X-Ray spectral evolution of PSR~J2032+4127 during the 2017 periastron passage

TL;DR

This study analyzes X-ray spectral data from multiple observatories to investigate how the spectral index of PSR J2032+4127 evolved during its 2017 periastron passage, revealing spectral softening and potential changes in shock-accelerated electrons.

Contribution

It provides the first detailed spectral evolution analysis of PSR J2032+4127 during periastron using broad spectral coverage from multiple X-ray observatories.

Findings

Spectral index softened after periastron

Detected change in spectral parameters before and after passage

Indications of altered physical state of shock-accelerated electrons

Abstract

We report X-ray data analysis results obtained from Chandra, XMM-Newton, NuSTAR and Swift observations of PSR J2032+4127 taken before, during, and after the periastron on 2017 November 13. We found the first clear evidence of a change in the X-ray spectral index over the passage period, thanks to a broad and sensitive spectral coverage by XMM-Newton and NuSTAR. We analysed the joint XMM-Newton and NuSTAR observation epochs with power-law and broken power-law model. We have obtained change in spectral parameters before and after the periastron passage for both models. The spectra get softened after the passage. The evolution of the spectral index and break energy before and after the periastron may indicate a change in the physical state of shock-accelerated electrons.

Tables

Table 1. Table 1: Observational data analysed in this paper. First column shows the observation dates. Next column shows the observation epoch w.r.t periastron date (MJD 58070). In third column shows the observing instrument. Fourth column shows observation ID. Fifth column shows the exposure time. Sixth column shows count rate during the observation.

Date	Epoch	Instrument	Obs-Id	Exposure	Rate
(MJD)	(Days)			Sec	counts/s
57442.34	-628.16	Chandra	18788	4896	0.03$\pm$0.003
57785.20	-285.30	Chandra	19607	26640	0.07$\pm$0.002
57901.66	-168.84	Chandra	19700	28160	0.15$\pm$0.002
57976.33	-94.17	SWIFT	93146011	3336	0.04$\pm$0.003
57987.51	-82.99	SWIFT	34282090	1166	0.04$\pm$0.006
57990.10	-80.40	SWIFT	34282091	1992	0.03$\pm$0.004
57991.36	-79.14	SWIFT	93146012	2651	0.04$\pm$0.004
57994.08	-76.42	Chandra	19701	28400	0.13$\pm$0.002
58002.05	-68.45	SWIFT	93148006	2804	0.04$\pm$0.004
58007.22	-63.28	SWIFT	93148007	1146	0.03$\pm$0.006
58017.00	-53.50	SWIFT	93148008	2437	0.05$\pm$0.004
58018.38	-52.12	SWIFT	34282094	1613	0.06$\pm$0.006
58019.91	-50.59	SWIFT	93146014	1455	0.04$\pm$0.007
58026.15	-44.35	SWIFT	93146015	2956	0.04$\pm$0.004
58032.59	-37.91	SWIFT	93148009	2614	0.05$\pm$0.004
58033.32	-37.18	SWIFT	93146016	3221	0.04$\pm$0.004
58039.11	-31.39	SWIFT	34282097	1418	0.05$\pm$0.006
58039.32	-31.18	SWIFT	93148010	3576	0.05$\pm$0.004
58046.09	-24.41	SWIFT	34282098	1988	0.05$\pm$0.005
58047.08	-23.42	SWIFT	93146018	2710	0.05$\pm$0.005
58047.35	-23.15	SWIFT	93148011	2083	0.03$\pm$0.004
58049.48	-21.02	SWIFT	88016001	1756	0.04$\pm$0.005
58049.51	-20.99	NuSTAR	30302002002	37843	0.06$\pm$0.001
58049.74	-20.76	XMM	801910201	22643	0.43$\pm$0.005
58050.74	-19.76	SWIFT	34282099	2894	0.04$\pm$0.004
58051.13	-19.37	SWIFT	93148012	1893	0.04$\pm$0.005
58053.00	-17.50	SWIFT	34282100	1096	0.04$\pm$0.006
58054.92	-15.58	SWIFT	93146019	2789	0.04$\pm$0.004
58057.51	-12.99	SWIFT	34282101	1626	0.03$\pm$0.005
58060.25	-10.25	Chandra	19702	19080	0.12$\pm$0.003
58060.64	-9.86	SWIFT	34282103	1981	0.03$\pm$0.004
58061.04	-9.46	SWIFT	93146020	3328	0.03$\pm$0.003
58062.20	-8.30	NuSTAR	90302321002	39826	0.03$\pm$0.001
58062.76	-7.74	SWIFT	93148013	3219	0.02$\pm$0.003
58062.78	-7.72	XMM	801910301	16657	0.22$\pm$0.004
58062.89	-7.61	Chandra	20836	9560	0.10$\pm$0.003
58065.41	-5.09	SWIFT	34282106	1848	0.02$\pm$0.004
58068.14	-2.36	SWIFT	93146021	2349	0.03$\pm$0.004
58069.78	-0.72	NuSTAR	30302002004	42705	0.03$\pm$0.001
58069.87	-0.63	SWIFT	34282108	1526	0.02$\pm$0.004
58070.50	0.00	XMM	801910401	11518	0.21$\pm$0.005
58071.85	1.35	SWIFT	34282109	2333	0.01$\pm$0.003
58074.65	4.15	SWIFT	34282110	1953	0.03$\pm$0.004
58075.58	5.08	SWIFT	93146022	2817	0.02$\pm$0.003
58076.10	5.60	SWIFT	34282111	2250	0.02$\pm$0.003
58077.50	7.00	SWIFT	93148015	3366	0.04$\pm$0.003
58078.51	8.01	NuSTAR	90302321004	40003	0.06$\pm$0.001
58078.96	8.46	SWIFT	34282112	1483	0.05$\pm$0.006
58079.05	8.55	XMM	801910501	17958	0.49$\pm$0.006
58081.35	10.85	SWIFT	34282114	1491	0.04$\pm$0.005
58082.21	11.71	SWIFT	93146023	1274	0.04$\pm$0.006
58083.14	12.64	SWIFT	34282115	1973	0.04$\pm$0.005
58084.14	13.64	SWIFT	93148016	2172	0.05$\pm$0.005
58085.00	14.50	SWIFT	34282116	2317	0.05$\pm$0.005
58087.21	16.71	SWIFT	34282117	2028	0.04$\pm$0.005
58089.13	18.63	SWIFT	93146024	2130	0.05$\pm$0.005
58091.46	20.96	NuSTAR	30302002006	41531	0.04$\pm$0.001
58091.72	21.22	XMM	801910601	16756	0.36$\pm$0.006
58092.73	22.23	SWIFT	93148017	3122	0.04$\pm$0.004
58095.38	24.88	SWIFT	34282119	1465	0.02$\pm$0.004
58095.44	24.94	SWIFT	10451001	3459	0.00$\pm$0.002
58127.99	57.49	Chandra	19608	29030	0.11$\pm$0.002
58193.59	123.09	Chandra	19698	29160	0.04$\pm$0.001

Table 2. Table 2: Spectral analysis results for joint observations of XMM-Newton and NuSTAR with absorbed power-law model. First column shows the observation dates. In second column interstellar absorption values are shown. Third column shows the power-law index. Fourth column shows the 0.3-10 keV unabsorbed flux calculated from analysis results. Fifth column shows the reduced χ 2 superscript 𝜒 2 \chi^{2} values with degrees of freedom. Next sixth to tenth columns show the cross-calibration constants for different instruments. The cross-calibration constant for EPIC-PN is kept fixed to unity during the analysis.

Date	$n_H$	$\Gamma$	Flux	${\chi }_{\nu }^2$	XMM-Newton			NuSTAR
(MJD)	(${10}^{22}c{m}^{-2}$)		(${10}^{-12}erg{s}^{-1}{\mathrm{cm}}^{-2}$)	(dof)	PN	MOS1	MOS2	FPMA	FPMB
58049	$0.85\pm 0.04$	$1.38\pm 0.03$	$4.66\pm 0.05$	1.09(463)	1.0	$0.97\pm 0.03$	$1.00\pm 0.03$	$0.96\pm 0.05$	$0.94\pm 0.05$
58062	$0.77\pm 0.06$	$1.37\pm 0.05$	$2.31\pm 0.04$	1.13(319)	1.0	$1.02\pm 0.05$	$1.08\pm 0.05$	$1.02\pm 0.07$	$0.88\pm 0.07$
58070	$0.68\pm 0.06$	$1.37\pm 0.06$	$2.00\pm 0.04$	1.10(238)	1.0	$0.98\pm 0.06$	$1.05\pm 0.07$	$0.91\pm 0.07$	$0.85\pm 0.07$
58079	$0.78\pm 0.03$	$1.53\pm 0.03$	$5.01\pm 0.06$	1.24(445)	1.0	$1.00\pm 0.03$	$1.02\pm 0.03$	$1.00\pm 0.05$	$0.94\pm 0.05$
58091	$0.81\pm 0.05$	$1.63\pm 0.05$	$3.52\pm 0.06$	1.04(350)	1.0	$0.98\pm 0.05$	$1.04\pm 0.05$	$0.98\pm 0.06$	$1.04\pm 0.07$

Table 3. Table 3: Spectral analysis results for Chandra observations with absorbed power-law model. First column shows the observation dates. In second column interstellar absorption values are shown. Third column shows the power-law index. Fourth column shows the 0.3-10 keV unabsorbed flux calculated from analysis results. Fifth column shows the reduced χ 2 superscript 𝜒 2 \chi^{2} values with degrees of freedom.

Date	$n_H$	$\Gamma$	Flux	${\chi }_{\nu }^2$
(MJD)	(${10}^{22}c{m}^{-2}$)		(${10}^{-12}erg{s}^{-1}{\mathrm{cm}}^{-2}$)	(dof)
57442	$0.54\pm 1.27$	$1.93\pm 1.36$	$0.66\pm 0.12$	1.75(4)
57785	$1.02\pm 0.18$	$2.03\pm 0.18$	$2.04\pm 0.08$	0.97(91)
57901	$0.97\pm 0.12$	$1.73\pm 0.12$	$4.09\pm 0.11$	0.74(189)
57994	$0.86\pm 0.13$	$1.45\pm 0.12$	$3.50\pm 0.10$	0.89(179)
58060	$0.87\pm 0.20$	$1.19\pm 0.16$	$3.28\pm 0.12$	1.12(119)
58062	$1.06\pm 0.38$	$1.29\pm 0.28$	$2.90\pm 0.17$	1.11(54)
58127	$1.07\pm 0.12$	$1.68\pm 0.12$	$3.24\pm 0.10$	0.90(156)
58193	$0.85\pm 0.22$	$1.76\pm 0.24$	$0.95\pm 0.05$	0.92(59)

Equations

$${\epsilon }_{br}\simeq 4\left(\frac{B}{1.8G}\right){\left(\frac{{\gamma }_1}{4\times 10^5}\right)}^{2}keV$$

Full text

X-rays: binaries – pulsars: individual (PSR J2032+4127) – stars: individual (MT 91-213) – stars: winds, outflows

††journal: ApJ††facilities: XMM-Newton, Swift(XRT and UVOT), CXO, NuSTAR††software: HEASOFT (v6.25; (2014), Heasarc), XSPEC (v12.10.1; Arnaud, 1996), CIAO (v4.9; Fruscione et al., 2006), SAS (v16.1; Gabriel et al., 2004)

1 Introduction

PSR J2032+4127 is a radio-loud GeV emitting pulsar, discovered by Fermi Large Area Telescope (Fermi-LAT) in a blind search of Fermi-LAT gamma-ray data (Abdo et al., 2009) and was subsequently detected in radio wavelength with the Green Bank Telescope (GBT; Camilo et al., 2009). It is one of the younger member of its class and has a spin period of 143 ms (Abdo et al., 2013). Several observations revealed a variable spin-down rate in the pulsar which is explained as an effect of Doppler shift due to the pulsar’s motion along the orbit of the binary system with long-period (Lyne et al., 2015). The companion star was identified as a Be star, MT 91-213, which has a mass of around 15 $M_{\sun}$ with a circumstellar variable disk within radius 0.2-0.5 AU (Ho et al., 2017). The pulsar spin-down luminosity(Ė) was determined to be around $1.7\times 10^{35}~{}erg~{}s^{-1}$ with a characteristic age of 180 kyr, and the binary system is at a distance of 1.44 kpc in the Cyg OB2 stellar cluster (Gaia Collaboration, 2018). Further observations precisely determined the orbital parameters with a binary period of 45-50 years, an eccentricity between 0.94 and 0.99 and a longitude of periastron between 21°and 52°. According to the best fit of radio timing solution the periastron passage was on 2017 November 13 with an approximate separation between PSR J2032+4127 and MT 91-213 of 1 AU (Ho et al., 2017; Coe et al., 2017).

Close to the periastron, due to the expected interaction between the matter of the stellar wind (or possibly the disk) and the pulsar wind, emission of low energy (radio to X-rays) to high energy (GeV or up to TeV) photons are predicted (Takata et al., 2017; Bednarek et al., 2018). Indeed, this object shows similarity with another $\gamma$-ray binary PSR B1259-63/LS 2883 (Chernyakova et al., 2015; Tam et al., 2015; Johnson et al., 2018; Tam et al., 2018). PSR B1259-63 has a spin period of 47.8 ms and orbits around the Be star LS 2883 with a period of 3.4 years in a highly eccentric orbit (e $\sim$ 0.87). It shows a spin down luminosity around $8.3\times 10^{35}~{}erg~{}s^{-1}$. It is known that PSR B1259-63 converts nearly all of its pulsar spin-down luminosity to GeV emission during parts of its orbit (Caliandro et al., 2015). Several models have been proposed to explain the non-thermal, broadband radiation from PSR B1259-63 as well as the GeV flares. These include synchrotron emission and/or inverse-Compton (IC) up-scattering off stellar photons or disk photons from the companion star by the accelerated electrons in the shock between the PW and stellar wind (Tavani & Arons, 1997; Kirk et al., 1999; Dubus, 2006; Bogovalov et al., 2008; Khangulyan et al., 2011; Takata et al., 2012), unshocked PW particles (Khangulyan et al., 2012), and Doppler boosting effects (Dubus et al., 2010; Takata et al., 2012). As it is accepted that both systems are similar (Ho et al., 2017; Coe et al., 2019), it is understandable that the origin of X-ray & TeV emission for PSR J2032+4127 should be pulsar spin-down luminosity.

Ho et al. (2017) and Li et al. (2017a) first reported the X-ray brightening from the direction of PSR J2032+4127, consistent with the increased shock emission. Ho et al. (2017) has predicted the timing of the periastron from orbital solution. Li et al. (2017b) has summarized The Neil Gehrels Swift Observatory (Swift), the Chandra X-ray Observatory (Chandra), The Nuclear Spectroscopic Telescope Array Mission (NuSTAR) and The European Space Agency’s (ESA) X-ray Multi-Mirror Mission (XMM-Newton) observations of PSR J2032+4127 up to early 2017 and tried to explain the pre-periastron X-ray behaviors of PSR J2032+4127. In continuation of this work, Li et al. (2018) reported the X-ray modulation using Swift data and $\gamma$-ray observations of PSR J2032+4127 over the 2017 periastron. The effect of an asymmetric stellar wind with polar gradient is investigated in Petropoulou et al. (2018). Optical variability around the periastron is monitored and reported by Kolka et al. (2017). The VHE gamma-ray counterpart of the 2017 periastron emission was observed by Very Energetic Radiation Imaging Telescope Array System (VERITAS) and Major Atmospheric Gamma Imaging Cherenkov (MAGIC) (Abeysekara et al., 2018). TeV spectral analysis data is adopted in this paper for comparison with X-Ray analysis result. Takata et al. (2017) explained the multi-wavelength phenomena in light of the shock scenario and discussed the possible formation of an accretion disk. However, the rather rich broad-band data and the complex X-ray flux variability still lacks a full theoretical understanding.

In this paper, we present the result throughout our analysis of the archival data of Swift, XMM-Newton, Chandra and NuSTAR to understand the detailed X-ray evolution through the periastron passage. In particular, we report the first accurate X-ray spectral index and interstellar absorption measurements over the 2017 periastron passage of PSR J2032+4127.

2 Data Analysis

During 2017 periastron PSR J2032+4127 was observed by Swift, XMM-Newton(P.I: Jules Halpern), Chandra(P.I.: Jules Halpern), NuSTAR(P.I: Jules Halpern). The observation details is shown in Table. LABEL:table1.

XMM-Newton have observed PSR J2032+4127 on 5 different epochs between MJD 58049 to 58091 with an average 17 ks exposure. XMM-Newton EPIC-PN and MOS data are used for the X-ray analysis in this paper. The data reduction were reprocessed with the software SASv16.1111https://www.cosmos.esa.int/web/xmm-newton/sas-threads, using the most updated calibration files (updated to 2018 May) (Strüder et al., 2001; Turner et al., 2001). The EPIC-PN event files were reprocessed from observation data files with epproc with ‘bad’(e.g., ‘hot’,‘dead’, ‘flickering’) pixels removed. The period of high background events were examined and excluded using the light curves in the energy band 10-12 keV. As the X-ray of PSR J2032+4127 is not bright and there is no pile-up effect, we extracted the source events from a circular region of radius 20″, using single and double events (PATTERN$\leq$4, FLAG=0). The background events were made from a source-free circular region of radius of 20″. We grouped the pn spectra to have at least 25 counts in each bin, so as to adopt the $\chi^{2}$ statistic for the spectral fitting. The ancillary response files (arfs) were extracted with arfgen. The EPIC-PN redistribution matrix file was extracted with rmfgen and used in spectral fitting. Similarly EPIC-MOS event files were reprocessed from observation data files with emproc with ‘bad’(e.g., ‘hot’,‘dead’, ‘flickering’) pixels removed. The period of high background events were examined and excluded using the light curves in the energy band above 10 keV. We checked for pile-up and the pile-up effect is not serious in the source center. We extracted the source events from a circular region of radius 20″, using single and double events (PATTERN$\leq$12). We grouped the pn spectra to have at least 25 counts in each bin, so as to adopt the $\chi^{2}$ statistic for the spectral fitting. The ancillary response files (arfs) were extracted with arfgen. We repeated the similar extraction method for MOS1 and MOS2 spectra. During fitting we used both of them as different data groups.

NuSTAR have observed PSR J2032+4127 almost simultaneously with XMM-Newton enabling us to perform a joint spectral analysis for XMM and NuSTAR. The NuSTAR event files are obtained with nupipeline of HEASOFTv6.25222https://heasarc.gsfc.nasa.gov/docs/software/heasoft/ software (Harrison et al., 2013). We have used SW_SAA=0 and SW_TENTACLE=0 during analysis to avoid background flaring. With nuproduct the source spectra are extracted from a circular region of 30″as the source position and the background is estimated from a source free region of same size. The spectra are grouped with 30 counts per bin for spectral analysis. The response functions and ancillary respond files are also extracted. Both FPMA and FPMB spectra are used for spectral analysis. During fitting we used both FPMA and FPMB as different data groups.

Chandra have observed PSR J2032+4127 on 5 different epochs around 2017 periastron between MJD 57785 and MJD 58062 with average 20 ks exposure. The data reduction is performed with CIAOv4.9333http://cxc.harvard.edu/ciao/ software (Weisskopf et al., 2000). The fits files are cleaned for high flaring backgrounds. The spectra are extracted from a circular region of 7″at the source position and background is estimated from a source free region with same radius from the cleaned fits file. We grouped ACIS spectra to have at least 15 counts in each bin for spectral analysis. The PI had chosen a smaller good exposure time in the proposal to avoid the pile-up effect. We have tested the spectra with XSPEC pile-up model but there is no pile-up effect observed in the spectra.

For Swift-XRT data reduction, the level 2 cleaned event files of Swift-XRT are obtained from the events of photon counting (PC) mode data with xrtpipeline (Burrows et al., 2005). The spectra are extracted from a circular region in the best source position with 20″radius. The background is estimated from an annular region in the same position with radii from 30″to 60″. The ancillary response files (arfs) are extracted with xrtmkarf. The PC redistribution matrix file (rmf) version (v.12) is used in the spectral fits.

The spectral analysis is performed with XSPEC(v12.10.1)444https://heasarc.gsfc.nasa.gov/xanadu/xspec/. We applied the absorption model (tbabs in XSPEC) to account for interstellar effect due to hydrogen column density (Wilms et al., 2000). Although the Galactic hydrogen column density of the position of PSR J2032+4127 is given as $(1.2-1.5)\times 10^{22}\mathrm{cm^{-2}}$ by Dickey & Lockman (1990); Kalberla et al. (2005), we kept the parameter free while fitting to investigate whether there exists any significant evolution in the absorption parameter during the periastron. We fit the spectrum using the power law model; tbabs $\times$ po. The uncertainties are given at 90% confidence levels for one parameter. The joint spectral analysis of XMM and NuSTAR spectral analysis is done in the 0.5-50 keV energy range. We multiplied the model with a constant parameter to better calibrate different detectors. The constant kept fixed to unity for the XMM EPIC-PN spectrum and remained free for EPIC-MOS1, MOS2, FPMA, FPMB. On MJD 58062 the 0.5-50 keV joint XMM+NuSTAR spectral analysis show the interstellar absorption around $0.77\pm 0.06\times 10^{22}\mathrm{cm^{-2}}$ along with the power-law index $\Gamma=1.37\pm 0.05$ and 0.3-10 keV unabsorbed power-law flux is around $0.23\pm 0.004\times 10^{-11}~{}erg~{}s^{-1}\mathrm{cm^{-2}}$. The cross-calibration constant for FPMA is obtained as $1.02\pm 0.07$ and for FPMB is $0.88\pm 0.07$ In Fig. 1(a), XMM+NuSTAR fitted spectra of MJD 58062 are shown. The XMM+NuSTAR spectral analysis results are shown in detail in Table. 2. The cross-calibration constants for different instruments, during the joint XMM+NuSTAR spectral analysis with absorbed power-law model, are also reported in Table. 2. Most of the cases the cross-calibration constant values are around unity. For a few cases larger deviations are obtained. May be they are due to the presence of stray light or some other effects (Wik et al., 2014).

The Chandra ACIS spectra analyzed with absorbed power-law model within 0.8-10 keV. from the spectral analysis the interstellar absorption is obtained around $1.06\pm 0.38\times 10^{22}\mathrm{cm^{-2}}$ along with the power-law index $\Gamma=1.29\pm 0.28$ and 0.3-10 keV unabsorbed power-law flux is around $0.29\pm 0.017\times 10^{-11}~{}erg~{}s^{-1}\mathrm{cm^{-2}}$. The fitted ACIS spectrum of MJD 58062 is shown in Fig. 1(b). The Chandra spectral analysis results are shown in detail in Table. 3.

From XMM+NuSTAR spectral analysis, the average $n_{H}$ value is obtained around $n_{H}=0.78\times 10^{22}\mathrm{cm^{-2}}$. Here all 1.0-10.0 keV Swift-XRT spectra are fitted with the same model component with fixed $n_{H}=0.78\times 10^{22}\mathrm{cm^{-2}}$. XRT unabsorbed flux values are shown in Fig. 2 for comparison. In all cases the unabsorbed power-law flux is calculated in 0.3-10 keV energy range in cgs units.

We have calculated the hardness ratio for the X-Ray data. Here hardness ratio is the ratio between 2.0-10.0 keV photons and 0.3-2.0 keV photons.

For Swift-UVOT data reduction, all extensions of sky images are stacked with uvotimsum. The source magnitudes are derived with 3-$\sigma$ significance level from the circular region of 5″radius in the best source position of the stacked sky images from all the filters with uvotsource. The background is estimated from an annular region in the same position with radii from 10″to 20″.

During XMM+NuSTAR joint observations the correlation between interstellar absorption and power-law index is calculated with 50 steps in both parameters within the error-bar of the parameter. Then 68%, 90% and 99% confidence contours are plotted with red, blue and gray curves in Fig. 3.

During the XMM+NuSTAR joint observations we have also performed spectral fit with absorbed broken power-law model. The fitted spectra for MJD 58070 with both absorbed power-law and broken power-law model are plotted in Fig. 4 for comparison.

3 Results

We analyze all pre-periastron X-ray data and confirm results published previously. Here we report the results of the spectral analysis of new Chandra, XMM-Newton, NuSTAR and SWIFT data. In 7 panel plot of the Fig. 2 we have plotted the analysis result and compared with the TeV analysis results obtained from Abeysekara et al. (2018).

In the top and second panel of Fig. 2 the TeV photon flux values are reported from VERITAS and MAGIC observations respectively. These data points are obtained from lower panel Fig. 1(b) of Abeysekara et al. (2018) for comparison. In the top panel the from MJD 58012 to MJD 58042 the VERITAS (E $>$ 200 GeV) photon counts are below $0.5\times 10^{-11}~{}Counts~{}\mathrm{cm^{-2}s^{-1}}$ after MJD 58045 the VERITAS counts started increasing gradually to $1.5\times 10^{-11}~{}Counts~{}\mathrm{cm^{-2}s^{-1}}$ just before the periastron. After the periastron it sharply increase to $2\times 10^{-11}~{}Counts~{}\mathrm{cm^{-2}s^{-1}}$ and sharply decrease to $0.75\times 10^{-11}~{}Counts~{}\mathrm{cm^{-2}s^{-1}}$ and then the count rate remain variable around $1.0\times 10^{-11}~{}Counts~{}\mathrm{cm^{-2}s^{-1}}$. In the second panel the MAGIC (E $>$ 200 GeV) count rates remain varying around $0.75\times 10^{-11}~{}Counts~{}\mathrm{cm^{-2}s^{-1}}$ during the pre-periastron time span. On periastron the count rate is on its peak at $1.5\times 10^{-11}~{}Counts~{}\mathrm{cm^{-2}s^{-1}}$. Then it decreases to $0.25\times 10^{-11}~{}Counts~{}\mathrm{cm^{-2}s^{-1}}$ within 7 days after the periastron. In the third panel the X-ray power-law index is reported. The XMM+NuSTAR power-law index remain steady around $1.38\pm 0.03$ from MJD 58049 to MJD 58070, the periastron. Then the spectrum gets softer gradually from $1.37\pm 0.03$ to $1.63\pm 0.05$ up to MJD 58091. This is shown with blue stars in the plot. The Chandra analysis results are also shown in the plot with green triangles for comparison. In the fourth panel the 0.3-10 keV unabsorbed X-ray power-law flux evolution with time is shown. The XMM+NuSTAR flux is shown with blue stars. Chandra flux is reported with Green triangles. The grey points represent the Swift-XRT flux values. From MJD 58050 to 58069 the flux decreases from $(4.66\pm 0.05)\times 10^{-12}~{}erg~{}s^{-1}\mathrm{cm^{-2}}$ to $(2.0\pm 0.04)\times 10^{-12}~{}erg~{}s^{-1}\mathrm{cm^{-2}}$ upto its periastron then it increases to $(5.01\pm 0.06)\times 10^{-12}~{}erg~{}s^{-1}\mathrm{cm^{-2}}$ then decreases to $(3.52\pm 0.06)\times 10^{-12}~{}erg~{}s^{-1}\mathrm{cm^{-2}}$, confirming the double-hump structure found previously. We have calculated the hardness ratio between 2.0-10.0 keV photons and 0.3-2.0 keV photons. The fifth panel show the hardness ratio evolution of the X-ray data. The XMM-PN data is shown with blue stars which shows a gradual decrease in hardness ratio from $2.04\pm 0.24$ to $1.48\pm 0.22$. Chandra data is reported with Green triangles. In the sixth panel we show the variation of interstellar absorption variation obtained from fitting. Here we only put Chandra(Green triangle) and XMM+NuSTAR(Blue star) data. Albeit with large error bars we note that within measurement uncertainties $n_{H}$ is consistent with no significant change within 99% confidence level (see Fig. 3) and the best-fit $n_{H}$ values are slightly smaller than the Galactic $n_{H}$ values (Dickey & Lockman, 1990; Kalberla et al., 2005), but similar to the foreground value estimated by the optical color excess of MT 91-213 (i.e. $n_{H}=0.77\times 10^{22}\mathrm{cm^{-2}}$) (Camilo et al., 2009; Li et al., 2017b). In the bottom panel we have shown the UVOT variation during the periastron. Here we can see a U band magnitude remained constant around 13 magnitude (Vega) and UVW1 filter magnitude remain constant around 14 Mag(Vega). This optical variation is believed to be observed due to optical evolution from the companion star.

In Fig. 3 we show the evolution of the 68%(red), 90%(blue) and 99%(gray) confidence contours between $n_{H}$ and $\Gamma$ obtained from the XMM+NuSTAR analysis (assuming power-law).

Any high energy exponential cutoff may represent a signature of an accretion disk around the compact object. We also analyzed the XMM+NuSTAR observation with absorbed power-law with exponential cutoff model and we did not observe any presence of cut-off in the observed data. This result confirms that there are no evidence of an accretion disc during periastron, similar to other gamma-ray binaries (Takahashi et al., 2009; An et al., 2015; Tam et al., 2015; Li et al., 2014).

Uchiyama et al. (2009) has reported, presence of a power-law break around $5.0\pm 0.7~{}keV$ for PSR B1259-63 over the periastron passage, as magnetic interaction between shock and pulsar wind. We have tried to fit XMM+NuSTAR spectra with absorbed broken power-law model. With broken power-law model we have obtained similar goodness of fit as power-law model for all five epochs. Here we also found a break in power-law, by $\Delta\Gamma\sim 0.35$ around $\varepsilon_{br}\sim 5~{}keV$, during pre-periastron period and increases to $\varepsilon_{br}=12.9\pm 3.9~{}keV$ by $\Delta\Gamma\simeq 0.7$ exactly at the periastron passage (see Fig. 4). May be this is due to some magnetic properties of wind. The relation between break energy and magnetization parameter of wind for PSR B1259-63 is given by:

[TABLE]

(Eq. 9; Uchiyama et al., 2009). If we assume PSR J2032+4127 and PSR B1259-63 are similar sources and Lorentz factor($\gamma_{1}\sim 4\times 10^{5}$) for pulsar wind then during periastron passage, $12.9\pm 3.9~{}keV$ break energy will represent pulsar wind magnetic field around $5.8\pm 1.7~{}G$ for PSR J2032+4127. Interestingly, we found no $n_{H}$ change at all in the broken power-law model. Finally, we note that no short-term evolution is observed within each XMM-Newton, NuSTAR and Chandra observation, indicating that the spectral changes happen in longer time scales.

4 Discussion & Conclusion

The X-ray flux derived from the more accurate X-ray measurements presented in this work is in excellent agreement with those obtained based on Swift-XRT only, which has more coverage in time albeit with large errors (Ho et al., 2017; Li et al., 2017b, 2018; Petropoulou et al., 2018). A model light curve developed by Takata et al. (2017) and Li et al. (2018) generally matches the Swift-XRT light curve reasonably well, including the pre-periastron X-ray peak at MJD 58020, and the abrupt drop just before the periastron. As discussed in Li et al. (2018), it is not obvious how the flare-like X-ray emission observed around MJD 58080-58100 is created in the wind-wind interaction model. Furthermore, with the detailed X-ray spectral analysis, we could deliver the evolution of the intrinsic X-ray PL index. Instead, the pulsar wind and Be stellar disk interaction may enhance the X-ray flux, if (1) the scale height of the Be stellar disk at the pulsar position is larger than the shock radius, such that the disk can confine most of the pulsar wind, enhancing the pulsar wind dissipation, and (2) a relatively large base density of the Be stellar disk (Li et al., 2018). One of our major results, namely, a softer intrinsic spectral index (around 1.6) at the post-periastron flare time as compared to that during and before periastron (around 1.4), is in line with a possible new emission region/mechanism at the flare time. The emission mechanism of X-ray photons are driven by Synchrotron emission for binary systems without stellar disc i.e. LS 5039 and 1FGL J1018.6-5856 (Takahashi et al., 2009; An et al., 2015). We note that for PSR B1259-63/LS 2883 system, a softer X-ray power-law index is clearly seen and is thought to be related to the disc passage. Synchrotron radiation is responsible for the emission of X-ray photons in this system (Chen et al., 2019). Coe et al. (2019) has reported the presence of circumstellar disk and the interaction of the compact object with the circumstellar disk for PSR J2032+4127 during the periastron. Now we can infer that the Inverse Compton Scattering may be the cause of the spectral softening for PSR J2032+4127 after periastron passage.

The Power-law index has shown a clear softening after the periastron, which may indicate the variation in physical state of the shock-accelerated electrons. The fit with broken power-law model also gives similar goodness of fit as we have obtained from power-law model. The increase in break energy from around 5 keV before periastron to around 13 keV at periastron may indicate some physical change during the periastron passage. We do not know the exact cause of the possible changing column density, it can be due to the stellar disk or other components of the stellar winds.

PSP, YC acknowledges sysu-postdoctoral fellowship. PSP, PHT, and YC are supported by NSFC through grants 11633007, 11661161010, and U1731136. We acknowledge the referee for advice to improve the manuscript.