Swift observations of SMC X-3 during its 2016-2017 super-Eddington outburst

TL;DR

This study monitored the 2016-2017 super-Eddington outburst of SMC X-3 with Swift, revealing its extreme luminosity, magnetic field, and pulse profile evolution, providing insights into neutron star accretion physics.

Contribution

First detailed analysis of SMC X-3's super-Eddington outburst with Swift, measuring orbital parameters, magnetic field, and spectral components during extreme luminosity.

Findings

X-ray luminosity reached ~10^39 erg/s during outburst

Spin frequency increased and approached equilibrium, indicating a strong magnetic field

Emergence of a low-temperature thermal component as flux decayed

Abstract

The Be X-ray pulsar, SMC X-3 underwent a giant outburst from 2016 August to 2017 March, which was monitored with the Swift satellite. During the outburst, its broadband flux increased dramatically, and the unabsorbed X-ray luminosity reached an extreme value of $\sim 10^{39}$ erg/s around August 24. Using the Swift/XRT data, we measure the observed pulse frequency of the neutron star to compute the orbital parameters of the binary system. After applying the orbital corrections to Swift observations, we find that the spin frequency increases steadily from 128.02 mHz on August 10 and approach to spin equilibrium $\sim 128.74$ mHz in 2017 January with an unabsorbed luminosity of $L_{\rm X} \sim 2\times10^{37}$ erg/s, indicating a strong dipolar magnetic field $B \sim 6.8\times10^{12}$ G at the neutron star surface. The spin-up rate is tightly correlated with its X-ray luminosity during the super-Eddington outburst. The pulse profile in the Swift/XRT data is variable, showing double peaks at the early stage of outburst and then merging into a single peak at low luminosity. Additionally, we report that a low temperature ($kT \sim 0.2$ keV) thermal component emerges in the phase-averaged spectra as the flux decays, and it may be produced from the outer truncated disk or the boundary layer between the exterior flow and the magnetosphere.

Tables

Table 1. Table 1 Log of Swift /XRT data

ObsID	Date	Exposure	Mode	$R_{\mathrm{Source}}$	$R_{\mathrm{Background}}$	$L_{0.6-10keV}$
		(second)		(pixel)	(pixel/pixel)	(1037 erg/s)
00034673001	2016-08-10	4671	WT	25	25/50	${35.3}_{-0.4}^{+0.4}$
00034673002	2016-08-12	1978	WT	25	25/50	${46.9}_{-0.7}^{+0.7}$
00034673003	2016-08-14	935	WT	25	25/50	${59.0}_{-1.1}^{+1.1}$
00034673004	2016-08-18	1997	WT	25	25/50	${68.3}_{-0.8}^{+0.8}$
00034673005	2016-08-20	2050	WT	25	25/50	${84.0}_{-1.0}^{+1.0}$
00034673006	2016-08-22	1958	WT	25	25/50	${90.1}_{-0.9}^{+0.9}$
00034673007	2016-08-24	1291	WT	25	25/50	${102.7}_{-1.3}^{+1.4}$
00034673008	2016-08-26	504	WT	25	25/50	${98.2}_{-1.9}^{+1.9}$
00034673009	2016-08-28	1583	WT	25	25/50	${98.2}_{-1.1}^{+1.1}$
00034673010	2016-08-30	953	WT	25	25/50	${88.1}_{-1.3}^{+1.3}$
00034673011	2016-09-01	793	WT	25	25/50	${92.9}_{-1.6}^{+1.6}$
00034673012	2016-09-03	1932	WT	25	25/50	${78.9}_{-1.0}^{+1.0}$
00034673013	2016-09-05	1345	WT	25	25/50	${56.6}_{-1.0}^{+1.0}$
00034673014	2016-09-06	2985	WT	25	25/50	${61.1}_{-0.6}^{+0.6}$
00034673015	2016-09-07	2977	WT	25	25/50	${61.3}_{-0.7}^{+0.7}$
00034673016	2016-09-08	2764	WT	25	25/50	${57.2}_{-0.7}^{+0.7}$
00034673017	2016-09-13	2973	WT	25	25/50	${45.1}_{-0.5}^{+0.5}$
00034673018	2016-09-14	2979	WT	25	25/50	${44.2}_{-0.5}^{+0.5}$
00034673019	2016-09-15	2981	WT	25	25/50	${42.8}_{-0.5}^{+0.5}$
00034673020	2016-09-17	3004	WT	25	25/50	${33.5}_{-0.4}^{+0.4}$
00034673021	2016-09-19	2918	WT	25	25/50	${30.8}_{-0.4}^{+0.4}$
00034673022	2016-09-21	2591	WT	25	25/50	${27.4}_{-0.4}^{+0.4}$
00034673023	2016-09-23	2992	WT	25	25/50	${26.0}_{-0.4}^{+0.4}$
00034673024	2016-09-25	2610	WT	25	25/50	${24.9}_{-0.4}^{+0.4}$
00034673025	2016-09-27	3289	WT	25	25/50	${23.6}_{-0.4}^{+0.4}$
00034673026	2016-09-29	2969	WT	25	25/50	${19.3}_{-0.4}^{+0.4}$
00034673027	2016-10-01	553	WT	25	25/50	${17.6}_{-0.7}^{+0.8}$
00034673028	2016-10-03	1718	WT	25	25/50	${16.2}_{-0.4}^{+0.4}$
00034673029	2016-10-06	726	WT	25	25/50	${17.5}_{-0.9}^{+1.0}$
00034673030	2016-10-07	2789	WT	25	25/50	${14.9}_{-0.3}^{+0.3}$
00034673031	2016-10-09	2839	WT	25	25/50	${13.2}_{-0.3}^{+0.3}$
00034673032	2016-10-11	1982	WT	25	25/50	${12.6}_{-0.3}^{+0.4}$
00034673033	2016-10-13	2028	WT	25	25/50	${12.2}_{-0.3}^{+0.3}$
00034673034	2016-10-14	1199	WT	25	25/50	${11.6}_{-0.4}^{+0.5}$
00034673035	2016-10-19	2493	WT	25	25/50	${10.2}_{-0.3}^{+0.3}$
00034673036	2016-10-20	2852	WT	25	25/50	${9.62}_{-0.26}^{+0.26}$
00034673037	2016-10-21	3435	WT	25	25/50	${9.31}_{-0.22}^{+0.23}$
00034673038	2016-10-23	3685	WT	25	25/50	${9.37}_{-0.22}^{+0.22}$
00034673039	2016-10-25	3626	WT	25	25/50	${8.51}_{-0.21}^{+0.22}$
00034673040	2016-10-27	2959	WT	25	25/50	${7.67}_{-0.25}^{+0.25}$
00034673041	2016-10-29	3984	WT	25	25/50	${9.04}_{-0.23}^{+0.23}$
00034673042	2016-11-06	5256	WT	25	25/50	${7.16}_{-0.17}^{+0.18}$
00034673043	2016-11-04	3973	WT	25	25/50	${7.59}_{-0.22}^{+0.22}$
00034673044	2016-11-08	4646	WT	25	25/50	${6.57}_{-0.18}^{+0.18}$
00034673045	2016-11-10	4453	WT	25	25/50	${6.30}_{-0.18}^{+0.18}$
00088012001	2016-11-13	1803	WT	25	25/50	${5.56}_{-0.26}^{+0.26}$
00034673046	2016-11-14	4452	WT	25	25/50	${5.78}_{-0.16}^{+0.16}$
00034673047	2016-11-16	4328	WT	25	25/50	${5.91}_{-0.19}^{+0.19}$
00034673048	2016-11-18	4628	WT	25	25/50	${5.04}_{-0.15}^{+0.16}$
00034673049	2016-11-20	4881	WT	25	25/50	${5.07}_{-0.16}^{+0.16}$
00034673050	2016-11-22	3287	WT	25	25/50	${4.21}_{-0.17}^{+0.17}$
00034673051	2016-11-24	4484	WT	25	25/50	${3.89}_{-0.14}^{+0.14}$
00034673053	2016-11-26	4430	WT	25	25/50	${3.82}_{-0.15}^{+0.15}$
00034673054	2016-11-28	4589	WT	25	25/50	${3.37}_{-0.14}^{+0.15}$
00034673055	2016-11-30	5026	WT	25	25/50	${3.35}_{-0.12}^{+0.13}$
00034673056	2016-12-02	4563	WT	25	25/50	${3.01}_{-0.13}^{+0.13}$

Table 2. Table 1 Log of Swift /XRT data

ObsID	Date	Exposure	Mode	$R_{\mathrm{Source}}$	$R_{\mathrm{Background}}$	$L_{0.6-10keV}$
		(second)		(pixel)	(pixel/pixel)	(1037 erg/s)
00034673057	2016-12-04	4915	WT	25	25/50	${2.57}_{-0.12}^{+0.12}$
00034673058	2016-12-06	4917	WT	25	25/50	${2.24}_{-0.11}^{+0.11}$
00034673059	2016-12-08	4526	WT	25	25/50	${2.68}_{-0.12}^{+0.13}$
00034673060	2016-12-10	4711	WT	25	25/50	${2.70}_{-0.11}^{+0.11}$
00034673061	2016-12-12	3073	WT	25	25/50	${2.92}_{-0.16}^{+0.16}$
00034673062	2016-12-14	3538	WT	25	25/50	${2.83}_{-0.13}^{+0.13}$
00034673063	2016-12-16	4380	WT	25	25/50	${3.08}_{-0.12}^{+0.13}$
00034673064	2016-12-28	4189	WT	25	25/50	${2.25}_{-0.11}^{+0.11}$
00034673065	2016-12-30	4288	WT	25	25/50	${2.36}_{-0.12}^{+0.12}$
00034673066	2017-01-01	2026	WT	25	25/50	${2.30}_{-0.18}^{+0.19}$
00034673067	2017-01-10	1179	WT	25	25/50	${1.37}_{-0.23}^{+0.26}$
00034673069	2017-01-13	1666	WT	25	25/50	${0.75}_{-0.11}^{+0.12}$
00034673071	2017-01-16	768	PC	15	15/30	${0.68}_{-0.08}^{+0.09}$
00034673073	2017-01-18	82	PC	15	15/30	$\cdots$ §
00034673074	2017-01-19	445	PC	15	15/30	${0.77}_{-0.11}^{+0.12}$
00034673075	2017-01-20	382	PC	15	15/30	${0.83}_{-0.11}^{+0.12}$
00034673076	2017-01-21	347	PC	15	15/30	${1.05}_{-0.14}^{+0.16}$
00034673077	2017-01-22	329	PC	15	15/30	${1.06}_{-0.15}^{+0.17}$
00034673078	2017-01-23	355	PC	15	15/30	${1.38}_{-0.15}^{+0.17}$
00034673079	2017-01-24	336	PC	15	15/30	${1.67}_{-0.17}^{+0.19}$
00034673080	2017-01-25	235	PC	15	15/30	${1.65}_{-0.19}^{+0.22}$
00034673081	2017-01-27	2295	WT	15	15/30	${1.98}_{-0.16}^{+0.16}$
00034673082	2017-01-29	237	PC	15	15/30	${1.75}_{-0.20}^{+0.23}$
00034673083	2017-01-31	394	PC	15	15/30	${1.86}_{-0.16}^{+0.17}$
00034673084	2017-02-02	552	PC	15	15/30	${1.76}_{-0.14}^{+0.15}$
00034673087	2017-02-20	138	PC	15	15/30	$\cdots$ §
00034673088	2017-02-24	385	PC	15	15/30	$\cdots$ §
00034673089	2017-02-26	411	PC	15	15/30	$\cdots$ §
00034673091	2017-03-07	198	PC	15	15/30	$\cdots$ §
00034673092	2017-03-08	57	PC	15	15/30	$\cdots$ §
00034673093	2017-03-09	345	PC	15	15/30	${0.46}_{-0.10}^{+0.13}$
00034673094	2017-03-10	384	PC	15	15/30	${0.46}_{-0.10}^{+0.12}$
00034673095	2017-03-11	350	PC	15	15/30	${0.42}_{-0.08}^{+0.09}$
00034673096	2017-03-23	229	PC	15	15/30	undetected
00034673097	2017-03-24	104	PC	15	15/30	undetected
00034673098	2017-03-26	192	PC	15	15/30

Full text

1. Introduction

High-mass X-ray binaries contribute a large fraction of X-ray emission in normal galaxies, and they are believed to reflect the recent star-formation activities in their host galaxies (e.g. grimm02; mineo12). According to the states of their optical companions, high-mass X-ray binaries can be subdivided into supergiant X-ray binaries and Be/X-ray binaries (BeXBs). A BeXB consists of a Be star and a compact object. Virtually, all confirmed compact objects in BeXBs are neutron stars (NSs), and all these systems show X-ray pulsations (see Reig 2011 for reviews). As young systems, NSs in BeXBs have high magnetic field ($B>10^{10}$ G); therefore, BeXBs provide unique natural laboratories for studying physics in extremely strong gravity and magnetic fields.

The direct measurement of a NS magnetic field strength can be achieved from the detection of a cyclotron scattering resonance feature (e.g. coburn02; yan12; furst14; walter15, and references therein). Additionally, investigating the interaction between the magnetosphere and the accretion matter, we can acquire the information of NS magnetic field indirectly (e.g. weng11; shi15; christodoulou16). That is, the effect of the magnetic field strength manifest itself by the size of its magnetosphere co-rotating with the central NS. The boundary of the magnetosphere is determined where the ram pressure of in-falling flow is balanced by magnetic pressure; thus, it expands with field strength and decreases with mass accretion rate (lamb73; ghosh79). As the accretion rate decreases below the critical value, the magnetospheric radius ($R_{\rm m}$) grows beyond the corotation radius ($R_{\rm co}=\sqrt[3]{\frac{GMP^{2}}{4\pi^{2}}}$), at which the Keplerian angular frequency is equal to the NS spin frequency, and the centrifugal barrier spins away accretion matter. If most of material is prevented from accreting onto NS, X-ray flux and pulsation decay sharply in a few days, i.e. the “propeller” effect (e.g. cui97; campana14). Alternatively, the magnetosphere is penetrated into the corotation radius at high luminosity, leading to the spin-up of a NS. If NSs are close to spin equilibrium, their magnetic fields can be estimated from long-term averaged spin parameters and X-ray luminosity (e.g. klus14; shi15). Meanwhile, the torque reversals between steady spin-up and spin-down are commonly shown in BeXBs (e.g. bildsten97).

Besides the long-term average spin evolution, the instantaneous torque measurements during episodic outbursts are essential to test accretion torque theories. Transient BeXBs experience periodic and less energetic ($L_{\rm X}<10^{37}$ erg/s) outbursts or rare giant outbursts, which are referred to as type I and type II outbursts, respectively (reig11). The tight relationships between spin-up rate and (pulsed) flux detected in the luminous outbursts of BeXBs (e.g. A0535+262 and 2S 1417-624) are interpreted as the sign of transient accretion disks around NSs, which are supported by the detection of simultaneous quasi-periodic oscillations (QPOs) (finger96; sartore15). It is worth to note that a small number of sources (e.g. SMC X-1, LMC X-4, 4U 0115+63, V0332+53) can reach a peak X-ray luminosity in excess of $10^{38}$ erg/s (e.g. li11; mushtukov15b, and references therein). Intriguingly, a growing number of ultraluminous X-ray sources (ULXs) in nearby galaxies have been found to exhibit coherent pulsations (bachetti14; furst16; israel16; israel17), indicating a connection to X-ray pulsars (shao15; mushtukov15b; kawashima16; king16; mushtukov17). Nowadays, super-Eddington accretion in magnetized NSs draw more attention (e.g. eksi15; pan16; tsygankov16; chen17). However, a detailed study on such dramatic phenomena is hampered by the lack of observations.

The Small Magellanic Cloud (SMC) is the second nearest galaxy ($d=62.1$ kpc; hilditch05; graczyk14; scowcroft16) after the Large Magellanic Cloud, and it has high-mass X-ray binaries in abundance due to the recent star-forming activities (zaritsky02; sturm13; yang17). SMC X-3 (also known as SXP 7.78) was discovered with SAS 3 X-ray observatory in 1978 (clark78), and was identified as an accreting pulsar with a detected pulsation of 7.78 second (edge04). The spectral type of the optical counterpart is identified as B1–B1.5 with $V=14.91$ (mcbride08). The orbital period $\sim 44.9$ days was detected in both X-ray and optical bands (corbet03; cowley04; galache08; bird12). However, its eccentricity and other orbital parameters are still unknown. Recently, SMC X-3 underwent a giant type II outburst in 2016 with a peak X-ray luminosity of $\sim 10^{39}$ erg/s, and it was monitored in Target of Opportunity mode by Swift since 2016 August 10. On 2016 November 8, we reported our preliminary results on analyzing the Swift data (weng16), which are the basis of this work. During preparation of this manuscript, townsend17 investigated the optical and X-ray data (including the Swift data) of SMC X-3, and obtained similar orbital parameters of the binary as given in our paper. In this paper, we focus on the Swift data and carry out a comprehensive analysis on these data to investigate the physics of super-Eddington accretion around a magnetized NS. The data reduction is described in the next section. In Section 3, we perform the timing analysis and calculate the orbital elements of the binary. In Section 4, we discuss the physical implications of these results and present our main conclusions.

2. Data Reduction

The MAXI/GSC was triggered by brightening of SMC X-3 on 2016 August 8 (negoro16), which was confirmed by Swift during its survey of the SMC (kennea16). In this paper, we analyze all Swift pointing observations taken between 2016 August 10 and 2017 January 1. The Swift Gamma Ray Burst Explorer carries three scientific instruments covering a broad energy range of $\sim 0.002-150$ keV: the Burst Alter Telescope (BAT), the X-ray Telescope (XRT), and the UV/Optical Telescope (UVOT) (gehrels04). The BAT daily light curve is adopted from krimm13 111http://swift.gsfc.nasa.gov/results/transients/. Meanwhile, both the XRT and the UVOT data are processed with the packages and tools available in heasoft 6.19.

When the source is bright, the observations are carried out in the windowed-timing (WT) mode. While after 2017 January 16, the count rate in 0.5–10 keV is less than 0.5 cts/s, and the observations are performed in the photon-counting (PC) mode without significant pile-up effects (Table 1). For the XRT data, the initial event cleaning is executed with the task xrtpipeline using standard quality cuts. The source and background events are extracted from a circle and an annulus region centered at the source position, respectively. The light curves are corrected for the telescope vignetting and point-spread-function losses with the task xrtlccorr, and then are subtracted by the scaled background count rate to yield the net light curves (Figure LABEL:lc). The hardness for each observation is calculated as the ratio of average count rates (CR) in (2.0–10.0 keV)/(0.5–2.0 keV) bands. The source becomes undetected in last three observations, the upper limit of count rates are estimated by using the X-ray image package XIMAGE.

The ancillary response files are created using the task xrtmkarf and the latest response files are taken from the CALDB database for the spectral analyses. The spectral fitting is restricted to the 0.6–10 keV energy range due to calibration residuals below 0.6 keV for the WT mode data222see http://swift.gsfc.nasa.gov/docs/heasarc/caldb/swift/docs/xrt/ SWIFTXRT-CALDB-09.pdf. For the PC mode data, we employ the C-statistic (cash79) instead of common $\chi^{2}$ for spectral fitting in 0.3–10 keV because of low count rates and short exposure times. Unfortunately, spectra are unavailable for some observations which have very limited photons (Table 1). The absorption column density along the line of sight to SMC X-3 is difficult to constrain and could yield an extremely small value ($nH<10^{14}$ cm*-2*) for some of the observations; therefore, we fix it to the Galactic absorption towards the direction of the source ($6.57\times 10^{20}$ cm*-2*, dickey90). At the early stage of the outburst, the phase-averaged spectra can be well fitted by an absorbed power-law (PL) model with a photon index of $\sim 0.7-1.2$. These results are consistent with those seen in NuSTAR data, which can be fitted by a cutoff PL model with a photon index $\sim 0.5-0.7$ and a folding energy of $\sim 11-15$ keV (pottschmidt16; tsygankov17). During 2016 September 25 and December 12, the soft excess emerges below 1 keV, which can be described by a black-body (BB) emission with $kT\sim 0.1-0.2$ keV and $R_{\rm BB}\sim 10^{2}-10^{3}$ km. The soft thermal component is variable and contributes a small fraction ($\sim 1-3$%) of total flux in 0.6–10 keV; however, because of the low S/N ratio of band-limited data, we cannot put a tight constraint on this component.

In order to rule out the instrumental influence, we also analyze the XMM-Newton EPIC-pn spectrum observed on 2016 October 14-15 and confirm the existence of the thermal component. The EPIC-MOS data were taken in imaging mode and suffered from the pile-up effect; therefore, we only use the EPIC-pn data which was in timing mode. The data in the first 4.5 kilo seconds are excluded because of background flares, and the spectrum is extracted from the rest data with an exposure time of 28 kilo seconds. The EPIC-pn spectrum cannot be well fitted by a single PL model with a reduced $\chi^{2}$ larger than 2.9. When a cool BB component is added, the reduced $\chi^{2}$ decreases to 1.07, and it further reduces to 0.75 with including an additional Gaussian line (phabs*(bbodyrad+powerlaw+gauss) in XSPEC, Figure LABEL:spec). The best fitted parameters are: $nH=1.4_{-0.2}^{+0.2}\times 10^{21}$ cm*-2*, $kT=0.19_{-0.01}^{+0.01}$ keV, $Norm_{\rm BB}=1136_{-392}^{+560}$, $\Gamma=0.99_{-0.01}^{+0.01}$, $Norm_{\rm PL}=1.54_{-0.03}^{+0.03}\times 10^{-2}$, $E_{\rm l}=6.65_{-0.10}^{+0.10}$ keV, $\sigma=0.35_{-0.10}^{+0.14}$ keV, $Norm_{\rm Gau}=1.64_{-0.45}^{+0.53}\times 10^{-5}$, and $\chi^{2}/dof=123.8/165$. More detailed analysis on the XMM-Newton data will be presented else where.