NuSTAR and XMM-Newton observations of SXP 59 during its 2017 giant outburst
aa r X i v : . [ a s t r o - ph . H E ] S e p MNRAS , 000–000 (0000) Preprint 19 September 2019 Compiled using MNRAS L A TEX style file v3.0
NuSTAR and
XMM–Newton observations of SXP 59 during its 2017giant outburst
Shan-Shan Weng ⋆ , Ming-Yu Ge † , Hai-Hui Zhao ‡ Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023, China Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
ABSTRACT
The Be X-ray pulsar (BeXRP) SXP 59 underwent a giant outburst in 2017 with a peak X-ray luminosity of . × erg s − . We report on the X-ray behaviour of SXP 59 with the XMM–Newton and
NuSTAR observations collected at the outburst peak, decay, and the lowluminosity states. The pulse profiles are energy dependent, the pulse fraction increases withthe photon energy and saturates at ∼
65% above 10 keV. It is difficult to constrain the changein the geometry of emitting region with the limited data. Nevertheless, because the pulseshape generally has a double-peaked profile at high luminosity and a single peak profile at lowluminosity, we prefer the scenario that the source transited from the super-critical state to thesub-critical regime. This result would further imply that the neutron star (NS) in SXP 59 hasa typical magnetic field. We confirm that the soft excess revealed below 2 keV is dominatedby a cool thermal component. On the other hand, the
NuSTAR spectra can be described asa combination of the non-thermal component from the accretion column, a hot blackbodyemission, and an iron emission line. The temperature of the hot thermal component decreaseswith time, while its size remains constant ( R ∼ . km). The existence of the hot blackbody athigh luminosity cannot be explained with the present accretion theories for BeXRPs. It meansthat either more sophisticated spectral models are required to describe the X-ray spectra ofluminous BeXRPs, or there is non-dipole magnetic field close to the NS surface. Key words: accretion, accretion discs — stars: neutron — pulsars: general — X-rays:binaries — X-rays: individual (SXP 59)
In general, Be X-ray binary (BeXRB) consists of a young neutronstar (NS) orbiting a Be type star. Most BeXRBs are transient inX-ray, and their variabilities are often classified into two typesof outbursts (see Bildsten et al. 1997; Reig 2011, for reviews).Type I outbursts are less energetic ( L peak < erg s − )and occur regularly as the enhancement of accretion during theperiastron passage. On the other hand, type II outbursts are rareand not fixed to the orbital phase. Their X-ray luminosity canexceed the Eddington luminosity for a NS. In particular, thepeak X-ray luminosities of the 2016-17 outburst of SMC X-3(e.g. Weng et al. 2017; Zhao et al. 2018) and 2017-18 outburst ofSwift J0243.6+6124 (Doroshenko et al. 2018; Wilson-Hodge et al.2018; Tao et al. 2019) are beyond erg s − , that is the thresholdof ultraluminous X-ray sources (ULXs, Kaaret et al. 2017).Hundreds of high-mass X-ray binaries (HXMBs) havebeen detected in the Galaxy and the Magellanic Clouds, and ⋆ E-mail: [email protected] † E-mail: [email protected] ‡ E-mail: [email protected] more than half of them are BeXRBs (Liu et al. 2005, 2006). Inaddition to the short distance (62.1 kpc; Hilditch et al. 2005;Graczyk et al. 2014; Scowcroft et al. 2016), the Small MagellanicCloud (SMC) has a large star formation rate (150 times of theGalaxy; Harris & Zaritsky 2004) and low interstellar absorption(Zaritsky et al. 2002; Willingale et al. 2013). It thus providesan ideal and large sample of BeXBRs for a detailed study inmultibands (e.g. Rajoelimanana et al. 2011; Bird et al. 2012;Coe & Kirk 2015). Historically, many X-ray observatories (e.g.
ROSAT , RXTE , Chandra , XMM–Newton ) had spent a lot oftime to survey HXMBs in the SMC (e.g. Kahabka et al. 1999;Galache et al. 2008; Sturm et al. 2013; Haberl & Sturm 2016;Yang et al. 2017). Since 2016 June, the Neil Gehrels
Swift
Observatory has started a high cadence shallow (with a typicalexposure of 60 s) survey of the SMC in order to monitor X-rayvariabilities of BeXRBs by taking its advantage of rapid slewing.During the first year operation, the
Swift
SMC survey (S-CUBED)successfully detected the type II outbursts from SMC X-3, SXP 59,and SXP 6.85 (see Kennea et al. 2018, for more details).SXP 59 was identified as an X-ray pulsar ( P = 59 . ± . s) in1998 due to its outburst, while the pulsations with the same periodwere also revealed in the ROSAT archive data (Marshall et al. c (cid:13) Weng et al. ∼ . d was reported with boththe RXTE observations (Galache et al. 2008) and the OGLE I -band light curves (Bird et al. 2012). S-CUBED detected the onsetof giant outburst from SXP 59 on 2017 March 30 (Kennea et al.2017), and the Swift
TOO observations were triggered to follow theoutburst. The source reached a peak luminosity on 2017 April 7( ∼ . × erg s − in 0.5–10 keV), then exponentially declinedwith an time-scale of ∼ . d, and returned to the pre-outburst fluxlevel on 2017 June 6 (Kennea et al. 2018). Investigating the XMM–Newton
TOO observation performed around the peak of outburst,La Palombara et al. (2018) revealed a soft excess below 2 keV inaddition to the primary power-law component. Since the double-peaked pulse profile detected at the high-luminosity level, they alsospeculated that the source was at the super-critical state having afan-beam emission geometry.In this paper, we carry out a detailed analysis on the high-quality data obtained from the
XMM–Newton and another three
NuSTAR observations executed at different flux levels to explorethe spectral evolution of SXP 59 during its 2017 giant outburst.Section 2 describes the observations together with the data analysis,and summarizes our results. We discuss the physical implicationsof these results in Section 3.
In 2017, the Neil Gehrels
Swift
Observatory carried out 92 ob-servations on SXP 59, including 65 S-CUBED observations. Inorder to avoid the pile-up effect, the TOO observations around theoutburst peak were executed with the window timing (WT) modeinstead of the photon counting (PC) mode. The
Swift /XRT data areprocessed with the packages and tools available in
HEASOFT xrtpipeline is used with standard quality cutsfor the initial event cleaning. We extract the source light curvesin 0.3–10 keV from a circle of 15 pixels centred at the sourceposition, and the background light curves from an annulus regionwith the radii of 15 and 30 pixels. The source light curves arecorrected for the telescope vignetting and point spread functionlosses with the task xrtlccorr , and then are subtracted bythe scaled background count rate to generate the net light curves(Figure 1). When the source was in quiescence state, it can hardlybe detected by the S-CUBED observations due to their shortexposures. Following the work in Kennea et al. (2018), we adoptfive counts as the threshold of detection, and calculate the upperlimits for non-detections. Based on the following
XMM–Newton spectral fitting results, we convert the count rate to the flux, andhence the luminosity assuming a distance of 62.1 kpc. The derivedcount rate to luminosity ratios for the WT and the PC modes are of1 count s − ∼ . × erg s − and ∼ . × erg s − ,respectively. As can be seen in Figure 1, the giant outburst lasted forabout two months with a fast-rise near exponential decay profile.These results are consistent with those reported in Kennea et al.(2018) (Figure 13 in their paper).In this work, we analyze the XMM–Newton observation per-formed on 2017 April 14, which was free of the backgroundcontamination. The data collected with the
XMM–Newton
EPICinstrument are reduced using the Science Analysis System software(
SAS ) version 14.0.0. Both the pn and MOS data were taken insmall window mode in order to minimize the pile-up effect. Weexclude all events at the edge of CCD and from bad pixels by L . - k e V ( er g s - ) XMM-NewtonXMM-Newton NuSTARNuSTAR
Window TimingPhoton Counting
Figure 1.
Swift /XRT light curve of SXP 59 since 2017 Jan 1 (MJD 57754).2 σ upper limits for non-detections are shown with black arrows. The redand blue arrows label the XMM–Newton and the
NuSTAR observations,respectively. setting FLAG=0, select the pn events with PATTERN in the 0-4range, and the MOS data with PATTERN
12. The source photonsare extracted from a circle aperture with a radius of 30 arcsec, andthe background is taken from the same CCD chip as the sourcewithin a circle of radius 50 arcsec.
NuSTAR is the first direct-imaging hard X-ray telescope, con-sisting of two focusing instruments and two focal plane modules,i.e. Focal Plane Modules A and B (hereafter FPMA and FPMB;Harrison et al. 2013). There are three
NuSTAR observations carriedout at the outburst peak, decay, and the low luminosity states,respectively (Table 1 and Figure 1). The source events are extractedfrom circular region with the radius of 60–100 arcsec, depending onthe count rates. Meanwhile, the background photons are extractedfrom the source-free region with a radius of 120 ′′ . These dataare processed with the task nupipeline , the spectra and thelight curves are produced with the command nuproducts . It isworth to note that, the first NuSTAR data were made 1–2 d beforethe
XMM–Newton observation. That is, these two observations arequasi-simultaneous.
Both
NuSTAR and
XMM–Newton spectra are fitted by empiricalmodels most often used in the literature with the
HEASOFT
X-rayspectral fitting package
XSPEC (Arnaud 1996). All models in thispaper also include the interstellar absorption ( tbabs in XSPEC ).The
NuSTAR spectra are grouped with grppha to ensure at least30 counts per bin. The FPMA and the FPMB spectra are fittedsimultaneously, with a constant multiplicative factor to compensatefor calibration differences. The FPMA constant is fixed at unity,whilst that for the FPMB is allowed to vary, with the yielded valuesin the range of 1.00–1.06.Because the
NuSTAR and
XMM–Newton data are operated indifferent energy ranges (3–79 keV and 0.5–10 keV), some emissioncomponent might be caught by only one of them. Thus, we firstlydecompose the spectral components with
NuSTAR and
XMM–Newton spectra separately, and aim to achieve a common model forthe broadband spectra. We begin by fitting the cut-off power-lawcomponent to the first
NuSTAR observation. The derived reducedchi-square is of . ( χ /dof = 1139 . / ), the iron linefeature and residuals at low and high-energy bands are displayed MNRAS , 000–000 (0000) iant outburst of SXP 59 Obs Date Observatory ObsID Exposure Epoch ν ˙ ν (ksec) (MJD-57850) ( − Hz) ( − Hz s − )2017 Apr 14 XMM–Newton
NuSTAR
NuSTAR
NuSTAR
Table 1.
Log of
XMM–Newton and
NuSTAR observations. -6-4-20246 χ tbabs*cutoff -6-4-20246 χ tbabs*(cutoff+gauss)
3 5 10 20 50 80Energy (keV)-6-4-20246 χ tbabs*(bbodyrad+cutoff+gauss) Figure 2.
Spectra of the first
NuSTAR observation are fitted themodels of tbabs*cutoffpl , tbabs*(cutoffpl+gaussian) ,and tbabs*(bbodyrad+cutoffpl+gaussian) , respectively. Pan-els from top to bottom show the corresponding fit residuals. in the top panel of Figure 2. Thus, a Gaussian line at ∼ . keV is added to account for the iron line component. The fittingis further significantly improved with an additional hot thermalcomponent ( kT ∼ . keV). The reduced chi-square decreasesfrom χ /dof = 1105 . / to χ /dof = 1047 . / , andthe fit residuals become flat in the whole energy band (bottompanel of Figure 2). The same situation occurs for the NuSTAR dataobtained at the outburst decay phase. Alternatively, the blackbodycomponent is required with a confidence level of 98% accordingto F -test, but the iron line is too weak to be detected in thelast NuSTAR observation. We, therefore, suggest that the
NuSTAR spectra can be described as a combination of a hot blackbody and acut-off power-law component, and the iron line emission is requiredat the high luminosity state (Table 2).For the
XMM–Newton data, we generate the spectral responsefiles with the
SAS tasks rmfgen and arfgen , and rebin thespectra by using the task specgroup to have at least 20 counts perbin to enable the use of chi-square statistics and not to oversamplethe instrument energy resolution by more than a factor of three.La Palombara et al. (2018) carried out a detailed analysis on the
XMM–Newton data, and concluded that the continuum spectrumwas dominated by the power-law component, and displayed asoft excess below 2 keV. The latter feature was further describedwith the sum of a cool blackbody and a hot thermal plasmacomponent. Here, we fit the pn and MOS1/2 data simultane-ously and confirm that all three components are required by thedata. Adopting the same model as used in La Palombara et al.(2018) [ tbabs*(apec+bbodyrad+powerlaw+gaussian) in XSPEC ] with the metal abundance of the APEC component fixed
Parameters
XMM + NuSTAR NuSTAR NuSTAR NuSTAR
Apr 12–14 Apr 12–13 Apr 24–26 Aug 12–13 nH ( cm − ) . +0 . − . kT apec (keV) . +0 . − . – – –Norm apec ( × − ) . +2 . − . – – ... kT lowBB (keV) . +0 . − . – – ...Norm lowBB . +184 . − . – – ... kT highBB (keV) . +0 . − . . +0 . − . . +0 . − . . +0 . − . Norm highBB ( × − ) . +2 . − . . +1 . − . . +1 . − . . +21 . − . Γ 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . E cut (keV) . +1 . − . . +2 . − . . +5 . − . . +6 . − . Norm cut − off ( × − ) . +0 . − . . +0 . − . . +0 . − . . +0 . − . E Gau (keV) . +0 . − . . +0 . − . . +0 . − . – σ (keV) . +0 . − . . +0 . − . . +0 . − . –Norm gauss ( × − ) . +1 . − . . +1 . − . . +1 . − . – L X ( erg s − ) 1.11 a b b b χ /dof Table 2.
Spectra are fitted with the model of tbabs*(apec+bbodyrad+bbodyrad+cutoffpl+gaussian) . a Unabsorbed luminosity is calculated in 0.5–79 keV by assuming adistance of 62.1 kpc. b Unabsorbed luminosity is calculated in 3–79 keV.All errors are in 90% confidence level. to 0.2 Z ⊙ , we obtain the similar values for all parameters: nH =0 . +0 . − . × cm − , kT apec = 0 . +0 . − . keV, Norm apec =6 . +2 . − . , kT lowBB = 0 . +0 . − . keV, Norm lowBB = 86 . +90 . − . , Γ =0 . +0 . − . , Norm PL = 2 . +0 . − . × − , E Gau = 6 . +0 . − . keV, σ = 0 . +0 . − . keV, Norm Gau = 3 . +2 . − . × − , and χ /dof = 575 . / ). But because the peak emission of thehot blackbody component needed by the NuSTAR data is beyond10 keV (Figure 3), its parameters cannot be constrained with the
XMM–Newton spectra alone.Since the separation of first
NuSTAR observationand the
XMM–Newton observation is less than 2 d, wealso try to fit them together with the common model of tbabs*(apec+bbodyrad+bbodyrad+cutoffpl+gaussian) as discussed above. The multiplicative constant for pn data is frozenat unity, and those for MOS1/2 and FPMA/B are allowed to vary.The derived constant factors for MOS1/2, FPMA, and FPMBare . ± . , . ± . , and . ± . , respectively.The unfolded spectra are plotted in Figure 3, and the spectralparameters are presented in Table 2 and Figure 4. The hot thermalplasma, the two blackbody and the non-thermal componentscontribute the X-ray emissions (in 0.5–79 keV) of ∼ . × erg s − , . × erg s − , . × erg s − , and . × erg s − , respectively. There is no obvious evidence of cyclotronabsorption line feature in either the XMM–Newton nor the
NuSTAR data. Finally, we would caution that the small discrepancy betweenthe joint-fitting results and those obtained from fitting the
XMM–Newton and the
NuSTAR data alone could be due to the calibrationdifferences and the spectral evolution within 2 d.
MNRAS , 000–000 (0000)
Weng et al. -4 -3 E f( E ) pnMOS1MOS2FPMAFPMB χ Figure 3.
A joint fit is applied to the first
NuSTAR and
XMM–Newton data with the model of tbabs*(apec+bbodyrad+bbodyrad+cutoffpl+gaussian) .Unfolded spectra (upper panel) and fit residuals (bottom panel) are plotted.Dash–dotted lines mark two blackbody components. k T BB h i g h ( k e V ) N o r m BB h i g h ( × - ) Γ X (10 erg/s)010203040 E c u t ( k e V ) Figure 4.
Spectral parameters vary as a function of X-ray luminosity (Table2).
In order to verify the existence of the blackbody components,we also try to use other commonly used models to describe thenon-thermal X-ray continuum (e.g. Coburn et al. 2002; West et al.2017), such as the negative and positive exponential cut-off (the so-called NPEX model, Mihara et al. 1998), the Fermi Dirac cut-off(the so-called FDCut model, Tanaka 1986), and the high-energycut-off power-law models ( highecut*powerlaw in XSPEC).These models predict that the spectra having a power-law profilebelow 10 keV and rolling off in different ways at high-energy band.The soft excess revealed below 2 keV is not sensitive to the adoptednon-thermal models. On the other hand, the temperature of hotthermal component does not change much while its emitting sizecould vary by a factor of < when different continuum models are used. That is much smaller than the radius of a NS. Alternatively,a more physical model, CompTT, is also used to fit the spectraresulting in the similar parameter values for the thermal component,but obtain a worse fit. Note that, compared to the cut-off power-law model, these models have more parameters, which sometimesare difficult to be constrained. In sum, we suggest that the spectralparameters yielded by the cut-off power-law model are reliable andcan be better constrained. The 0.3–12 keV source events are extracted from
XMM–Newton
EPIC data and are barycentrically corrected with the command barycen . Meanwhile, for the
NuSTAR data, the source eventsare extracted in 3–79 keV for the period calculation. For eachobservation, an accurate template profile with 50 phase bins iscreated by folding the whole event data. Then we divide oneobservation into several segments having equal exposure (4000s), and derive the pulse times of arrivals (TOAs) of the pulsar bycomparing the template profile with the one from each segment, asdetailed in the following: (1) search for the best spin frequencyusing the Pearson χ method; (2) fold the pulse profile withthe starting time of the observation as the reference epoch; (3)Calculate the phase shift using the cross-correlation between thepulse profile and the template profile, which represents the TOAof each observation. Finally, we determine the rotation frequenciesand their derivatives for each observation by fitting the TOAs withTEMPO2 (Hobbs et al. 2006, Table 1).We also produce the light curves in time resolution of 0.1 s.The barycentric corrected light curves are folded over the best-fitting period, and the pulse fractions are calculated as P F =( C max − C min ) / ( C max + C min ) , where C max , C min are themaximum and the minimum count rates of the profile. The evo-lutions of the pulse profile and pulse fraction are plotted in Figures5 and 6, respectively. However, we cannot investigate the pulsemodulation above 50 keV (30 keV) for the first two (the last) NuSTAR observations owing to the low count rate.
Our results are summarized as follows: (I) During the 2017 giantoutburst, SXP 59 reached a peak luminosity of ∼ . × erg s − , that is 60% Eddington luminosity of a NS. (II) Inves-tigating the XMM–Newton data, we confirm that the soft excessreported by La Palombara et al. (2018) consists of a cool thermalcomponent ( kT BB ∼ . keV) with a size of km and ahot thermal plasma . (III) The hard X-ray spectra ( > keV)are modelled by three components: a hot blackbody component( kT BB ∼ . − keV), a non-thermal component, and an ironemission line. The temperature of blackbody decreases with time,while its normalization remains constant ( ∼ . , Figure 4),corresponding to a size of R ∼ . km. (IV) The pulse profilesgiven by the first two NuSTAR data are energy dependent and havetwo narrow peaks at phase of ∼ NuSTAR observations.
MNRAS , 000–000 (0000) iant outburst of SXP 59 N o r m a li ze d C o un t R a t e N o r m a li ze d C o un t R a t e N o r m a li ze d C o un t R a t e N o r m a li ze d C o un t R a t e Figure 5.
Evolution of energy-dependent pulse profiles. P u l s e F r a c t i o n ( % ) Figure 6.
Energy-dependent pulse fraction.
The accretion geometry in BeXRBs is mainly governed bythe NS magnetic field strength ( B ) and the accretion rate(Basko & Sunyaev 1976; Riffert & Meszaros 1988; Kraus et al.1995; Becker et al. 2012; Mushtukov et al. 2018). For the caseof low accretion rate, the falling material is funnelled by themagnetic field to small regions around the polar caps of NSs (i.e.hot spots). The X-ray flux is mainly contributed by the thermalcomponent from the hot spots with a temperature of > keV anda small radius of < km, e.g. SAX J2103.5+4545 (˙Inam et al.2004), 1A 0535+262 (Mukherjee & Paul 2005), RX J1037.5-5647(La Palombara et al. 2009). Theoretically, the size of the hot spot increases with luminosity (Lamb et al. 1973; Frank et al. 2002;Mushtukov et al. 2015). When the interaction between the thermalphotons and the falling material (bulk motion Comptonization) isnon-negligible, the observed spectrum would be deviated from theblackbody form, but can be fitted the CompTT model in XSPEC (e.g. Doroshenko et al. 2010; Tsygankov et al. 2019). As theaccretion is larger than the critical value, the accretion column isformed and blocks the sight of hot spots. That is, the X-ray fluxis dominated by the non-thermal component from the accretioncolumn, and no emission from hot spots is expected.The change of beam pattern (i.e. the existence of accretioncolumn or hot spots at the stellar surface, the so-called fan beamand pencil beam) results in different pulse profiles. It has beenobserved in several giant outbursts of BeXRBs that, the pulseshapes transit from double peaks at high luminosity to single peakat low luminosity, and the pulse fraction increases with energy,e.g. 1A 0535+262 (Bildsten et al. 1997), SMC X-3 (Weng et al.2017; Zhao et al. 2018), and Swift J0243.6+6124 (Tsygankov et al.2018; Wilson-Hodge et al. 2018). Such evolution sequence can beinterpreted as the different radiation beam patterns working in thesuper-critical and sub-critical accretion regimes (Basko & Sunyaev1976; Becker et al. 2012; Mushtukov et al. 2015). Taking accountof the exact Compton scattering cross section in a strong magneticfield, Mushtukov et al. (2015) argued that the critical luminositywas not a monotonic function of B , and it reached a minimum of afew erg s − when the cyclotron energy was about 10–20 keV(fig. 5 in their paper).SXP 59 entered into a type II outburst in 2017 and becameone of the brightest BeXRBs with a peak X-ray luminosity of . × erg s − . Investigating the XMM–Newton and
NuSTAR observations executed at different flux levels, we find that thepulse profiles evolve both with the photon energy and the X-rayluminosity (Figure 5). In general, the pulse profiles above 2 keVexhibit two narrow peaks at the high luminosity, and turn intoa single peak in the last
NuSTAR data. Although it is difficultto constrain changes in the geometry of emitting region withthe data presented in this work, our results are in favor of thescenario that the source transited from the super-critical state tothe sub-critical state as observed in 1A 0535+262 and SMC X-3. The critical luminosity is of . × erg s − < L crit < . × erg s − ., that is a typical value for a Be X-ray pulsar(e.g. Becker et al. 2012; Mushtukov et al. 2015). It might furthersuggest a typical magnetic field ( ∼ − G) for the NS inSXP 59, although we cannot put tight constraint at current stage. Itworth to note that the cyclotron absorption line feature is the directevidence for the NS magnetic field; however, it could be transientand too weak to be detected. For instance, the bursting pulsar,GRO J1744-28 was discovered in 1995 (Fishman et al. 1995) andsince then has been observed frequently by X-ray missions (e.g.
BeppoSAX , RXTE , XMM–Newton , Chandra , and
NuSTAR ); but theweak absorption feature at ∼ kT BB ∼ . keV) with a large emission area emerged in the XMM–Newton dataof SXP 59 (La Palombara et al. 2018). The spectral modelling pa-rameters along with the significantly small pulse fraction detectedbelow 1 keV ( < , Figure 5), are in favor of the scenariothat the central hard X-rays are reprocessed by the inner region ofthe accretion disc (Hickox et al. 2004; La Palombara et al. 2018).The X-ray continuum above 2 keV of SXP 59 is dominated by MNRAS , 000–000 (0000)
Weng et al. the non-thermal component from the accretion column, and canbe phenomenologically fitted by a cut-off power-law componentplus a hot blackbody emission. In this work, we do not findcorrelation between the parameters of the cut-off power-law model( E cut and Γ ) and the luminosity in the giant outburst of SXP 59(Table 2 and Figure 4). On the other hand, the behavior ofhot blackbody emission is quite puzzling. If the source is atthe sub-critical state, this component is generally considered tobe from the base of accretion column, and contributes a largeportion of X-ray flux (e.g. La Palombara et al. 2009). However,the prediction that the hot spot shrinks by a factor of ∼ during the outburst decay of SXP 59, conflicts with the constantnormalization derived from the data (Figure 4). On the other side,theoretically, we can not receive the hot spot emissions directlyat the high luminosity due to the accretion column. Nevertheless,the hot blackbody component is needed to fit the spectra of someluminous Be X-ray pulsars ( L X > − erg s − ), e.g.GX 1+4 (Yoshida et al. 2017), EXO 2030+375 (Reig & Coe 1999),SXP 59 (this work), in particular, Swift J2043.6+6124 (Tao et al.2019). The unexpected hot blackbody emission challenges thecanonical accretion theories, which are mostly based on a puredipole magnetic field. These observational results would indicatethat either more physical spectral models are required to describethe spectra of luminous X-ray pulsars, or that the magnetic filedconfiguration deviates from a dipole field close to the NS surface. ACKNOWLEDGEMENTS
We thank the anonymous referee for the helpful comments, whichsignificantly improve this work. SSW thanks Hua Feng and LianTao for valuable discussions. We acknowledge the use of publicdata from the High Energy Astrophysics Science Archive ResearchCenter Online Service. This work is supported by the NationalNatural Science Foundation of China under grants 11673013,11703014, 11503027, 11573023, U1838201, U1838104, and theNatural Science Foundation from Jiangsu Province of China (grantno. BK20171028).
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