± . cyc (marked by the black line). The functional form for sources in magenta is E cut ∝ E . ± . cyc (black dashed line). In order to make a comparison with the latest result, we digitizedthe graph in Staubert 2003 to fit their Fig. 8 and find that in their work, they report: E cut ∝ E . − . , . cyc which is consistent with our results for both groups within errors.It should however be noted that if we allow for an offset, we get a different best fit result of E cut = 8 + E . cyc and E cut = 5 × E . cyc . Therefore, while various forms work in the correlationbetween these quantities and the correlation is not mathematically unique, it is evidentvisually that the blue branch does have a steeper slope in this graph. We also remark herethat the values of E cyc we obtain from this work are close to values obtained in Coburn et al. © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul E cut which is possibly not surprising since wedo not expect a one-to-one correspondence on the values of cutoff energies from RXTE and Suzaku as they cover different energy ranges and also because for some sources, the X-rayspectrum evolve with flux (see Reig & Nespoli 2013). W c versus E cyc The variation of the CRSF width versus E cyc is shown on the right side of Fig. 7. In agreementwith the results of Coburn et al. (2002), we observe a linear correlation between the twoquantities. We are aware that using a HIGHECUT model can sometimes lead to artificialwidening of the CRSF energy if E cyc and E cut are close to each other. To mitigate this,we took great care in constraining the width of the CRSF properly and cross-checked thevalues with those available in literature. For example, the three sources (1A 1118-61, GX301-2 and GX 304-1), where we obtain large widths are consistent with their literature values(Suchy et al. 2012, 2011; Jaisawal, Naik & Epili 2016). From our fits of the broadband data,we find W c ∝ E (2 . ± . cyc . Overall, as we see from Table 2 and in Fig. 8 that the higher thevalue of cyclotron line energy, the deeper the line is. α flux versus continuum flux From Fig. 9, we see that the
Suzaku data of the considered sources suggest a strong corre-lation between the continuum flux and the Fe K α flux. Such a correlation is expected andwas also previously reported by Gim´enez-Garc´ıa et al. (2015) and Torrej´on et al. (2010) butover a smaller range of continuum flux. α iron line versus L X On the right side of Fig. 9, we show the lack of any clear correlation between the equivalentwidth of the iron K α line and the source X-ray luminosity. An anticorrelation between thesetwo parameters have been reported earlier in the literature by Gim´enez-Garc´ıa et al. (2015),Vasylenko, Zhdanov & Fedorova (2015), and Torrej´on et al. (2010). This anticorrelation isusually interpreted in terms of the so called Baldwin effect (Baldwin 1977). As previousstudies were carried out in a limited energy range, we checked that our results did not We remark here that all spectra used for the current analysis were cumulated outside X-ray eclipses. © , 000–000, 000–000
Suzaku data of the considered sources suggest a strong corre-lation between the continuum flux and the Fe K α flux. Such a correlation is expected andwas also previously reported by Gim´enez-Garc´ıa et al. (2015) and Torrej´on et al. (2010) butover a smaller range of continuum flux. α iron line versus L X On the right side of Fig. 9, we show the lack of any clear correlation between the equivalentwidth of the iron K α line and the source X-ray luminosity. An anticorrelation between thesetwo parameters have been reported earlier in the literature by Gim´enez-Garc´ıa et al. (2015),Vasylenko, Zhdanov & Fedorova (2015), and Torrej´on et al. (2010). This anticorrelation isusually interpreted in terms of the so called Baldwin effect (Baldwin 1977). As previousstudies were carried out in a limited energy range, we checked that our results did not We remark here that all spectra used for the current analysis were cumulated outside X-ray eclipses. © , 000–000, 000–000 omprehensive analysis α emissionand the photoelectric cross section drops rapidly so that photons above 12 keV do notcontribute much in this process) and the energy range 4.95-7.75 keV as done in Torrej´on et al.(2010). In none of these cases we could find a clear indication of the anticorrelation reportedpreviously. In addition, we have also explored similar correlation using XMM data in adifferent work where we do not find any such relation between EW and luminosity (seeFig. 2 of Pradhan, Bozzo & Paul 2018).The existence of this X-ray Baldwin effect has been a matter of much debate for AGNsand possibly depend on different class of AGNs. A systematic analysis of many AGNs usingXMM and INTEGRAL data showed a very weak correlation between the EW of Fe K α lineand luminosity (see Vasylenko, Zhdanov & Fedorova 2015 and references therein). We willreturn to this discussion in section 5. α versus N H As visible from Fig. 10, we found a clear linear correlation between the hydrogen columndensity of the different sources and the equivalent width of their K α lines. Here N H = N H1 + N H2 * C V , where N H1 is the hydrogen column density along our line of sight to thesource, N H2 accounts for local absorption and C V is the covering fraction, the latter havinga wide range of 0.1-0.96 (see Table 2).Generally, it is well known that when a relatively limited energy range is used for theX-ray spectral fitting on data with limited statistical quality (eg 0.5-10.0 keV), the derivedvalues of the absorption column density and the power-law spectral index can be positivelycorrelated (a larger absorption column density can be used in such restricted energy rangeto fit the spectrum equally well with a steeper power-law). We also checked apriori thevariation of Γ as a function of N H to cross-check some of our results and find that this isnot the case for our spectral analysis, mainly thanks to the wide energy coverage of theinstruments onboard Suzaku (see contour plots, Fig. A3 and A4 in the Appendix). © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul
In this paper, we took advantage of the broad energy coverage of the instruments on-board
Suzaku to perform a systematic study of all observed neutron star HMXBs, including thehigh magnetic field LMXB pulsars displaying a cyclotron absorption line in their spectra. Theaim of our analysis was to explore a number of correlations between the spectral parametersof these sources reported previously in the literature. We used for the analysis of all sourcesa similar spectral model, in order to carry out a consistent investigation of all their spectralparameters. While detailed individual studies of most of these sources are already reportedin literature, our aim with this paper is to outline a comprehensive behaviour of HMXBs as aclass. Such a study was last carried out nearly two decades back in early 2000s (Coburn et al.2002).We summarize the main results of the paper below:(i) The broadband X-ray spectra of all HMXBs that we considered in this paper can bedescribed by a powerlaw component modified by a cutoff energy (where PIN data is usable).This spectral shape is usually interpreted in terms of Comptonization of the seed photonsproduced in the thermal mound of the neutron star accretion column by free electrons in theaccreting material. It is therefore expected that the spectral cutoff energies are proportionalto the electron temperature.A lack of correlation between E cut and L X has been reported earlier by White, Swank & Holt(1983). They point out, however, that the low luminosity systems in their sample do exhibita somewhat less sharp cutoffs at higher energies.In this study, we found all analyzed systems distributing on two different branches in the E cut and L X plot. For sources in Branch 1 (represented in blue in all plots), the cut-offenergy, that is a measure of the electron temperature, vary from 12-24 keV and increaseswith the mass accretion rate (in turns regulating the X-ray luminosity). For sources followingthe Branch 2 (magenta), E cut remains in a narrower range from 3-10 keV, even when L X changes by a factor of ∼ only on the luminosity. As we showed in Section 3, this different behaviourcannot either be simply ascribed to switches between a pencil and a fan beam emissiongeometry due to the lack of clear systematic variations in the pulse profiles of the analysedsources. To the best of our knowledge, so far, no theoretical explanation has been proposedin the literature to interpret this behaviour. © , 000–000 omprehensive analysis L X is known to exist in neutron star LMXBs andblack hole systems (for luminosities lower than ‘critical’ luminosity) where accretion takesplace through a disc (Allen et al. 2015; Wu & Gu 2008). Wijnands et al. (2015) suggestedthat in case of strongly magnetized neutron stars the presence of a magnetic field couldsignificantly alter the spectra, such that a direct comparison between HMXBs and LMXBsis not possible. For the present study, we make use of systems containing in all cases stronglymagnetized neutron stars (B & G) and accreting both from disks and from stellar winds.We found that the anticorrelation between Γ and L X still holds, indicating that in HMXBs,the Comptonization process makes the spectrum harder at increasing L X at least in thesub-critical regime (even though it might break down at luminosities higher than 10 ergs s − ).For black hole binaries, since this anti-correlation is valid for luminosities below a crit-ical value, we also cross-checked the X-ray luminosity of each pulsar against the criticalluminosity of each pulsar using Eqn. 3 (Becker et al. 2012) below. L crit = 1 . × erg s − × (cid:18) Λ0 . (cid:19) − / × w − / × (cid:18) M . ⊙ (cid:19) / (cid:18) R
10 km (cid:19) / (cid:18) B surf G (cid:19) / (3)where R , M , and B are, the radius, mass, and surface magnetic field strength (B in termsof ∼ G) of the neutron star, Λ = 1, and w = 1 for wind-accreting systems. For all thosesources with measured B (through CRSF line energy), we find that besides Her X-1, 4U0115+63, Cen X-3 and 1A 1118-61, all other sources are indeed in the sub-critical regime.(iii) An anticorrelation of E fold with L X indicates that with increasing luminosity, E fold (aproxy for electron temperature of the ‘infalling’ plasma) decreases. As the luminosity in-creases, the radiation field from the neutron star begin to affect the accretion flow andCompton cooling becomes more efficient (since scattering rate of photons off electrons in-crease). This leads to the shift of electron temperature toward lower energies with increasingluminosity giving rise to this anticorrelation of E fold with L X .(iv) From the variation of folding energy with cutoff energies, we see that smaller cutoffenergy imply larger folding energies. It has also been reported by earlier authors that thenon cyclotron-line pulsars should exhibit larger values of folding energy, (less steep spectralbreaks) due to their lack of the spectral trough caused by an absorption like feature in CRSF(Makishima et al. 1999). However, when we compared the folding energy of cyclotron linesources with the folding energy of non-cyclotron line sources, we see no such trend. © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul (v) The variation of E cut with E cyc has been studied in a number of earlier works (Makishima et al.1990, 1999; Coburn et al. 2002). Makishima et al. (1990) obtained a linear correlation be-tween E cut and E cyc (E cyc = 1.4-1.8 E cut ). From the measurements of E cut , they thus inferredthat the magnetic field of HMXBs was spanning a relatively narrow range (1-4 × G).Nine years later, these results were updated by Makishima et al. (1999). These authors useda larger sample of sources to prove that there exists a saturation of E cut at high values ofE cyc ( E cut ∝ E . cyc ). They interpreted this finding by suggesting that the presence of a ther-mal emission component can affect the position of the spectral energy break. Coburn et al.(2002) reconfirmed the same relationship, adding also new constrains on the saturation of E cut . The latter seems to be detected only below 35 keV. They also suggested the possiblepresence of two linear relations between E cut and E cyc , one below 35 keV and one above.Our current study has an added advantage of the broadband energy coverage compared tothese previous works in literature. We find that for higher values of magnetic field, the cutoffenergies tend to saturate for both these groups. This is possibly because there could be someother relativistic effects in the creation of the continuum that become important at at highervalues of magnetic field.(vi) The right panel of Fig. 7 shows that in the present study we found a relativelywell marked linear correlation between the energy of the cyclotron line and it’s width.Coburn et al. (2002) mentioned that the FWHM of a CRSF changes with the viewing angle θ of the observer with respect to the magnetic field as follows: W c ∝ E C p kT e | cos( θ ) | (4)This implies that two quantities, the characteristic electron temperature, kT e and θ (an-gle between the observer line of sight and the neutron star magnetic field) for all sourcesconsidered in this paper are not dramatically different. The same linear correlation was alsofound by Coburn et al. (2002) and are indicative of small values of kT e . The reason for thisis that the matter being accreted onto the hot spots form an accretion column and in thesteady state, the amount of matter falling in balances the matter spreading out at the basewhere the mound parameters (area, density etc) are similar for most sources irrespective ofaccretion rate. Our results support their argument since despite five orders of magnitudechange in L X in the current work, our findings are indicative of the same linear correlation.Alternatively, this correlation can also be explained if the temperature is tied to the magnetic © , 000–000 omprehensive analysis θ is also very small. Since thebulk motion of the electrons (which in turn depend on the accretion rate) also play a rolein line broadening, we should have expected this correlation to smear out. This brings us toa very interesting point as has been discussed in Coburn et al. (2002) that accretion couldhave an influence on the relative orientation of spin and magnetic axes, with the spin axispresumably being influenced by the age of the system and the accretion timescales making θ very small. This correlation can be further tested for individual sources by detailed pulseprofile modelling of each source and measuring the width of the CRSF line with varying θ .It is interesting to mention here that in Staubert et al. 2019, there are two groups inwidth of CRSF versus energy (their Fig. 12) where the authors argue that the second slopeare mostly consist of ‘outlier” sources. We find similar scatter in the depth of CRSF versusCRSF energy (Fig. 8) although the sources do not hold a on-to-one correspondence in boththe works .(vii) Our analysis also confirmed the presence of a strong correlation between the X-raycontinuum of all the sources where a K α iron emission line is found and the line flux. Thisis expected, since the Fe K α line is thought to be produced in these systems due to thereprocessing of the X-ray continuum by iron atoms in the matter surrounding the neutronstar (being either the material from the stellar winds in HMXBs or the disk in LMXBs).As was also discussed by Torrej´on et al. (2010) and Gim´enez-Garc´ıa et al. (2015), we thusexpect the Fe K α line flux to increase with the flux of the continuum.Historically, an inverse correlation was obtained between the EW of C IV lines and theUV luminosity in AGNs (Baldwin effect; Baldwin 1977). Analogously, correlation studies be-tween the EW of K α lines and L X have been carried out for AGNs and XRBs providing indi-cations for an inverse correlation (Gim´enez-Garc´ıa et al. 2015; Vasylenko, Zhdanov & Fedorova2015; Torrej´on et al. 2010). This anticorrelation between the EW of K α lines and L X iscalled the X-ray Baldwin Effect. At odds with the results of Gim´enez-Garc´ıa et al. (2015)and Torrej´on et al. (2010), we did not detect any significant correlation between the EW ofthe Fe K α lines and the source X-ray luminosity. As discussed by Torrej´on et al. (2010), we Note that there is often a variation in CRSF parameters over different time and/or spin phases © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul noticed in our case that a marginal correlation (not statistically significant) is visible whenthe EW of the K α line is plotted against the X-ray flux but the correlation disappears whenthe luminosity is used in place of the flux.The non-confirmation of the X-ray Baldwin effect for the Fe K α in X-ray binaries isprobably not surprising since there is no physical reason for the effect to hold true for XRBswith the neutral iron line. In case of AGNs the physical reason for the anti-correlation of EWof C IV lines with luminosity is that for higher luminosity the atoms are highly ionised anddo not produce C IV lines in same proportion. However, in the case of the neutral 6.4 keViron line in X-rays, if the increase in luminosity cause the ionisation to be so high as toremove the K-shell electrons, we should be seeing the Hydrogen like and Helium like ironatoms and the iron line would instead be seen at 6.7 and 6.9 keV instead of the neutral K α line at 6.4 keV. On the contrary, very few HMXBs like Cen X-3 (Naik, Paul & Ali 2011),OAO 1657-415 (Pradhan, Raman & Paul 2019),for example, show these emission lines.(viii) Finally, we also reported on the positive correlation between the EWs of the ironK α line and the absorption column density local to the HMXB sources ( N H ). This cor-relation is expected because a larger N H implies that more stellar wind material aroundthe neutron star is involved in the formation of a stronger iron line (see e.g., Inoue 1985;Pradhan et al. 2014, 2015; Gim´enez-Garc´ıa et al. 2015; Pradhan et al. 2019) except in somesources with accretion disk like SMC X-1, where a relatively low column density is seen(Pradhan, Maitra & Paul 2020). In others like the persistent Be XRB, SW J2000.6+3210,the iron line is almost undetectable since there is not enough matter surrounding the neutronstar to facilitate fluorescence (Pradhan et al. 2013).Although we have very few SFXTs compared to classical sg HMXBs in the current work,we note that the absorption column density (and EW) for these SFXTs are smaller whencompared to classical sgXBs (see Table 2). This motivated us to look into our findings withmore details by including a larger sample of SFXTs. We also therefore extended this studyby including XMM data and have discussed the findings in detail in Pradhan, Bozzo & Paul2018 which we refer to the reader for further details. We find that the lower N H and lowerEW should be expected for SFXTs. Such a difference is either due to faster (or rarer)stellar winds in SFXTs or due to the inhibition of accretion in SFXTs most of the time byother mechanisms like magnetic gating (Bozzo, Falanga & Stella 2008) leading to inefficientphotoionization of the stellar wind.We reported in the plots of Fig. 9 and Fig. 10 also the LMXBs considered in this paper for © , 000–000 omprehensive analysis In this section, we summarize the main results of our work discussed above. This classanalysis of the broad band X-ray spectrum of 39 accreting neutron star X-ray binariesindicate some interesting findings. (i) We find that the relationship between the cut-off energyand X-ray luminosity follow a bi-modal behaviour. The interpretation of such a dichotomyis not straightforward and is not a result of different companion stars (LMXBs, Be XRBs,sgXBs) or beaming patterns (explored through pulse profiles). We encourage further studiesusing physical continuum and line models in order to investigate this behaviour. (ii) Wealso find that the dependence of cut-off energies on the CRSF energy is not unique. Wealso confirm the previous findings of Coburn et al. 2002 that the width (and depth) of theCRSF is linearly correlated to the CRSF energy. (iii) We confirm the correlation betweenthe iron K α emission line and the X-ray continuum flux, between the EW of the iron K α line and absorption. This is expected since such lines are formed by the fluorescence of theX-ray continuum photons in interstellar matter around the NS in case of HMXBs. We alsonote that the EW and absorption are different between SFXTs and classical HMXBs andinterpret that as being caused by difference in stellar wind properties between these twosystems or a result of inhibited accretion in SFXTs during most times. Finally, (iv) we notethat the photon index and E fold is negatively correlated with luminosity, thus suggesting thatCompton cooling becomes more efficient at higher luminosities which makes the spectrumharder and also lowers the electron temperature of the plasma.Overall, we have updated the correlation between spectral parameters of accreting neu-tron stars taking advantage of the broadband energy coverage of Suzaku . Such a study waslong overdue in literature with the last such study made almost two decades back. © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul Vela X−1(2219, 5.5) XTE J1946+274(6281, 7)
4U 0114+65(3662, 6)
GX 304−1(22466, 7)
OAO 1657−415(5524, 6) N o r m a li ze d I n t e n s it y GRO J1008−57(12664, 6.5)
4U 1909+07(3356, 6)
4U 2206+54(729, 3.5) KS 1947+300(128377, 5) EXO 2030+375(58003, 7) SMC X−1(292633, 5)
SW J2000.6+3210(953, 5) Her X−1(36976, 19.5) Cen X−3(36259, 15.7)
4U 1626−67(4009, 19)
4U 0115+63(23965, 12.5)
4U 1907+09(495, 16) N o r m a li ze d I n t e n s it y
4U 1538−522(6472, 16) GX 301−2(1627, 29) Cep X−4(4888, 16)
IGR J16393−4643(2439, 20) N o r m a li ze d I n t e n s it y GX 1+40 0.5 1 1.5 20.811.2 PhaseA 0535+026
Figure 4.
Left: HXD-PIN (15-70 keV) pulse profiles of pulsars in the magenta branch. Right (top): HXD-PIN (15-70 keV)pulse profiles of pulsars in the blue branch. The first number in parenthesis in both the figures is the X-ray luminosity in unitsof 10 erg/s and the second number is the cutoff energy in keV. Right (bottom): Pulse profiles for three sources, LMC X-4,GX 1+4 and A 0535+026 which could not be fit with the HIGHECUT model. See text for details. © , 000–000 omprehensive analysis
10 100 1000 10 Γ L X (in units of 10 erg s −1 ) LMXBsBe XRBssg HMXBsSFXTs Γ =1.89*L X33−0.068 Γ =1.76*L X33−0.058
10 100 1000 10 E f o l d ( k e V ) L X (in units of 10 erg s −1 ) LMXBsBe XRBssg HMXBsSFXTs
Figure 5.
Top: Variation of photon index with luminosity. The black solid line represents the best-fit to the data (Γ ∝ L − α X with α = 0.058 ± α = 0.068 ± E fold energy with X-ray luminosity. Both the figures are marked with thesame colour coding as in Figure 1. © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul E f o l d ( k e V ) E cut (keV) LMXBsBe XRBssg HMXBsSFXTs
Figure 6.
Variation of E fold with E cut marked with the same colour coding as in Figure 1.
20 40 601020 E c u t ( k e V ) E cyc (keV)E cut = 2.1 E cyc0.29 E cut = E cyc0.82 U +
09 4 U − C e n X − C e p X − U − GX − U + V e l a X −
4U 1822−37 X TE J +
274 4 U −
37 1 A − GX − H e r X −
20 40 6005101520 σ ( k e V ) E cyc (keV) σ α E cyc2.2 U +
09 4 U −
522 4 U + V e l a X − C e n X − C e p X − U −
4U 1626−67 X TE J + U − GX − A − GX − Her X−1
Figure 7.
Left: E cut versus E cyc showing two scaling laws for two groups. Right: Positive correlation between CRSF width W c versus E cyc . All the figures are marked with the same colour coding as in Figure 1. © , 000–000, 000–000
Left: E cut versus E cyc showing two scaling laws for two groups. Right: Positive correlation between CRSF width W c versus E cyc . All the figures are marked with the same colour coding as in Figure 1. © , 000–000, 000–000 omprehensive analysis
20 30 40 50 60123 D e p t h E cyc (keV) U +
09 4 U −
522 4 U + V e l a X − C e n X − C e p X −
4U 1822−37 U − X TE J +
4U 1700−37 GX − A − GX − Her X−1
Figure 8.
Plot of CRSF depth versus CRSF energy. All the figures are marked with the same colour coding as in Figure 1. −12 −11 −10 −9 −8 −7 − − − . F e K α ( pho t on s c m − s − ) Continuum flux (erg/s/cm ) LMXBsBe XRBssg HMXBsSFXTs
Figure 9.
Plot of the iron line flux versus continuum flux marked with the same colour coding as in Figure 1. © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul E W ( k e V ) N H *10 atoms cm −2 LMXBsBe XRBssg HMXBsSFXTs
10 100 1000 10 E W ( k e V ) L X (in units of 10 erg s −1 ) LMXBsBe XRBssg HMXBsSFXTs
Figure 10.
Left: Plot of the equivalent width versus luminosity. Right: Plot of absorption column density versus the EW ofiron line. We use for all plots the same color coding of Fig. 1. © , 000–000, 000–000
Left: Plot of the equivalent width versus luminosity. Right: Plot of absorption column density versus the EW ofiron line. We use for all plots the same color coding of Fig. 1. © , 000–000, 000–000 o m p r e h e n s i ve a n a l y s i s Figure 11.
Spectra of all considered sources together with residuals from the best fits. All best fit results are reported in Table 2 −3 no r m a li ze d c oun t s s − k e V − Her X−1 ( d a t a − m od e l ) / e rr o r Energy (keV) −3 no r m a li ze d c oun t s s − k e V −
4U 0115+63 ( d a t a − m od e l ) / e rr o r Energy (keV) −3 no r m a li ze d c oun t s s − k e V − Cen X−3 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −5 −4 −3 no r m a li ze d c oun t s s − k e V −
4U 1626−67 ( d a t a − m od e l ) / e rr o r Energy (keV) −4 −3 no r m a li ze d c oun t s s − k e V − XTE J1946+274 ( d a t a − m od e l ) / e rr o r Energy (keV) −3 no r m a li ze d c oun t s s − k e V − Vela X−1 ( d a t a − m od e l ) / e rr o r Energy (keV) −4 −3 no r m a li ze d c oun t s s − k e V −
4U 1907+09 ( d a t a − m od e l ) / e rr o r Energy (keV) −4 −3 no r m a li ze d c oun t s s − k e V −
4U 1538−522 ( d a t a − m od e l ) / e rr o r Energy (keV) −4 −3 no r m a li ze d c oun t s s − k e V − GX 301−2
105 20 50−202 ( d a t a − m od e l ) / e rr o r Energy (keV) −3 no r m a li ze d c oun t s s − k e V −
1A 1118−61 ( d a t a − m od e l ) / e rr o r Energy (keV)10 −4 −3 no r m a li ze d c oun t s s − k e V −
4U 0114+65 ( d a t a − m od e l ) / e rr o r Energy (keV) no r m a li ze d c oun t s s − k e V − GX 304−1 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −5 −4 −3 no r m a li ze d c oun t s s − k e V − OAO 1657−415
105 20 50−4−2024 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −4 −3 no r m a li ze d c oun t s s − k e V − Cep X−4 ( 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 − GRO J1008−57 ( d a t a − m od e l ) / e rr o r Energy (keV)10 −4 −3 no r m a li ze d c oun t s s − k e V −
4U 1909+07
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 − IGR J16393−4643
105 20−202 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −4 −3 no r m a li ze d c oun t s s − k e V −
4U 2206+54 ( 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 − SW J2000.6+3210 ( d a t a − m od e l ) / e rr o r Energy (keV) © R A S , M N R A S , P . P r adha n , B . P a u l , E . B o zz o , C . M a i t r a , B . C . P a u l Figure 12.
Spectra of all considered sources together with residuals from the best fits. All best fit results are reported in Table 2..contd −3 no r m a li ze d c oun t s s − k e V − LMC X−4 ( 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 − KS 1947+300
102 5 20 50−202 ( 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 − EXO 2030+375
102 5 20 50−202 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −4 −3 no r m a li ze d c oun t s s − k e V − SMC X−1 ( d a t a − m od e l ) / e rr o r Energy (keV) −3 no r m a li ze d c oun t s s − k e V − V 0332+53 ( d a t a − m od e l ) / e rr o r Energy (keV) −3 no r m a li ze d c oun t s s − k e V − A 0535+026 ( 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 −
4U 1822−37 ( 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 − GX 1+4
105 20 50−4−202 ( 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 − IGR J16318−4848
10 20 50−202 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −5 −4 −3 no r m a li ze d c oun t s s − k e V − IGR J16207−5129
105 20 50−202 ( 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 −
4U 1700−37
102 5 20 50−2024 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −4 −3 no r m a li ze d c oun t s s − k e V − IGR J18410−0535 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −5 −4 −3 no r m a li ze d c oun t s s − k e V − IGR J17544−2619 ( d a t a − m od e l ) / e rr o r Energy (keV) −5 −4 −3 no r m a li ze d c oun t s s − k e V − IGR J16195−4945 ( d a t a − m od e l ) / e rr o r Energy (keV) −3 no r m a li ze d c oun t s s − k e V − IGR J16493−4348 ( d a t a − m od e l ) / e rr o r Energy (keV)10 −3 −3 −3 no r m a li ze d c oun t s s − k e V − IGR J16465−4507 ( d a t a − m od e l ) / e rr o r Energy (keV) 0.012×10 −3 −3 no r m a li ze d c oun t s s − k e V − IGR J16479−4514 ( d a t a − m od e l ) / e rr o r Energy (keV) −3 −3 −3 no r m a li ze d c oun t s s − k e V − IGR J17391−3021 ( d a t a − m od e l ) / e rr o r Energy (keV) −4 −3 no r m a li ze d c oun t s s − k e V − IGR J08408−4503 ( d a t a − m od e l ) / e rr o r Energy (keV) 10 −4 −3 no r m a li ze d c oun t s s − k e V − IGR J00370+6122 ( d a t a − m od e l ) / e rr o r Energy (keV) © R A S , M N R A S , able 1: Observation Log and distances to the different sources considered inthe present paper.Source OBSID WINDOW MODE DISTANCE (kpc) ReferenceHer X-1 100035010 1/8 6.6 ± ± ± ± ± . +5 . − . Nespoli, Fabregat & Mennickent 20084U 1538-522 407068010 1/4 6.4 ± ∗ Kaper, van der Meer & Najarro 20061 A1118-61 403049010 1/4 5.2 ± ± ± ± ± ± ± . +3 . − . Mason & Cordova 1982GX 1+4 405077010 1/4 3-15 Chakrabarty & Roche 1997GRO J1008-57 902003010 1/4 5 ∗ Coe et al. 19944U1909+07 405073010 1/4 7.00 ± ∗ Chaty et al. 20084U 2206+54 402069010 1/4 2.90 ± ∗ Masetti et al. 2008LMC X-4 702036020 1/8 50 ∗ Hung et al. 2010KS1947+300 908001020 1/4 10.4 ± ± MC X-1 706030100 Off 60.0 ∗ Neilsen, Hickox & Vrtilek 2004V 0332+53 904004010 1/4 7.5 ± ± . +8 . − . Nespoli, Fabregat & Mennickent 2008IGR J18410-0535 505090010 Off 3 . +2 . − . Nespoli, Fabregat & Mennickent 2008IGR J17544-2619 402061010 1/4 3.20 ± ∗ Tomsick et al. 2006IGR J16465-4507 401052010 Off 9 . +14 . − . Heras & Walter 2004IGR J16479-4514 406078010 Off 7.50 ± ∗ Rahoui et al. 2008IGR J08408-4503 404070010 Off 3.0 ∗ Masetti et al. 2006IGR J00370+6122 402064010 1/4 3.3 ∗ Reig et al. 2005 ∗ Distance error is not known so error is assumed as 1 kpc.
Table 2: Parameters of the continuum and absorption features. Errors quoted are for 90per cent confidence rangeSource N a H1 N a H2 C V Γ Γ bnorm E cut E fold E C D W bb (kT) bb cnorm χ /dof(keV) (keV) (keV) (keV)Her X-1 0.02 - - 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . . . . +0 . − . . +0 . − . - - 1 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +2 . − . . +0 . − . . +0 . − . . +0 . − . - - 0 . +0 . − . . +0 . − . . +0 . − . . +2 . − . . +0 . − . . +0 . − . . +1 . − . . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +3 . − . . +1 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +3 . − . . +0 . − . . +0 . − . .
37 - - 1.64/6644U 1907+09 2 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +2 . − . . +1 . − . . +0 . − . . +0 . − . . +0 . − . - - 1.07/882 U 1538-522 1 . +0 . − . - - 1 . +0 . − . . +0 . − . . +1 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - 1.22/710GX 301-2 14 . +0 . − . . +1 . − . . +0 . − . . +0 . − . . +1 . − . . +5 . − . . +4 . − . . +0 . − .
19 - - 1.11/5291A 1118-61 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +1 . − . - - 1.61/4684U 0114+65 4 . +0 . − . . +15 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +2 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +2 . − . . +2 . − . . +0 . − . . +2 . − . - - 1.39/673OAO 1657-415 16 . +0 . − . . +5 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - - - 1.31/420Cep X-4 0 . +0 . − . . +59 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +0 . − . n . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +4 . − . - 41 . +1 . − . . +3 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +8 . − . . +0 . − . . +9 . − . . +0 . − . . +1 . e − − . e − GX 1+4 nhe . +0 . − . . +7 . − . . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +1 . − . - - - - - 1.65/519GRO J1008-57 ∗∗ . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - 0 . +0 . − . . +0 . − . . +0 . − . - - 1 . +0 . − . . +0 . − . . +0 . − . . +2 . − . - - - - - 1.27/288IGR J16393-4643 26 . +0 . − . - - 0 . +0 . − . . +0 . − . . +1 . − . . +1 . − . - - - - - 1.22/2824U 2206+54 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +4 . − . - - - 1 . +0 . − . . +0 . − . . +0 . − . - - 0 . +0 . − . . +0 . − . . +0 . − . . +7 . − . - - - 1 . +0 . − . . +0 . − . . +8 . − . . +0 . − . . +0 . − . . +0 . − . . f +1 . − . . +0 . − . - - - 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - 0 . +0 . − . . +0 . − . . +0 . − . . +4 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - - - 1.35/452SMC X-1 0.05 - - 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - 0 . +0 . − . . +0 . − . . +0 . − . - - 1 . +0 . − . . +0 . − . . +1 . − . . +0 . − . - - 1 . +0 . − . . +0 . − . - - - - - - - 1.26/259IGRJ16318-4848 122 . +3 . − . - - 1 . +0 . − . . +0 . − . . +1 . − . . +4 . − . - - - - - 1.26/223IGRJ16207-5129 12 . +1 . − . - - 1 . +0 . − . . +0 . − . . +5 . − . . +18 . − . - - - - - 0.99/297IGR J18410-0535 1 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +31 . − . - - - - - 1.07/554IGR J17544-2619 1 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +1 . − . . +1 . − . - - - - - 1.07/496IGR J16195-4945 8 . +0 . − . - - 1 . +0 . − . . +0 . − . - - - - - - - 1.20/697IGR J16465-4507 1 . +0 . − . . +1 . − . . +0 . − . . +0 . − . . +0 . − . - - - - - - - 1.03/695IGR J16479-4514 2 . +1 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - - - - - 0.85/150IGR J17391-3021 1 . +0 . − . . +1 . − . . +0 . − . . +0 . − . . +0 . − . - - - - - - - 0.89/211IGR J08408-4503 0.1 4 . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - - - - - 1.22/504IGR J00370+6122 0 . +0 . − . . +1 . − . . +0 . − . . +0 . − . . +0 . − . - - - - - - - 0.96/521 a In units of 10 atoms cm − ; b In units of photons keV − cm − s − at 1 keV; c In units of L / D , where D is the distance to the source in units of 10 kpc. ∗ The cyclotron line features are at 10 keV, an energy range that is not covered by
Suzaku data. ∗∗ The cyclotron line feature is at 86 keV, i.e., beyond the energy range covered by
Suzaku data in this paper. f Here FDCUT is used, n NPEX is used, n he NEWHCUT is used with width = 20 keV able 3: Cyclotron line harmonics detected in a few sources among those usedin the present paper.Source E C D W E C D W (keV) (keV) (keV) (keV)4U 0115+63 17 . +0 . − . ± . +0 . − . . +1 . − . ± . +0 . − . . +0 . − . . +1 . − . - - -4U 0114+65 36 . +3 . − . . +0 . − . EL (keV) EQ (keV) EL (keV) EQ (keV) EL (keV) EQ (keV) EL (keV) σ (keV)Her X-1 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − .
4U 0115+63 6 . +0 . − . . +0 . − . - - - - - -Cen X-3 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - -4U 1626-67 6 . +0 . − . . +0 . − . - - - - 0 . +0 . − . . +0 . − . - - - - - - 1 . +0 . − . . +0 . − . . +0 . − . - - - - - -Vela X-1 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - 0 . +0 . − . . +0 . − . . E − . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - -4U 1528-522 6 . +0 . − . . +0 . − . - - - - - - X 301-2 6 . +0 . − . . +0 . − . - - - - 2 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - -4U 0114+65 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - -GX 304-1 6 . +0 . − . . +0 . − . - - - - - -OAO 1657-415 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - -Cep X-4 6 . +0 . − . . +0 . − . - - - - - -4U 1700-37 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - -A0535+026 6 . +0 . − . . +0 . − . - - - - - -4U 1822-37 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . - -GX 1+4 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - -GRO J1008-57 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - -4U 1909+07 6 . +0 . − . . +0 . − . - - - - - -IGR J16393-4643 6 . +0 . − . . +0 . − . - - - - - -4U 2206+54 6.4 0 . +0 . − . - - - - - -SW J2000.6+3210 6 . +0 . − . . +0 . − . - - - - - -LMC X-4 6 . +0 . − . . +0 . − . - - - - 0 . +0 . − . . +0 . − . KS 1947+300 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - - -EXO 2030+375 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - 2.5 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - - 1 . +0 . − . . +0 . − . . +0 . − . . +0 . − . V 0332+53 - - - - - - - -IGR J16493-4348 6 . +0 . − . . +0 . − . - - - - - -IGRJ16318-4848 6 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . - -IGRJ16207-5129 6 . +0 . − . . +0 . − . - - - - - -IGR J18410-0535 6 . +0 . − . . +0 . − . - - - - - -IGR J17544-2619 6 . +0 . − . . +0 . − . - - - - - -IGR J16195-4945 6 . +0 . − . . +0 . − . - - - - - -IGR J16465-4507 6.4 0.001 - - - - - -IGR J16479-4514 6 . +0 . − . . +0 . − . - - - - - -IGR J17391-3021 - - - - - - - - GR J08408-4503 - - - - - - - -IGR J00370+6122 - - - - - - - - P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul
Table 5.
Literature values of cut-off energies from RXTE data. To maintain consistency with the cutoff energy measurements,we take these values from the same instrument.Source Ecut positive error negative error RefHer X-1 22 1.4 0.8 (Coburn et al. 2002)4U 0115+6 10 0.5 0.4 (Coburn et al. 2002)Cen X-3 21.3 0.2 0.4 (Coburn et al. 2002)4U 1626-67 6.8 0.3 0.3 (Coburn et al. 2002)XTE J1946+274 22 0.8 0.9 (Coburn et al. 2002)Vela X-1 17.9 0.3 0.4 (Coburn et al. 2002)4U 1907+09 13.5 0.2 0.2 (Coburn et al. 2002)4U 1538-52 13.57 0.04 0.05 (Coburn et al. 2002)GX 301-2 17.3 0.1 0.2 (Coburn et al. 2002)1A 1118–61 5.88 0.17 0.19 (Devasia et al. 2011)GX 304-1 6.08 0.16 0.19 (Rothschild et al. 2017)Cep X-4 16.3 0.1 0.1 (Koyama et al. 1991)4U 1909+07 7.8 0.5 0.5 (F¨urst et al. 2011)KS 1947+300 6.5 0.5 0.5 (Tsygankov & Lutovinov 2005)15.8 0.5 0.5 (Tsygankov & Lutovinov 2005)4U 2206+54 7.3 0.1 0.1 (Corbet & Peele 2001)EXO 2030+375 7.7 0.2 0.2 (Epili et al. 2017)SMC X-1 13.7 3.4 3.4 (Inam, Baykal & Beklen 2010)6.6 1.6 1.6 (Inam, Baykal & Beklen 2010)
ACKNOWLEDGMENT
The authors would like to acknowledgment the referee for his/her thorough and constructivecomments that greatly improved the quality of the paper. PP would like to thank RamanResearch Institute, Bengaluru and St Joseph’s College, Darjeeling for the infrastructure fa-cilities provided during the preparation of this work. PP would also like to thank DipankarBhattacharya for useful discussions and also the members of XMAG for their useful com-ments. Finally, PP would like to acknowledge the grant received as a part of Minor ResearchProject from University Grants Commission, India that partly supported this work. Thisresearch has made use of data and/or software provided by the High Energy AstrophysicsScience Archive Research Center (HEASARC), which is a service of the Astrophysics ScienceDivision at NASA/GSFC.
DATA AVAILABILITY
The data underlying this article will be shared on reasonable request to the correspondingauthor. © , 000–000 omprehensive analysis REFERENCES
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4U 0114+65 . . . P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) + XTE J1946+274 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) + GX 304−1 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) +
4U 1700−37 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) + OAO 1657−415 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) +
4U 1909+07 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) + GRO J1008−57 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) + SW J2000.6+3210 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) +
4U 2206+54 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) + SMC X−1 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) + EXO 2030+375 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) +
4U 1822−37 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) + KS 1947+300 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) + IGR J16207−5129 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) + IGR J18410−0535 P a r a m e t e r : E c u t ( k e V ) Parameter: Fe energy (keV) + IGR J17544−2619
Figure A1.
Contour plots between cutoff energy and iron line energy for sources in group 2 where these two values are closeto each other. Note that for most of the sources, the iron line energy is centered at the neutral K α line energy of 6.4 keV. © , 000–000 omprehensive analysis . × − . × − . × − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV)+
1A 1118−61 . × − . × − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + Vela X−1 × − . × − × − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) +
4U 0114+65 × − × − × − × − × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + XTE J1946+274 × − × − × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + GX 304−1 . × − . × − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) +
4U 1700−37 × − . × − × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + OAO 1657−415 . × − × − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) +
4U 1909+07 × − . × − × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + GRO J1008−57 × − − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + SW J2000.6+3210 . × − . × − . × − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) +
4U 2206+54 × − − . × − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + SMC X−1 × − × − × − − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + EXO 2030+375 . × − × − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) +
4U 1822−37 × − − . × − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + KS 1947+300 − . × − × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + IGR J16207−5129 . × − × − . × − × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + IGR J18410−0535 × − − . × − P a r a m e t e r : F e K α no r m Parameter: E cut (keV) + IGR J17544−2619
Figure A2.
Contour plots between cutoff energy and iron line normalization for sources in group 2 (magenta) where these twovalues are close to each other © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul . . . . P a r a m e t e r : Γ Parameter: NH (10 ) + EXO 2030+375 P a r a m e t e r : Γ Parameter: NH (10 ) +
1A 1118−61 P a r a m e t e r : Γ Parameter: NH (10 ) + Cen X−3 P a r a m e t e r : Γ Parameter: NH (10 ) +
4U 1626−67 P a r a m e t e r : Γ Parameter: NH (10 ) +
4U 1538−522 . . P a r a m e t e r : Γ Parameter: NH (10 ) + Vela X−1 . . . . P a r a m e t e r : Γ Parameter: NH (10 ) + IGR J16493−4348 P a r a m e t e r : Γ Parameter: NH (10 ) + Cep X−4
115 120 125 1300.80.911.11.2 P a r a m e t e r : Γ Parameter: NH (10 ) + IGR J16318−4848 . . . P a r a m e t e r : Γ Parameter: NH (10 ) + V0332+54
12 14 16 180.9511.051.11.15 P a r a m e t e r : Γ Parameter: NH (10 ) + GX 301−2 . . . P a r a m e t e r : Γ Parameter: NH (10 ) +
4U 0115+63 P a r a m e t e r : Γ Parameter: NH (10 ) +
4U 1907+09 P a r a m e t e r : Γ Parameter: NH (10 ) + GX 304−1 P a r a m e t e r : Γ Parameter: NH (10 ) +
4U 1700−37 P a r a m e t e r : Γ Parameter: NH (10 ) + GRO J1008−57 P a r a m e t e r : Γ Parameter: NH (10 ) + OAO 1657−415 P a r a m e t e r : Γ Parameter: NH (10 ) +
4U 2206+54
Figure A3.
Contour plots between NH1 and gamma © , 000–000, 000–000
Contour plots between NH1 and gamma © , 000–000, 000–000 omprehensive analysis P a r a m e t e r : Γ Parameter: NH (10 ) + XTE J1946+274 . . . . . . P a r a m e t e r : Γ Parameter: NH (10 ) +
4U 0114+65 P a r a m e t e r : Γ Parameter: NH (10 ) +
4U 1909+07 P a r a m e t e r : Γ Parameter: NH (10 ) + KS 1947+300 . . . . P a r a m e t e r : Γ Parameter: NH (10 ) + IGR J18410−0535 P a r a m e t e r : Γ Parameter: NH (10 ) + A 0535+026 P a r a m e t e r : Γ Parameter: NH (10 ) + IGR J16195−4945 . . . . P a r a m e t e r : Γ Parameter: NH (10 ) + IGR J16493−4348
11 12 13 14 . . . . P a r a m e t e r : Γ Parameter: NH (10 ) + IGR J16207−5129 P a r a m e t e r : Γ Parameter: NH (10 ) + IGR J16465−4507 P a r a m e t e r : Γ Parameter: NH (10 ) + IGR J16479−4514 . . . . P a r a m e t e r : Γ Parameter: NH (10 ) + IGR J00370+6122 . . . P a r a m e t e r : Γ Parameter: NH (10 ) + IGR J17544−2619 . . P a r a m e t e r : Γ Parameter: NH (10 ) + SW J2000.6+3210 P a r a m e t e r : Γ Parameter: NH (10 ) + IGR J17391−3021
13 13.5 14 14.5 151.221.241.261.281.3 P a r a m e t e r : Γ Parameter: NH (10 ) + GX 1+4
Figure A4.
Contour plots between NH1 and gamma © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul
19 19.2 19.4 19.6 19.8 2011.51212.51313.5 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + Her X−1
11 11.5 12 12.5 1377.27.47.67.88 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) +
4U 0115+63 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + Cen X−3 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) +
4U 1626−67 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + XTE J1946+274 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + Vela X−1 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) +
4U 1907+09
15 15.5 16 16.5 17 17.51313.51414.51515.5 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) +
4U 1538−522
21 222022242628 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + GX 301−2 . . P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) +
1A 1118−61 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) +
4U 0114+65 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + GX 304−1 . P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + OAO 1657−415
15 15.5 16 16.5 178.599.51010.5 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + Cep X−4
Figure A5.
Contour plots between cutoff energy and folding energy © , 000–000, 000–000
Contour plots between cutoff energy and folding energy © , 000–000, 000–000 omprehensive analysis P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) +
4U 1700−37 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) +
4U 1822−37 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + GRO J1008−57 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) +
4U 1909+07
18 19 20 2189101112 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + IGR J16393−4643 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) +
4U 2206+54 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + SW J2000.6+3210 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + KS 1947+300 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + EXO 2030+375 P a r a m e t e r : Γ Parameter: NH (10 ) + SMC X−1
13 14 15 16 172830323436 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + IGR J16318−4848 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + IGR J16207−5129 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + IGR J18410−0535 P a r a m e t e r : E f o l d ( k e V ) Parameter: E cut (keV) + IGR J17544−2619
Figure A6.
Contour plots between cutoff energy and folding energy © , 000–000 P. Pradhan, B.Paul, E. Bozzo, C. Maitra, B.C. Paul
19 19.2 19.4 19.6 19.8 203737.53838.539 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) + Her X−1 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) + Cen X−3 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) +
4U 1626−67 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) + XTE J1946+274 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) + Vela X−1
15 16 171818.218.418.618.819 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) +
4U 1907+09 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) +
4U 1538−522
20 22 24404550 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) + GX 301−2 . . P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) +
1A 1118−61 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) +
4U 0114+65 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) + GX 304−1
15 15.5 16 16.5 172929.53030.531 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) + Cep X−4 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) +
4U 1700−37 P a r a m e t e r : E c y c ( k e V ) Parameter: E cut (keV) +
4U 1822−37
Figure A7.
Contour plots between cutoff energy and cyclotron line energy © , 000–000, 000–000