A multi-wavelength study of SXP 1062, the long period X-ray pulsar associated with a supernova remnant

TL;DR

This study provides a comprehensive multi-wavelength analysis of SXP 1062, a long-period X-ray pulsar in a Be X-ray binary, revealing its accretion behavior, magnetic field estimates, and association with a supernova remnant.

Contribution

It offers the first detailed multi-wavelength observational campaign of SXP 1062, proposing a new accretion scenario and magnetic field estimation without requiring an extremely strong magnetic field.

Findings

X-ray and optical outbursts are coincident, indicating Type I outbursts at periastron.

The Be star's disc is likely face-on, with the neutron star's orbit inclined.

Magnetic field estimates do not require an extremely strong magnetic field.

Abstract

SXP 1062 is a Be X-ray binary located in the Small Magellanic Cloud. It hosts a long-period X-ray pulsar and is likely associated with the supernova remnant MCSNR J0127-7332. In this work we present a multi-wavelength view on SXP 1062 in different luminosity regimes. We consider monitoring campaigns in optical (OGLE survey) and X-ray (SWIFT telescope). During these campaigns a tight coincidence of X-ray and optical outbursts is observed. We interpret this as typical Type I outbursts as often detected in Be X-ray binaries at periastron passage of the neutron star. To study different X-ray luminosity regimes in depth, during the source quiescence we observed it with XMM-Newton while Chandra observations followed an X-ray outburst. Nearly simultaneously with Chandra observations in X-rays, in optical the RSS/SALT telescope obtained spectra of SXP 1062. On the basis of our multi-wavelength campaign we propose a simple scenario where the disc of the Be star is observed face-on, while the orbit of the neutron star is inclined with respect to the disc. According to the model of quasi-spherical settling accretion our estimation of the magnetic field of the pulsar in SXP 1062 does not require an extremely strong magnetic field at the present time.

Tables

Table 1. Table 1: Log of X-ray \chandra  and \xmm  observations analyzed in this paper.

#	Instrument	ObsID	MJD	Date	Exp Time (ks)
1	EPIC-MOS1/\xmm	0721960101	56606.79	2013-10-11	77.1
1	EPIC-MOS2/\xmm	0721960101	56606.79	2013-10-11	77.2
1	EPIC-pn/\xmm	0721960101	56606.80	2013-10-11	66.2
2	ACIS/\chandra	15784	56827.80	2014-06-19	29.6
3	ACIS/\chandra	15785	56837.49	2014-06-29	26.8
4	ACIS/\chandra	15786	56846.30	2014-07-08	26.3
5	ACIS/\chandra	15787	56856.91	2014-07-18	25.0

Table 2. Table 2: Equivalent widths of the H α 𝛼 \alpha line in the optical spectra of SXP 1062.

MJD	$EW$ (Å)	Reference
	H$\alpha$
55494	$-23\pm 1$	Hénault-Brunet et al. (2012)
56214	$-26.7\pm 0.1$	Sturm et al. (2013)
56827	$-36.3\pm 0.6$	This work
56835	$-34.0\pm 0.6$	This work
56847	$-34.1\pm 0.6$	This work
57694	$-33\pm 1$	This work

Table 3. Table 3: Outburst history of SXP 1062.

Outburst	MJD	$\Delta$t (days)	$\Delta$I (mag)
1	$55500.09\pm 0.97$		$\stackrel{>}{\sim }0.55$
2	$56166\pm 14$	$666\pm 7$	$\stackrel{>}{\sim }0.15$
3	$56835.9\pm 4.5$	$670\pm 8$	$\stackrel{>}{\sim }0.11$

Table 4. Table 4: Previously published absorbed X-ray fluxes and un-absorbed X-ray luminosities for SXP 1062 together with measurements obtained during this work.

Date	MJD	$\Delta E$	$F_X$ (erg cm-2 s-1)	$L_X$ (erg s-1)	Reference
2010-03-25	55280	$0.2-12$ keV	$\left({1.7}_{-0.3}^{+0.2}\right)\times {10}^{-12}$	$\left({6.3}_{-0.8}^{+0.7}\right)\times {10}^{35}$	Hénault-Brunet et al. (2012)
2012-10-14	56214	$0.2-10$ keV	$\left(6.9\pm 0.2\right)\times {10}^{-12}$	$2.6\times {10}^{36}$	Sturm et al. (2013)
2013-10-11	56606.80	$0.2-12$ keV	$\left({1.39}_{-0.01}^{+0.01}\right)\times {10}^{-12}$	$\left(5.4\pm 0.1\right)\times {10}^{35}$	This work
2014-06-19	56827.80	$0.3-10$ keV	$\left({6.2}_{-0.5}^{+0.1}\right)\times {10}^{-12}$	$\left(2.6\pm 0.1\right)\times {10}^{36}$	This work
2014-06-29	56837.49	$0.3-10$ keV	$\left({7.6}_{-0.2}^{+0.1}\right)\times {10}^{-12}$	$\left(3.0\pm 0.1\right)\times {10}^{36}$	This work
2014-07-08	56849.30	$0.3-10$ keV	$\left({6.0}_{-0.2}^{+0.1}\right)\times {10}^{-12}$	$\left(2.4\pm 0.1\right)\times {10}^{36}$	This work
2014-07-18	56856.91	$0.3-10$ keV	$\left({4.2}_{-0.1}^{+0.1}\right)\times {10}^{-12}$	$\left(1.6\pm 0.1\right)\times {10}^{36}$	This work

Table 5. Table 5: Spectral models of SXP 1062 in quiescence and post-outburst (see text for details).

MJD	$N_H$	$\Gamma$	$k{T}_{\mathrm{BB}}$	$k{T}_{\mathrm{Thermal}}$	${\chi }^2$
	(${10}^{22}$ cm-2)		[keV]	[keV]
\xmm observations during quescence
56606.79	${0.5}_{-0.1}^{+0.2}$	${0.8}_{-0.1}^{+0.2}$	${1.7}_{-0.2}^{+0.2}$	$0.8\pm 0.1$	1.05
\chandra observations following outburst
56827.80	${177}_{-31}^{+38}$	$-0.1\pm 0.2$			1.22
56837.49	${42}_{-5}^{+5}$	$0.4\pm 0.1$			1.10
56846.30	${31.6}_{-3.5}^{+3.9}$	$0.5\pm 0.1$			1.09
56856.91	${20.2}_{-3.2}^{+3.6}$	$0.5\pm 0.1$			0.99

Table 6. Table 6: Spin, P spin subscript 𝑃 spin P_{\rm spin} , and spin derivative, P spin subscript 𝑃 spin P_{\rm spin} , measurements of SXP 1062

Date	MJD	Telescope	$P_{\mathrm{spin}}$	$\Delta t$	${\dot{P}}_{\mathrm{spin}}$	Confidence
			[s]	[d]	[s d-1]
2010-03-25	55280	\xmm	$1062$	18	$0.24\pm 0.07$	99.999%
2012-10-14	56214	\xmm	$1071.01\pm 0.16$	915	$0.0062\pm 0.0012$	43.658%
2013-10-11	56606.80	\xmm	$1077.97\pm 0.28$	393	$0.0177\pm 0.0009$	76.465%
2014-06-19	56827.80	\chandra	$1091.1\pm 1.2$	221	$0.059\pm 0.006$	95.982%
2014-06-29	56837.49	\chandra	$1087.1\pm 0.9$	9	$-0.45\pm 0.16$	99.999%
2014-07-08	56846.30	\chandra	$1079.3\pm 1.9$	9	$-0.86\pm 0.23$	99.999%
2014-07-18	56856.91	\chandra	$1086.0\pm 4.4$	11	$0.61\pm 0.44$	99.999%

Table 7. Table 7: Main properties of the two established Be X-ray binaries sub-groups.

	Transient	Persistent
Quiescence $L_X$	erg s-1	$\sim {10}^{34-35}$ erg s-1
Outbursts	Two different types	Relatively quiet systems
	Type I: Periodic with orbital period and  erg s-1	Sporadic and non-predictable increases of $L_X$
	Type II: Random with $L_X\sim {10}^{38}$ erg s-1	Increases of less than one order of magnitude
Pulse period $P_{\mathrm{spin}}$	$\sim 10$ s	$\stackrel{>}{\sim }200$ s
Orbital period $P_{\mathrm{orb}}$	d	$\stackrel{>}{\sim }200$ d
Eccentricity $e$	$\stackrel{>}{\sim }0.3$

Table 8. Table 8: Log of optical RSS/ \salt   observations obtained with the VPH PG2300 grating.

#	MJD	Date	$\Delta \lambda$ (Å)
1	56827.80	2014-06-20	$6082-6925$
2	56835.49	2014-06-27	$6082-6925$
2		2014-06-27	$3835-4924$
2		2014-06-27	$3835-4924$
3	56847.30	2014-07-09	$6082-6925$
3		2014-07-09	$3835-4924$
3		2014-07-09	$3835-4924$
4	57694	2016-11-02	$6082-6925$

Equations

$${\dot{P}}_{\mathrm{spin}}^{\mathrm{obs}}(t)=\frac{d{P}_{\mathrm{spin}}^{\mathrm{obs}}}{dt}=\frac{d{P}_{\mathrm{spin}}(t)}{dt}+\frac{1}{c}\frac{d}{dt}\left(P_{\mathrm{spin}}(t)v_{\mathrm{orb}}(t)\right),$$

$$v_{\mathrm{orb}}(t)=\frac{2\pi a_{\mathrm{X}}\sin i}{P_{\mathrm{orb}}\sqrt{1-e^2}}\left(\cos (\theta (t)+\omega )+e\cos (\omega )\right),$$

$$e=\frac{\Delta M}{M_1+M_2-\Delta M}$$

$$P_{\mathrm{eq}}=940{\mu }_{30}^{12/11}(P_{\mathrm{orb}}/10\mathrm{d}){\dot{M}}_{16}^{-4/11}{v}_{w8}^4\mathrm{s}.$$

$${\mu }_{30}\approx 7{\left(\frac{\dot{M}}{5\times 10^{15}{\mathrm{g}\mathrm{s}}^{-1}}\right)}^{1/3}{\left(\frac{v_{\mathrm{w}}}{200{\mathrm{km}\mathrm{s}}^{-1}}\right)}^{-11/3}.$$

$$\begin{array}{r}{\dot{P}}_{\mathrm{sd}}\approx 7\times 10^{-3}\left(\frac{{\Pi }_{\mathrm{sd}}}{7}\right){\left(\frac{\dot{M}}{5\times 10^{15}{\mathrm{g}s}^{-1}}\right)}^{3/11}\\ \left(\frac{P_{\mathrm{spin}}}{1080\mathrm{s}}\right){\mu }_{30}^{13/11}{\mathrm{s}\mathrm{d}}^{-1}\end{array}$$

$${\dot{P}}_{\mathrm{su}}=P_{\mathrm{spin}}^2{P}_{\mathrm{orb}}^{-1}\dot{M}{R}_{\mathrm{B}}^2{I}^{-1},$$

Full text

1 Introduction

Be X-ray binaries (BeXBs; Reig, 2011) are a subgroup of high mass X-ray binaries. The donor stars in these interesting objects are non-supergiant, fast-rotating B-type stars with circum-stellar decretion discs. The compact objects, in most confirmed BeXBs, are magnetized rotating neutron stars (NSs). Therefore, the majority of BeXBs are X-ray pulsars (Nagase, 1989). The accretion in BeXBs is likely powered by the interaction between the decretion disc of the Be star and the NS (Okazaki & Negueruela, 2001).

The subject of this study is an X-ray pulsar discovered with \chandra and \xmm in March 2010 in the Wing of the Small Magellanic Cloud (SMC) galaxy (Hénault-Brunet et al., 2012; Haberl et al., 2012). From the analysis of these first observations a long X-ray pulse period $P_{\rm spin}\sim 1062$ s was found, accordingly the pulsar was named SXP 1062. The optical counterpart of SXP 1062  is the Be star 2dFS 3831 (B0-0.5III; Evans et al., 2004).

SXP 1062 is especially interesting because it is the first X-ray pulsar discovered within its likely parental supernova remnant (SNR). The association of SXP 1062 with MCSNR J0127-7332111http://sci.esa.int/xmm-newton/49789 allows to estimate the age of the NS. Two independent groups obtained compatible values for the kinematic age of MCSNR J0127-7332 of $\sim$2$-$4$\times 10^{4}$ years (Hénault-Brunet et al., 2012), and $\sim$1.6$\times 10^{4}$ years (Haberl et al., 2012). According to standard models, at this age the NSs are too young to be in the accretor phase, and, consequently, are not expected to be X-ray pulsars (Lipunov, 1992, and references therein).

A number of models and scenarios are suggested to explain the physics of SXP 1062. Haberl et al. (2012) proposed that its NS was born with unusually long initial spin period significantly larger than $0.1$ s. Popov & Turolla (2012) suggested that the NS is spinning close to the equilibrium period and has a magnetic field of B\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}10^{13} G at present time, while initially it had a strong magnetic field in excess of $B\sim 10^{14}$ G. Ikhsanov (2012) put forward a magnetic accretion scenario, while Fu & Li (2012) explored the possibility that SXP 1062 is a present day accreting magnetar.

In this paper we use a complex multi-wavelength approach and analyse a large set of data with the goal to shed new light on the origin and properties of SXP 1062. The data were collected during the quiescent stage as well as at outburst. The optical observations were obtained with the \salt telescope; we also use publicly available OGLE data. The X-ray observations analysed in this paper are obtained with \swift (long time monitoring), \xmm (in quiescence) and \chandra (in outburst). The optical and X-ray observations were coordinated during outburst. The paper is organized as follows. Section 2 presents the new data and observations. Section 3 is dedicated to the data analysis and results. In Section 4 we compare our results with previous results and discuss the enigmatic properties of SXP 1062. Finally, in Section 5 we present a summary and our final conclusions.

2 Observations

2.1 X-ray data

The X-ray Telescope (XRT) mounted on the \swift observatory (Gehrels et al., 2004) operates in the energy range $0.3-10$ keV. XRT was monitoring SXP 1062 between 2012-10-09 and 2014-10-26. Figure 1 displays the \swift X-ray lightcurve of SXP 1062.

During quiescence of SXP 1062 (pink vertical line in the bottom panel of Fig. 1) we obtained an \xmm observation with the European Photon Imaging Camera (EPIC; Turner et al., 2001; Strüder et al., 2001) (Table 1). EPIC comprises a set of three X-ray CCD cameras: EPIC-MOS1, EPIC-MOS2, and EPIC-pn.

During the \swift monitoring campaign an X-ray outburst was detected on 2014-06-01. The detection of the X-ray outburst triggered our target of opportunity \chandra observations with the Advanced CCD Imaging Spectrometer (ACIS; Garmire, 2001). We obtained four \chandra observations (see Table 1). Dates of observations are marked in Fig. 1 as green vertical lines. The first \chandra observation was performed using the Continuous Clocking Mode which is recommended for very bright sources as it prevents the photon pile-up. The other three exposures were obtained with the standard Timed read out mode.

2.2 Optical data

2.2.1 RSS/SALT

Optical observations were obtained by the 11 m telescope \salt telescope nearly simultaneously with the \chandra observations during SXP 1062 outburst. We obtained four sets of observations (see Table 8). The epochs of three data sets obtained in 2014 are indicated in the top-panel of Fig. 1 as red vertical lines.

The optical spectroscopy was collected using the Robert Stobie dual-beam Visible/Near-IR spectrograph telescope (RSS; Kobulnicky et al., 2003). The data sets consist of long-slit spectra using two different long-slit set-ups. The first covers wavelengths between $6082$ Å and $6925$ Å, i.e., the H$\alpha$ emission line, with a slit width of either $1.25^{\prime\prime}$ (first observation) or $1.5^{\prime\prime}$ (rest of observations). The second set-up covers the range between $3835$ Å and $4924$ Å, i.e., H$\beta$ and H$\gamma$ emission lines with a slit width of $1.5^{\prime\prime}$.

The data were first processed using the PySALT222http://pysalt.salt.ac.za package. Subsequent flat-fielding, background subtraction, wavelength calibration, and extraction of $1D$ spectra were performed with the Image Reduction and Analysis Facility (IRAF333http://iraf.noao.edu). After wavelength calibration and extraction, the final spectra were red-shift corrected for the systemic velocity of the SMC (150 km s*-1*).

The equivalent width ($EW$) calculated by fitting a double Gaussian model are summarized in Table 2 together with the previously published values for comparison.

Figure 2 displays the observed H$\gamma$, H$\beta$ and H$\alpha$ profiles obtained from the RSS/\salt post-outburst observations. The strong H$\beta$ and H$\alpha$ lines show non-split symmetric shapes. The spectrum around the H$\gamma$ line is more noisy and the line structures apparent in some observed spectra are likely due to the noise.

2.2.2 OGLE

The Optical Gravitational Lensing Experiment (OGLE) Monitoring system provides optical I-band photometry of X-ray sources444http://ogle.astrouw.edu.pl/ogle4/xrom/xrom.html located in the fields observed with roughly daily sampling by the OGLE-IV Survey (Udalski, 2008). To date there are seven seasons of data available for SXP 1062 covering the time interval from MJD 55414.4 (2010-08-06) to MJD 57773.039 (2017-01-20).

3 Data Analysis & Results

3.1 Determination of orbital period based on the optical and X-ray

light curves

In general, Be stars show photometric variability on various time scales (Porter & Rivinius, 2003). Stellar rotation and pulsations are held responsible for fast variability, while long-term variability on time scales of a year is typical for formation and dissipation of the disc (Jones et al., 2008). Reig & Fabregat (2015) point out that since the disc constitutes the main reservoir of matter available for accretion, a correlation between X-ray and optical emission should be expected. This is indeed often observed (e.g. Coe et al., 2009). In particular, a few sources are known where the minimum magnitude in optical coincides with the X-ray outburst (e.g., SXP 46.6, see Fig. 4 in McGowan et al., 2008). Importantly, the amplitude of the orbital variation $\sim 0.6$ mag observed in SXP 1062 is very similar to those observed in other systems, such as e.g. AX J0049.4-7323, (Cowley & Schmidtke, 2003).

Among possible explanations of optical outbursts is the tidal interaction of the neutron star with the Be disk. Such interactions lead to strong deformations of the disk during periastron passage (Okazaki & Negueruela, 2001). As discussed by McGowan et al. (2008) and Coe et al. (2009), this might lead to an increase in disk size, which then translates to an increase in optical brightness. Even spectral changes in the optical related to the brightness in the spectral energy distribution of BeXB systems have been observed in several systems. This can be explained by changes in the disk size which alters the contribution to the spectral energy distribution at longer wavelength (see the discussion in Vasilopoulos et al., 2014, and references therein). However, the physical situation is likely more complex because in some BeXBs, e.g. A0535+262, the opposite behavior is observed - during the X-ray outburst, the optical and IR fluxes are reduced (Camero-Arranz et al., 2012; Naik et al., 2012).

No detailed numeric simulations of NS and Be-disk capable to predict the optical and X-ray light curves of individual systems exist yet. However, the coupling between the disc material and X-rays powered by accretion is strongly supported by observed coincidence between optical and X-ray variability.

While not all BeXBs show X-ray outbursts at every periastron passage, on the basis of the previous significant work outlined above, we suggest that the time interval between outbursts in SXP 1062 is the binary orbital period. Future observations constraining binary parameters are required to firmly confirm or disprove this suggestion.

As can be seen in the upper panel in Fig. 1, SXP 1062 shows regular outbursts in the optical. Schmidtke et al. (2012) proposed that the time interval of $656\pm 2$ d between the first two optical outbursts is the orbital period of SXP 1062. Sturm et al. (2013) noticed the fast rise exponential decay (FRED)-shaped profile (Bird et al., 2012) of these optical outbursts, which supports their orbital origin, i.e., the outbursts occur at periastron passage of the NS.

The current OGLE-IV I-band light curve covers more than 6 yr. Three equi-distant outbursts were observed confirming their periodic nature and allowing to better constrain the orbital period. Unfortunately, during the latest outburst predicted for 2016-04-26 (MJD 57504), there was a gap in the OGLE observations. Hence, the latest predicted outburst was not recorded.

To further tighten the orbital period, we selected the minimum magnitude detected in the optical OGLE I-band light curve as the mid-time for the outbursts. The spacing of the OGLE observations is somewhat sparse (roughly once a day), therefore we cannot precisely determine the exact time of the start of the outbursts. To overcome this difficulty, we took the time interval between the data points immediately before and after the mid-time as the uncertainty (second column of Table 3). As a next step, we calculated the time intervals between the outbursts (third column of Table 3), and the weighted average of these time intervals.

One shall be aware, that in some rare cases, such as XTE J1946+274, the X-ray outbursts might not be locked with an orbital period, or happen more than once per orbit (Wilson et al., 2003). Nevertheless, the simplest assumption is that X-ray outbursts in SXP 1062 occur during the periastron passage. As can be seen in Fig. 1, the X-ray outbursts from SXP 1062 are regular and happen nearly at the same time as the optical ones. During our \swift monitoring campaign we have detected an X-ray outburst in excellent agreement with the predictions. This gives further credibility to the scenario where X-ray and optical outbursts in SXP 1062 occur simultaneously at the periastron passage of the NS. Figure 1 also suggests that the minimum optical magnitude of each outburst is apparently increasing with time, i.e. $\Delta$I is decreasing. This could be either of physical origin or due to the sparse data sampling.

3.2 X-ray spectrum in quiescence measured by EPIC/XMM-Newton

X-ray spectra during outburst and quiescence were obtained by \chandra and \xmm, respectively (see section 2.1). The spectral analysis was performed using the X-ray spectral fitting package XSPEC (Arnaud, 1996). All spectra were fitted using a model which includes three absorption components. The first component accounts for the absorption in the Milky Way with a fixed column density $6\times 10^{20}$ cm*-2* and solar abundances (Wilms et al., 2000). The second component accounts for the local absorption in the SMC, and has a fixed column density $2\times 10^{21}$ cm*-2* (Oskinova et al., 2013) and SMC abundances (0.2 times solar for elements heavier than He; Russell & Dopita, 1992). The third component, also with SMC abundances, accounts for the absorption intrinsic to SXP 1062. We keep this absorption component as a free parameter during the spectral fitting procedure.

X-ray luminosities in the energy range 0.2-15 keV assuming a distance modulus to the SMC Wing of $DM=18.7$ (Cignoni et al., 2009) as well as X-ray fluxes are given in Tables 4.

We start by considering the X-ray spectra measured during the quiescence by \xmm  (see Fig. 3). As a first step we have simultaneously fitted all three EPIC spectra (pn, MOS1 and MOS2) with an absorbed power law. The model fit shows residuals in the soft part of the spectra ($\chi^{2}=1.36$). Therefore, as a next step we tried to refine the model adding a black-body component. This led to a statistical improvement of the fit ($\chi^{2}=1.26$). We also tested a combination of a power law and an optically thin thermal plasma component (APEC; Smith et al., 2001) with SMC abundances. However, including this component does not improve the fit. Finally, the best fit is obtained using a power law together with a black-body component, and the thermal plasma component ($\chi^{2}=1.05$). This best-fit model is shown in Fig. 3, and the corresponding parameters for the various models are given in Table 5. Similar X-ray spectral properties of SXP 1062 were previously derived by Hénault-Brunet et al. (2012) from the analysis of observations obtained in March 2010.

A black-body spectral component characterized by kT\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}1.5 keV seems to be a common feature of X-ray spectra of low luminosity (L_{\rm X}\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}10^{36} erg s*-1*) and long spin period (P_{\rm spin}\lower 2.15277pt\hbox{;\buildrel>\over{\sim};}100 s) X-ray pulsars (e.g. La Palombara et al., 2013). This component contributes 30-40% of the source flux below 10 keV and implies a small emission radius ($R_{\rm BB}<0.5$ km) which is typically attributed to the emission from the NS polar caps with a size of $\sim 0.1R_{\rm NS}$ (Hickox et al., 2004).

The X-ray luminosity of the black-body component in the X-ray spectrum of SXP 1062 in quiescence, $L_{\rm X}\approx\left(1.8\pm 0.1\right)\times 10^{35}$ erg s*-1*, amounts to $\sim$40% of the total X-ray emission below $10$ keV, similar to other long-period pulsars. Using the Stefan-Boltzmann law, and the temperature given in Table 5, we estimate the size of the polar cap emission region in SXP 1062 to $R_{\rm BB}=400^{+140}_{-90}$ m.

Our analysis shows that in SXP 1062 the thermal plasma spectral component accounts for $\sim$20% of the X-ray flux in the softest energy band ($0.2-1.0$ keV). Massive stars with spectral types earlier than B2 are sources of thermal X-ray emission (e.g., Berghoefer et al., 1997). The typical X-ray luminosity of a B0III star does not exceed $\sim$1032 erg s*-1* and the bulk of this emission is quite soft with temperatures of about 106 K (Raassen et al., 2005; Fossati et al., 2015). Yet, the luminosity of coronal plasma in SXP 1062 is nearly one order of magnitude larger, $L_{\rm X}\approx 6\times 10^{33}$ erg s*-1*. Hence, the intrinsic X-ray emission from the stellar wind of the B0IIIe-type donor star cannot fully account for the thermal radiation observed from this source. We speculate that this soft component originates, at least partly, in the diffuse emission from the maternal SNR.

3.3 Post-outburst X-ray spectra measured by \chandra

\chandra

obtained four spectra following the outburst detected by \swift (see Fig. 1). The first post-outburst observation (ObsID 15784) has significantly lower X-ray flux than the following observation (ObsID 15785). This sharp post-outburst drop in X-ray flux and its subsequent recovery is also evident in the XRT/\swift light curve. As discussed later in Section 4.1, the flux decrease is mainly due to the strong increase in the absorbing column.

To model the \chandra spectra we started with fitting a simple absorbed power law (see Fig. 4 and Table 5). Subsequently, by analogy with the quiescence spectra we attempted to include a thermal plasma component, but the fits did not improve.

Iron K$\alpha$ emission is often observed in persistent high-mass X-ray binaries (e.g., Giménez-García et al., 2015) and in transient BeXBs during outbursts (Reig, 2011) due to the increase of matter density surrounding the NS. Sturm et al. (2013) found an indication for the presence of an Fe-K$\alpha$ line in their \xmm spectra of SXP 1062 during an outburst in 2012. We also tested for the presence of the iron fluorescence emission line at 6.4 keV in our \chandra spectra but this did not lead to a significant improvement of the fit. This non-detection might be due to a poor signal to noise ratio in our ACIS spectra compared to previous \xmm observations.

3.4 X-ray pulse periods and profiles measured by \xmm and \chandra

To study the pulsational behavior of SXP 1062 we consider the energy bands where the signal from the source dominates over noise, i.e. $0.2-12$ keV for EPIC and $1-8$ keV for ACIS (see Figs. 3 and 4). EPIC-pn and ACIS light curves were extracted with a time binning of 50 s, corrected to the Solar System barycentre using the appropriate software routines, and background subtracted. Over a time interval of $\sim$29 days and after removing high background intervals, joined ACIS light curves cover 107 ks.

The ACIS and the EPIC-pn light curves were searched for periodic signals between 100 and 10000 s using the SCARGLE routine of the Starlink software555http://starlink.jach.hawaii.edu/starlink. This routine performs a fast implementation of the Lomb-Scargle periodogram using Fast Fourier Transforms to increase the speed of computation (Press & Rybicki, 1989). We performed a significance calculation by enabling the SIG option of PERIOD which runs a Fisher randomization test with a number of permutations set by the user (1000 in our case) at the same time as the period search is executed. This task gives as result two false alarm probabilities: FAP1, which is the probability that, given the frequency search parameters, there is no periodic component present in the data with this period; and FAP2, which is the probability that the period is not actually equal to the quoted value but is equal to some other value. We obtained a period of $\sim$1079 s (see bottom panel of Fig. 5) with ${\it FAP1}=0$ and ${\it FAP2}=0$ for the merged ACIS light curve, and a $P_{\rm spin}\sim 1077$ s (see top panel of Fig. 5) with ${\it FAP1}=0$ and ${\it FAP2}=0$ for the EPIC-pn light curve. According to the PERIOD user manual, these FAP values imply that the false alarm probabilities lie between 0.00 and 0.01 with 95% confidence. Both periodograms show several peaks (see Fig. 5), the main peak is the spin period of SXP 1062 at that time, while the other peaks correspond to harmonics of the fundamental frequency.

Period determinations for the EPIC-pn and the four ACIS light curves were also performed with an epoch-folding analysis implemented in the DES7 software package (Larsson, 1996). This routine folds the data at a number of different test periods (this number was set to 200 periods in this analysis) around an initial input period. The input period is the output obtained with the Lomb-Scargle periodograms shown in Fig. 5. For each period, the $\chi^{2}$ over the resulting pulse profile is computed, Fig. 6 shows an example of the distribution of $\chi^{2}$ vs. different test periods for one of our ACIS observations. A best-fit period is determined by fitting a $\chi^{2}$ template function to the observed $\chi^{2}$ distribution (Fig. 6 also shows this $\chi^{2}$ template). This $\chi^{2}$ template function is obtained by performing the same analysis to an artificial light curve that takes the time sampling of the data into account and, in an iterative procedure, the pulse shape of the oscillation. Uncertainties are estimated by Monte Carlo simulations. We have performed 500 Monte Carlo simulations in this analysis. A set of synthetic pulse light curves with the same time sampling and noise level as the data are created and analysed. The distribution of the periods determined during these simulations is used as a measurement of period uncertainty. The results of the analysis are shown in Table 6 together with the previous published spin periods for SXP 1062.

To calculate the period derivatives (see Table 6) we assumed a constant spin down/up between every two subsequent $P_{\rm spin}$ measurements of the pulsar. This is a good approximation for \chandra given the short time interval between the individual measurements. However, the time interval between the EPIC-pn and the first ACIS measurement is too long with an X-ray outburst occurring in between. Therefore, this derivative can only be considered as an average value during that epoch, or even as a minimum value of the spin down if we consider that the pulsar started to spin up just after the outburst.

X-ray light curves were folded over the corresponding pulse period with the dedicated XRONOS666http://heasarc.gsfc.nasa.gov/docs/xanadu/xronos/xronos.html tool efold. This routine folds the light curve over a given period and normalizes it to the corresponding average count rate. Pulse profiles obtained from EPIC-pn data are shown in Fig. 7.

X-ray pulsars exhibit a wide variety of pulse shapes which differ from one source to another and which are strongly dependent not only on the energy band but also on the X-ray luminosity. During quiescence the mass accretion rate is steady and low, the gas can freely fall onto the magnetic poles of the NS, and hence form a pencil beam emission. Therefore, X-ray pulsars in quiescence usually show smooth and single-peaked profiles. However, during periastron passage, the accretion of matter results in an increase of the X-ray flux, and consequently pulse profiles usually show the presence of dips at certain pulse phases which are more prominent at soft X-ray energies than at higher energies (e.g., Naik, 2013).

Previous quiescence observations of SXP 1062 in 2010 showed indications of a double peak in the pulse profile, while during the outburst observed in 2012 there was only one clear peak at energies above 1 keV (see Fig. 4 of Sturm et al., 2013). This behavior is completely opposite to what is expected. However, during the quiescence observation reported in this paper we observe one smooth peak (see Fig. 7), and there might be a small dip; while, during the \chandra post-outburst observations we can clearly see several dips (see Fig. 8); which is what we were expecting.

3.5 Period derivative and orbital Doppler effect

The measured pulse period derivative of any X-ray pulsar is a combination of the intrinsic spin-up or spin-down and the Doppler shift caused by the orbital motion:

[TABLE]

where $v_{\rm orb}$ is the radial velocity, i.e. the projected orbital velocity along the line of sight:

[TABLE]

where $a_{\rm X}\sin i$ is the projected semi-major axis of the pulsar, $P_{\rm orb}$ is the orbital period, $e$ is the eccentricity, and $\omega$ is the longitude of periastron. The true anomaly $\theta(t)$ is found by solving Kepler’s equation.

We check whether the spin period derivative obtained in this work, and also during previous analyses, could be explained as a consequence of the orbital motion of the pulsar along its binary orbit. Following Eq. 1 we calculate the period derivative caused by the orbital Doppler effect assuming no intrinsic changes in the actual spin period and all the change we observe is only due to the orbital motion. This derivative depends on the orbital parameters of the binary system.

Unfortunately, the orbit of SXP 1062 is not known. To roughly estimate a lower limit for the eccentricity we assume that the progenitor binary had a circular orbit and zero kick velocity. Then, after the SN explosion:

[TABLE]

(Verbunt & Phinney, 1995), where $M_{1}$ and $M_{2}$ are the masses of the stars before the SN explosion and $\Delta M$ is the mass loss of the system during this explosion. Hénault-Brunet et al. (2012) estimated an evolutionary mass of $M_{1}\sim 15$ M⊙ for the Be-companion of SXP 1062. Assuming that the NS in SXP 1062 has the canonical mass of a NS (we neglect the difference between baryonic and gravitational masses), i.e., $1.4$ M${}_{\odot}=M_{2}-\Delta M$ (e.g., Lattimer & Steiner, 2014), we estimate the mass loss to be $\Delta M>14$ M⊙.

Consequently, the eccentricity is expected to be close to unity. For our purpose we adopt a conservative approach and use as lower limit for the eccentricity $e>0.4$. Note, that lower eccentricity values for the orbit result in a higher probability for the spin period derivative to be intrinsic. We adopt $e<0.88$, which is the highest eccentricity known to date for a BeXB (2S 1845$-$0242; Finger et al., 1999), as the upper limit for the eccentricity. Consequently, we assume the eccentricity to be uniformly distributed between 0.4 and 0.88. Finally, we adopt an appropriate range of possible orbital parameters as follows:

$P_{\rm spin}=1062$ s as published by Hénault-Brunet et al. (2012) for simplicity. 2. 2.

$P_{\rm orb}=668\pm 10$ d (see Section 3.1). 3. 3.

0.4\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}e\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}0.88 4. 4.

The longitude of periastron ($\omega$) is a geometric effect. Thus, we allow any value between -180∘ and +180∘ and assume a uniform distribution. 5. 5.

Following the third Kepler law, the semi-major axis of the orbit of the NS is $a_{\rm X}=1713.46$ light-s. The orbital inclination is not known, therefore, we let it vary between [math] and $90^{\circ}$.

We performed 100000 Monte Carlo simulations where we calculated the spin period derivative choosing randomly the orbital parameters within the previously estimated ranges. The maximum of the simulated $\dot{P}_{\rm spin}(t)$ for each Monte Carlo run is binned into a histogram that results in a distribution of probability to observe a certain $\dot{P}_{\rm spin}$-value caused by the orbital motion of the binary. Fig. 9 shows this distribution of probabilities. We assume pulse period derivatives out of this distribution to be intrinsic to the pulsar, while those which are within this distribution have different probabilities of being intrinsic depending on their position with respect to the distribution (see last column of Table 6).

4 Discussion

4.1 The Be star decretion disc and the X-ray flux

The H$\alpha$ line is the primary indicator for the presence of a decretion disc around a Be star and its $EW$ provides information about the size of this disc. In Section 2.2.1 we presented \salt observations at different epochs which allow us to study the time evolution of H$\alpha$ and H$\beta$ emission lines and their $EW$. The non-split shape of Balmer lines and the time evolution of the absorbing column deduced from X-ray spectra indicates that we likely observe the Be disc face on.

Reig et al. (1997) and, most recently Haberl & Sturm (2016) showed a correlation between the orbital periods and the $EW$ of the H$\alpha$ line in BeXBs which follows a linear trend with larger H$\alpha$ emission for longer orbital periods. This correlation was explained in the framework of the truncation disc model. The disc truncation is responsible for the so-called Type II X-ray outbursts, and inhibits the growth of the decretion disc (Negueruela et al., 2001; Okazaki & Negueruela, 2001). Interestingly, SXP 1062 does not follow the H$\alpha$-orbital period correlation, likely its Be-disc is smaller than usual for its orbital period.

As can be seen from Table 2 the equivalent width of H$\alpha$ in optical spectra of SXP 1062 keeps increasing over years, however it drops after the X-ray outburst, as can indeed be expected for a BeXB. This change provides further confirmation that the NS interacts with the Be-disc during the outburst. However, the decrease in the disc size after the outburst is not dramatic, indicating that the disc of the donor star in SXP 1062 is likely not truncated during the outburst.

4.2 Evolution of the spectral parameters

As shown in sections 3.2 and 3.3, the basic X-ray spectrum of SXP 1062 is an absorbed power law. This is similar to X-ray spectra of other BeXBs in the SMC (Haberl et al., 2008).

Our data set allows us to investigate how the X-ray spectrum of SXP 1062 changes in the different luminosity regimes, i.e. during quiescence and post-outburst. As seen in Table 5 immediately after the outburst the absorption column is strongly increased compared to the quiescence, and then decreases with time. At the same time, the spectrum initially softens (power-law index drops), and then hardens post-outburst. This points out to the accumulation of matter in the vicinity of the X-ray source towards and during the outburst, and a fast depletion afterwards.

We tentatively interpret this behavior in the framework of a model that assumes that the outburst is triggered by the passage of the NS through the Be-disc. The orbit of the NS is probably inclined to the disc. According to this scenario, after the NS pierces the Be-disc, it is observed through the disc material. As the time progresses, the column density decreases to its low quiescence value. Similar behavior is also observed in other systems, e.g. SXP 5.05 (Coe et al., 2015). Future work, especially hydrodynamic modelling of winds from fast rotating Be stars, shall clarify whether the scenario we consider here is viable.

4.3 Spin period evolution and magnetic field

In this work we present new spin-period measurements for SXP 1062. With these new data we confirm that the pulsar appears to be spinning down continuously since it was discovered in March 2010 until at least, October 2013, which is the date of our quiescence \xmm observation. Our first \chandra post-outburst spin period (1091 s; 2014-06-19) is longer than observed in October 2013 (1077.97 s), consequently, the pulsar could even have been spinning down until some time before the outburst detected by \swift in June 2014 (see Fig. 10). However, we have observed for the first time a spin up for SXP 1062 just after the outburst detected by \swift. We also observe how SXP 1062 seems to recover its usual spin down in the last observation. To confirm this spin down we would need more observations.

Next we estimate the magnetic field of SXP 1062. The present day magnetic field of the NS in SXP 1062 is not known. An interesting proposal has been made by Fu & Li (2012) and Ikhsanov (2012) and discussed later by other authors, that this compact object can have a magnetar-scale field. In this case, the NS would belong to the hypothetical class of accreting magnetars proposed by Reig et al. (2012). Besides SXP 1062, some other long period X-ray pulsars are suggested to be accreting magnetars (e.g. Sanjurjo et al., 2017). Especially after the recent discovery of ultra-luminous X-ray sources with NSs the accreting magnetar idea gained further support (Ekşi et al., 2015; Mushtukov et al., 2015). However, the possibility that Myr old accreting NSs have very strong magnetic fields questions the standard scenario of field evolution in NSs (Pons et al., 2009; Turolla et al., 2015)

Our target, SXP 1062, represents an extremely rare case of a relatively young NS with known age. This object provides unique insights to the NS magnetic field evolution. Therefore, we believe that despite the challenges related to the scarcity of the data it is of great importance to constrain its magnetic field.

There are various methods commonly applied for indirect estimates of the NS magnetic field based on its spin behavior (e.g. Shi et al., 2015; D’Angelo, 2017, and references therein). Such methods, based on older models of accretion, have been used in the past to derive strong magnetic fields for NSs in Be/X-ray binaries (e.g. Klus et al., 2014; Ho et al., 2014, and references therein). In the following we combine the spin period evolution and system parameters of SXP 1062 to estimate the magnetic field strength of its NS. Our analysis is based on a recent model of quasi-spherical settling accretion developed by Shakura et al. (2012).

4.3.1 Spin period equilibrium hypothesis

We start with a magnetic field estimate based on the hypothesis of spin equilibrium. This assumption is often used to derive field estimates in the case of X-ray pulsars. It is supposed that in a stationary situation spin-up and spin-down torques balance each other, and so the spin period is equal to the equilibrium value (Davidson & Ostriker, 1973). This quantity depends on several parameters of the system (accretion rate, properties of the accretion flow, parameters of the binary system, etc.). In particular, it depends on the magnetic field of the NS. Therefore, if all other parameters are more or less well known we can estimate the magnetic field using the following equation from Postnov et al. (2015) (see details on the derivation of this formula in Shakura et al. 2013):

[TABLE]

Here $v_{\rm w8}$ is the stellar wind velocity in units of $10^{8}$ cm s*-1*, $\dot{M}_{16}$ is the mass accretion rate in units of $10^{16}$ g s*-1*, and $\mu_{30}$ is the magnetic moment in units of $10^{30}$ G cm3 ($\mu_{30}=1$ corresponds to $B=10^{12}$ G on the equator for the standard $R_{\rm NS}\sim 10$ km; note, that for $R_{\rm NS}\sim 15$ km (Bogdanov, 2013), the field $B$ would be half an order of magnitude smaller for the same $\mu$). This equation is applicable to systems with quasi-spherical accretion with \dot{M}\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}10^{16} g s*-1* (so-called settling accretion regime which is applicable to X-ray pulsars with L_{\rm X}\lower 2.15277pt\hbox{;\buildrel<\over{\sim};}10^{36} erg s*-1*, see Shakura et al., 2012).

Substituting the parameters for SXP 1062 we obtain:

[TABLE]

Assuming wind velocities $v_{\rm w}\sim 200$ km s*-1*, which is typical for quasi-spherical winds observed from Be stars (Waters et al., 1988), the estimated magnetic field has a standard value of $B\sim 7\times 10^{12}$ G. If we assume higher wind velocities the magnetic field would even be lower. Consequently, according to this estimate, we are not dealing with a present-day magnetar.

4.3.2 Out of equilibrium hypothesis

Long-term spin down

We have seen that the pulsar might be out of equilibrium because we observe a continuous spin down over years (see Fig. 10). Therefore, we can use the data which correspond to the spin down of the pulsar to obtain another estimate of the magnetic field. Again, we use an equation from Postnov et al. (2015):

[TABLE]

Here $\Pi_{\mathrm{sd}}$ is a parameter of the theory of settling accretion, its typical value is $\sim$5$-$10. Postnov et al. (2015, and references therein) demonstrate that this parameter does not change much from system to system. As we cannot derive it independently, we choose a typical value $\Pi_{\mathrm{sd}}=7$. The variation of this parameter might have a very limited (less than a factor of two) influence on the estimate of $\mu$. From the observations of SXP 1062 we can estimate an average $\dot{P}_{\mathrm{sd}}\approx 0.02$ s d*-1*. Then we obtain $\mu_{30}\approx 3$, which corresponds to $B\sim 3\times 10^{12}$ G. Taking into account many uncertainties in models and parameters, this result is in reasonable correspondence with the estimate obtained above from the equilibrium period. Note, that these values are in correspondence with the saturation value for magnetar field decay (Pons et al., 2009; Gourgouliatos & Cumming, 2014).

Spin up during the outburst

Finally, we discuss the spin up rate $\dot{P}_{\mathrm{su}}$ observed during the outburst detected by our \swift monitoring campaign. For this case we can neglect the braking torque. Then the equation for the evolution of the period reads:

[TABLE]

where $I$ is the moment of inertia of the NS, we assume a standard value $10^{45}$ g cm2 for it. $R_{\mathrm{B}}$ is the Bondi radius. This equation provides an upper limit for the modulus of $\dot{P}_{\rm su}$, but realistic values are not much smaller (Lipunov, 1992).

Note, that the maximum spin up happens during outbursts which appear close to the periastron. Then, we cannot take an average value for $R_{\rm B}$ which depends on $v_{\rm orb}$ and hence on the eccentricity. For larger eccentricities we obtain larger spin up. If we take $e=0.7$, $\dot{M}=10^{17}$ g s*-1*, stellar mass $15\,M_{\odot}$ and $v_{\rm w}=200$ km s*-1*, we obtain $\dot{P}_{\mathrm{su}}\approx 0.5$ s d*-1*. The observed average value for SXP 1062 is $\dot{P}_{\rm su}\sim 0.5$ s d*-1*. Then, we can conclude that the spin-up can be described by relatively highly eccentric orbits, which coincides with the estimation we have performed of the orbital parameters (see Section 3.5).

These simple estimates agree within uncertainties with those presented in Sec. 3 and are in line with the theoretical expectations for magnetic field evolution of magnetars. Therefore, we can explain the spin period derivative observed in SXP 1062 applying the theory of quasi-spherical accretion (Shakura et al., 2012) without the need of an extremely strong magnetic field. Future and in depth theoretical modelling of SXP 1062 is necessary to fully verify this conjecture which is of general interest in the context of yet poorly understood magnetic field evolution of NSs.

4.4 On the classification of SXP 1062

BeXBs are classified into two broad subgroups: transient BeXBs and persistent BeXBs (Reig, 2011), which may overlap in part of their properties. In Table 7 we summarize the key characteristics of these sub-groups.

SXP 1062 has properties that are shared by both of these sub-groups. Its large X-ray luminosity in quiescence (see Table 4), the long binary orbital period $P_{\rm orb}=668\pm 10$ days, and its long pulse period $P_{\rm spin}\sim 1070$ s, are typical for persistent BeXBs. Also, to date no known BeXB system containing a NS with $P_{\rm spin}>100$ s has an eccentricity above 0.5 (Townsend et al., 2011). On the other hand, the Type I outburst reported in this work, although moderate, is a characteristic of transient BeXBs. Therefore, the properties of SXP 1062 suggest that systems exist which can be classified as member of both groups and that transient and persistent BeXBs are not completely separated sub-groups.

5 Summary and Conclusions

In this work we present a coordinated optical and X-ray study of the X-ray pulsar SXP 1062 during quiescence and outburst. The main results of our study are:

• $-$

We observed a third Type I outburst in SXP 1062. The outburst occurred at a regular interval from two previously observed. The binary period is constrained to $P_{\rm orb}\approx 668\pm 10$ d. Type I outbursts are characteristic for transient BeXB. Thus SXP 1062 shares observational characteristics with persistent as well as transient BeXBs.

• $-$

The profiles of the H$\alpha$ line indicate that we likely observe the Be-disc face on, while the temporal evolution of its $EW$ shows that the disc is not truncated in the aftermath of the outburst.

• $-$

We confirm the earlier reports on the presence of a black body spectral component in the quiescent X-ray spectrum of SXP 1062.

• $-$

Our analysis of the pre- and post-outburst spectra reveals an abrupt increase in the absorption column just after the outburst. Taking into account the H$\alpha$ line profile, we propose that the disc of the Be star is observed face on, while the orbit of the NS is inclined to the disc.

• $-$

Studies of the NS spin evolution reveal that the NS had been intrinsically spinning down at least from March 2010 until October 2013. We report a brief post-outburst spin up of the X-ray pulsar.

• $-$

We estimate the magnetic field for SXP 1062, assuming different hypotheses for the spin period evolution (e.g., close to equilibrium, out of equilibrium) and the quasi-spherical accretion model (Shakura et al., 2012). From these calculations we find no need for an extremely high magnetic field at present day for the pulsar in SXP 1062.

Acknowledgments

The authors thank the referee for useful comments and suggestions that helped to improve the paper. SBP thanks Profs. N.I. Shakura and K.A. Postnov for discussions. AGG and LO are supported by the Deutsches Zentrum für Luft und Raumfahrt (DLR) grants FKZ 50 OR 1404 and FKZ 50 OR 1508. LO acknowledging partial support by the Russian Government Program of Competitive Growth of Kazan Federal University. MK acknowledges funding by the Bundesministerium für Wirtschaft und Technologie under Deutsches Zentrum für Luft- und Raumfahrt grants 50 OR 1113 and 50 OR 1207. SBP is supported by the Russian Science Foundation grant 14-12-00146.MPES received funding through the Claude Leon Foundation Postdoctoral Fellowship program and the National Research Foundation.

Appendix A LOG of SALT observations