Accretion Torque Reversals in GRO J1008-57 Revealed by Insight-HXMT
W. Wang, Y. M. Tang, Y. L. Tuo, P. R. Epili, S. N. Zhang, L. M. Song, F. J. Lu, J. L. Qu, S. Zhang, M. Y. Ge, Y. Huang, B. Li, Q. C. Bu, C. Cai, X. L. Cao, Z. Chang, L. Chen, T. X. Chen, Y. B. Chen, Y. Chen, Y. P. Chen, W. W. Cui, Y. Y. Du, G. H. Gao, H. Gao, Y. D. Gu, J. Guan, C. C. Guo, D. W. Han, J. Huo, S. M. Jia, W. C. Jiang, J. Jin, L. D. Kong, C. K. Li, G. Li, T. P. Li, W. Li, X. Li, X. B. Li, X. F. Li, Z. W. Li, X. H. Liang, J. Y. Liao, B. S. Liu, C. Z. Liu, H. X. Liu, H. W. Liu, X. F. Lu, Q. Luo, T. Luo, R. C. Ma, X. Ma, B. Meng, Y. Nang, J. Y. Nie, G. Ou, X. Q. Ren, N. Sai, X. Y. Song, L. Sun, L. Tao, C. Wang, L. J. Wang, P. J. Wang, W. S. Wang, Y. S. Wang, X. Y. Wen, B. Y. Wu, B. B. Wu, M. Wu, G. C. Xiao, S. Xiao, S. L. Xiong, Y. P. Xu, R. J. Yang, S. Yang, J. J. Yang, Y. J. Yang, B. B. Yi, Q. Q. Yin, Y. You, F. Zhang, H. M. Zhang, J. Zhang, P. Zhang, W. Zhang, W. C. Zhang, Y. F. Zhang, Y. H. Zhang, H. S. Zhao, X. F. Zhao, S. J. Zheng, Y. G. Zheng, D. K. Zhou
AAccretion Torque Reversals in GRO J1008-57 Revealed by
Insight-HXMT
W. Wang a,b , Y. M. Tang a,b , Y. L. Tuo c,d , P. R. Epili a,b , S. N. Zhang c,d , L. M. Song c , F. J. Lu c , J. L. Qu c , S. Zhang c , M.Y. Ge c , Y. Huang c , B. Li c , Q. C. Bu c , C. Cai c , X. L. Cao c , Z. Chang c , L. Chen e , T. X. Chen c , Y. B. Chen f , Y. Chen c ,Y. P. Chen c , W. W. Cui c , Y. Y. Du c , G. H. Gao c,d , H. Gao c,d , Y. D. Gu c , J. Guan c , C. C. Guo c,d , D. W. Han c , J. Huo c ,S. M. Jia c , W. C. Jiang c , J. Jin c , L. D. Kong c,d , C. K. Li c , G. Li c , T. P. Li c,d,g , W. Li c , X. Li c , X. B. Li c , X. F. Li c , Z. W.Li c , X. H. Liang c , J. Y. Liao c , B. S. Liu c , C. Z. Liu c , H. X. Liu c , H. W. Liu c , X. F. Lu c , Q. Luo c,d , T. Luo c , R. C.Ma c,d , X. Ma c , B. Meng c , Y. Nang c,d , J. Y. Nie c , G. Ou c , X. Q. Ren c,d , N. Sai c,d , X. Y. Song c , L. Sun c , L. Tao c , C.Wang d , L. J. Wang c , P. J. Wang c,d , W. S. Wang h , Y. S. Wang c , X. Y. Wen c , B. Y. Wu c,d , B. B. Wu c , M. Wu c , G. C.Xiao c,d , S. Xiao c,d , S. L. Xiong c , Y. P. Xu c,d , R. J. Yang i , S. Yang c , J. J. Yang c , Y. J. Yang c , B. B. Yi c,j , Q. Q. Yin c , Y.You c , F. Zhang c , H. M. Zhang c , J. Zhang c , P. Zhang c , W. Zhang c,d , W. C. Zhang c , Y. F. Zhang c , Y. H. Zhang c,d , H. S.Zhao c , X. F. Zhao c,d , S. J. Zheng c , Y. G. Zheng c,h , D. K. Zhou c,d a School of Physics and Technology, Wuhan University, Wuhan 430072, China b WHU-NAOC Joint Center for Astronomy, Wuhan University, Wuhan 430072, China c Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China d University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, China e Department of Astronomy, Beijing Normal University, Beijing 100088, China f Department of Physics, Tsinghua University, Beijing 100084, China g Department of Astronomy, Tsinghua University, Beijing 100084, China h Computing Division, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China i College of physics Sciences and Technology, Hebei University, Baoding, Hebei Province 071002, China j School of Physics and Optoelectronics, Xiangtan University, Xiangtan, Hunan 411105, China
Abstract
GRO J1008-57, as a Be / X-ray transient pulsar, is considered to have the highest magnetic field in known neutron starX-ray binary systems. Observational data of the X-ray outbursts in GRO J1008-57 from 2017 to 2020 were collectedby the Insight-HXMT satellite. In this work, the spin period of the neutron star in GRO J1008-57 was determined to beabout 93.28 seconds in August 2017, 93.22 seconds in February 2018, 93.25 seconds in June 2019 and 93.14 secondsin June 2020. GRO J1008-57 evolved in the spin-up process with a mean rate of − (2 . ± . × − s / d from 2009 –2018, and turned into a spin down process with a rate of (6 . ± . × − s / d from Feb 2018 to June 2019. During thetype II outburst of 2020, GRO J1008-57 had the spin-up torque again. During the torque reversals, the pulse profilesand continuum X-ray spectra did not change significantly, and the cyclotron resonant scattering feature around 80 keVwas only detected during the outbursts in 2017 and 2020. Based on the observed mean spin-up rate, we estimated theinner accretion disk radius in GRO J1008-57 (about 1 - 2 times of the Alfv´en radius) by comparing di ff erent accretiontorque models of magnetic neutron stars. During the spin-down process, the magnetic torque should dominate overthe matter accreting inflow torque, and we constrained the surface dipole magnetic field B ≥ × G for the neutronstar in GRO J1008-57, which is consistent with the magnetic field strength obtained by cyclotron line centroid energy.
Keywords: accretion, accretion disk, pulsars: general, pulsars: individual(GRO J1008-57)
1. Introduction
GRO J1008-57 is a high-mass X-ray binary (HMXB)consisting of a neutron star and a Be star companion(Coe et al. 1994). GRO J1008-57 was discovered bythe Burst and Transient Source Experiment (BASTE) onboard the Compton Gamma-Ray Observatory (CGRO)in 1993. Pulsed flux in the 20–50 keV increased up to 1.1 Crab on July 18, 1993, and the spin period of ∼ e = ± a x sin i = ±
60 (light-second) , P orb = ± ± / ASMlight curve data of GRO J1008-57 discovered two mod-
Preprint submitted to Journal of High Energy Astrophysics February 25, 2021 a r X i v : . [ a s t r o - ph . H E ] F e b lation periods at ∼ . / X-ray pulsars. In last 15 years, Type II outburstsin GRO J1008-57 have occurred in June 2004, March,2009, November 2012, November 2014, January 2015,August 2017, June 2020. Specially, outburst events inSeptember 2014 (Type I, periastron outburst), Novem-ber 2014 (type II outburst) and January 2015 (aphelion,Type II outburst) became the unique ” Triple Peak” out-bursts, and this ”triple-peaked” outburst behavior hadnot been seen in any other source (K¨uhnel et al. 2017).The cause of the Type II outburst is currently unknown,needs to be studied furthermore (K¨uhnel et al. 2017).Moritani et al. (2013) suggested that in a highly cen-trifugal Be / X-ray binaries, if Be disk is not aligned withthe orbital plane of the binaries, the neutron star cancapture a large amount of matter during the event pe-riod, producing a Type II outbursts with high brightnesswhen the misaligned Be disk passes through the neutronstar’s orbit.Based on the BASTE data, Wilson et al. (1994) de-tected the pulse period between 20 keV and 160 keV,which was 93.548 ± ± ± ∼ .
62 s in the 1993 outburst observed byASCA. In 2007 November and December outbursts,pulsations with a period of 93.737 s were clearly de-tected in the light curves of the pulsar up to the 80 –100 keV energy band (Naik et al. 2011). During twooutbursts in June 2004 and March 2009, the pulsationperiods of ∼ ∼ ∼ × − s / d and after 2009, it may change to a spin-uptrend. Recently, the Insight-HXMT collaborations re-ported a pulse period of ∼ .
283 s in the 2017 outburst(Ge et al. 2020).It has been reported that the highest energy of cy-clotron resonant scattering features (CRSFs) was mea- sured in the hard X-ray spectrum of GRO J1008-57. Inthe early CGRO / OSSE measurements, a marginal fea-ture around 88 keV (with only 2 σ ) was reported (Groveet al. 1995). Yamamoto et al. (2014) reported that the76 keV absorption characteristics (as the CRSF) weredetected during the November 2012 outburst. Wang(2014) found that the CRSF energy of GRO J1008-57was ∼
74 keV in the 2009 outburst. Bellm et al. (2014)confirmed the 78 keV line feature ( ∼ σ ) with the NuS-TAR and Suzaku data. The Insight-HXMT collabora-tions (Ge et al. 2020) reported the CRSF with very highstatistical significance ( > σ ) at a mean centroid en-ergy of ∼
90 keV (with the line model gabs ) and ∼ cyclabs ) during the 2017 out-burst.China’s first X-ray astronomical telescope satel-lite, the Hard X-ray Modulation Telescope (hereafterInsight-HXMT) was launched successfully in June 2017(Zhang et al. 2020). Insight-HXMT has collected sev-eral X-ray observations on GRO J1008-57 from 2017 to2020, covering four outbursts: two Type II outbursts inAugust 2017 and June 2020, Type I outbursts in Febru-ary 2018 and June 2019. With more observations ofInsight-HXMT, we can study the spin period evolutionof GRO J1008-57 in last four years, and probe the spec-tral properties in di ff erent outbursts.The observations and data analysis of Insight-HXMTon GRO J1008-57 were introduced in §2. In §3, the spinproperties of the neutron star in GRO J1008-57 werestudied, the torque reversals of the neutron star were re-vealed. In §4, the spectral properties in four outburstswill be shown for comparison. The conclusion and dis-cussion are presented in §5.
2. Observations and data analysis of Insight-HXMT
Insight-HXMT has three main payloads: the HighEnergy X-ray Telescope (HE, Liu et al. 2020), theMedium Energy X-ray Telescope (ME, Cao et al. 2020),and the Low Energy X-ray Detector (LE, Chen et al.2020).(HE) NaI (CsI) detector has a range of 20–250 keV withthe e ff ective area of 5100 cm . The collimatorsof HE define 15 narrow field of view (FOV, 5.7 ◦ × ◦ ), 2 wide FOV(5.7 ◦ × ◦ ) and a blind FOVwhich was covered with 2 mm tantalum.(ME) Si-PIN detector has a range of 5–30 keV with thee ff ective area of 952 cm . ME consists of 3 detec-tor boxes. Each box has 576 Si-Pin detector pixels2 able 1: Insight-HXMT data used in this work. Obs. ID Obs. date Start(UTC) Duration (s) MJDP0114520001 2017-08-11 21:58:37.0 80789 57976P0114520003 2017-08-18 11:30:22.0 212530 57983P0114520005 2018-02-02 10:40:17.0 17589 58151P0114520006 2018-02-09 00:12:19.0 17875 58158P0114520007 2018-02-10 06:26:41.0 24004 58159P0114520008 2018-02-12 22:06:24.0 17989 58161P0114520009 2018-02-15 02:37:24.0 23432 58164P0114520010 2018-02-16 19:59:42.0 17643 58165P0114520011 2018-02-18 11:46:21.0 17641 58167P0114520012 2018-02-21 11:21:55.0 17589 58170P0114520014 2019-07-02 15:26:57.0 34667 58666P0201012012 2019-06-22 05:25:13.0 35571 58656P0201012014 2019-06-24 05:12:55.0 40372 58658P0201012016 2019-06-26 16:13:46.0 23362 58660P0201012018 2019-06-27 16:09:15.0 23332 58661P0201012020 2019-06-29 14:18:31.0 36084 58663P0201012355 2020-06-01 10:38:04.0 34534 59001P0201012356 2020-06-03 02:22:48.0 17431 59003P0201012357 2020-06-04 05:24:21.0 17433 59004P0201012358 2020-06-05 05:15:10.0 17644 59005P0201012359 2020-06-06 13:02:55.0 17624 59006P0201012360 2020-06-07 12:53:46.0 17622 59007P0201012361 2020-06-08 17:30:50.0 17622 59008P0201012362 2020-06-09 17:21:44.0 17623 59009P0201012363 2020-06-10 17:12:42.0 17621 59010P0201012364 2020-06-11 12:17:31.0 17621 59011P0201012365 2020-06-12 15:19:24.0 17621 59012P0201012366 2020-06-13 15:10:31.0 17622 59013P0201012367 2020-06-14 11:50:53.0 17621 59014P0201012368 2020-06-15 14:53:03.0 17619 59015P0201012369 2020-06-16 11:33:28.0 19622 59016P0201012440 2020-06-18 11:16:17.0 34803 59018P0201012441 2020-06-19 09:32:23.0 17624 59019P0201012442 2020-06-20 12:34:47.0 17626 59020P0201012443 2020-06-21 10:50:56.0 17625 59021P0201012444 2020-06-22 15:28:53.0 17625 59022 read out by 18 ASIC (Application Specified Inte-grated Circuit). For each detector box, the collima-tors of ME confine 15 ASICs as narrow FOV(1 ◦ × ◦ ), 2 ASIC as wide FOV(4 ◦ × ◦ ) and one blindFOV.(LE) SCD detectors range from 1 to 15 keV with thee ff ective area of 384 cm . LE has three detectionboxes. Twenty collimators have the small FOVs,1.6 ◦ × ◦ ; Six with the wide FOVs, 4 ◦ × ◦ andtwo blind FOVs.This work has used two data sets of P0114520,P0201012 (Observation ID). In Table 1, the descriptionof the observed data by Insight-HXMT was presented.The Insight-HXMT Data Analysis Software Package(HXMTDAS) V2.02 was used in this work. All sciencedata of HE, ME and LE telescopes used small FOV de-tectors. We filtered the data with the following crite-ria: (1) pointing o ff set angle < . ◦ ; (2) pointing direc-tion above Earth > ◦ ; (3) geomagnetic cut-o ff rigidity Detailed introduction to data bases can be found athttp: // value >
8; (4) time since SAA passage >
300 s and timeto next SAA passage >
300 s; (5) for LE observations,pointing direction above bright Earth > ◦ . The meth-ods of standard data reduction for the Insight-HXMTwere introduced in previous publications (Huang et al.2018; Xiao et al. 2020). Insight-HXMT has gonethrough a series of performance verification tests sincethe launch, at present shown the good calibration andestimation of the instrumental background (Li et al.2020). Here we briefly summarized the data analysisprocedures for the HXMTDAS V2.02.(i) Calibration: Remove spike events caused by elec-tronic system and calculate PI column valuesof event according to the Calibration Database(CALDB).(ii) Screening:(a) Generate a FITS file of good time interval(GTI).(b) Exclude some of the photons in event filethen screen the data. The calibrated EVT fileis filtered by applying cleaning criteria to pro-duce a cleaned EVT file.(iii) High level product extraction:(a) Extract spectra.(b) Extract light curves.(c) Generate the response files of energy spectra.(d) Generate background files of lightcurves / spectra.In the timing analysis, we have made the barycen-tric correction of the light curves using the tool hxbary .Based on the orbital ephemeris given by Coe et al.(2007), we made orbital motion correction. For thespectral analysis, we have used the energy bands as 3–10 keV (LE), 10–26 keV (ME) and 26-120 keV (HE)respectively, according to the present calibration results(Li et al. 2020).
3. Spin period of the neutron star in GRO J1008-57
The timing resolutions of Insight-HXMT can reach2 µ s (HE), 20 µ s (ME), and 1 ms (LE), respectively.The temporal analysis here aimed to derive the rotationperiod of the neutron star in GRO J1008-57 for all ob-served data from 2017 – 2020. In Fig. 1, we showedthe flux variations of GRO J1008-57 from August 2017to June 2020 in three energy bands: 3 – 10 keV, 10 –263 -11 -10 -9 -8 HE ME LE F l ux ( e r g s / c m ^ / s ) MJD
Figure 1: The flux variations of Be X-ray pulsar GRO J1008-57 from2017 to 2020 determined by Insight-HXMT in three energy bands: 3–10 keV, 10 – 26 keV, 26 – 100 keV. The three observational epochscovered two type II outbursts in August 2017 and June 2020, and twotype I outbursts in February 2018 and June 2019. keV, 26 – 120 keV. The X-ray fluxes during two typeI outbursts were much lower than those of two type IIoutbursts in 2017 and 2020.We search for the periodical signal in a time seriesby folding data, determines the chi-square ( χ ) of thefolded light curve then plots the χ values versus theperiods. The efsearch (a build-in function in HEAsoft)was used to complete the folding of the light curve andfind the period. Using the efsearch task, we get the plotsof χ values versus the periods. The true period can bedefined as the position corresponding to the maximumvalue of the χ . Therefore, we have used a Gaussiancurve to fit the center position of the χ curves. In ad-dition, efsearch might depend on the epoch (Li et al.2012), so we corrected it as follows: calculate the χ with di ff erent epochs, T ( epoch ) = t + . i P / N , where i =
0, 1, 2, ..., 9, and N is the number of phase bins inpulse profile. Then we averaged ten sets of χ versusperiod, fitted the peak with quadratic and find the max-imum which should be the estimated period. The 1 σ error could be given when the quadratic is lowered by1.0.In the process of searching for the period, we havetried to obtain the more precise values with the highsignal-to-noise observed data. In the type II outburstsin 2017 and 2020, we used the all data of LE, ME, HEdetectors in the high flux levels, and the spin period val-ues are basically same within the error of ∼ .
001 s. Inthis case, in order to get a higher quality period, HE,
Table 2: Measurements of the spin period of the neutron star in GROJ2008-57.
MJD Spin Period / s Mission Reference49182 93.5870 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± / HE + ME + LE this work57977 93.2868 ± / HE + ME + LE this work57983 93.2659 ± / HE + ME + LE this work57984 93.2666 ± / HE + ME + LE this work57985 93.2640 ± / ME this work58151 93.2117 ± / HE this work58158 93.2155 ± / HE this work58159 93.2208 ± / ME this work58161 93.2206 ± / ME this work58164 93.2186 ± / ME this work58165 93.2200 ± / LE this work58167 93.2140 ± / LE this work58170 93.2260 ± / HE this work58656 93.2567 ± / HE this work58658 93.2625 ± / HE this work58660 93.2524 ± / ME this work58661 93.2568 ± / ME this work58663 93.2560 ± / LE this work58666 93.2545 ± / ME this work59002 93.1445 ± / HE + ME + LE this work59003 93.1358 ± / HE + ME + LE this work59004 93.1352 ± / HE + ME + LE this work59008 93.1358 ± / HE + ME + LE this work59010 93.1285 ± / HE + ME + LE this work59012 93.1272 ± / HE + ME + LE this work59014 93.1275 ± / HE + ME + LE this work59016 93.1198 ± / HE + ME + LE this work59018 93.1219 ± / HE + ME + LE this work
ME and LE files are used together here to reduce errorsand find more accurate period. For the low flux levels,like the end of the 2007 outburst and type I outbursts in2018 and 2019, we only used the detectors which havethe better signal-to-noise light curve data, then obtainedthe spin period values.In the Table 2, the spin period values of GRO J1008-57 in the four outbursts in August 2017, February 2018,June 2019 and June 2020 are presented. The variationof the spin period from 2017 – 2020 is shown in Fig.2. The neutron star in GRO J1008-57 showed a spin-up behavior from 2017 - 2018, while from 2018 - 2019,the accretion torque of the neutron star changed, and thestar became to spin down. During the type II outburst in2020, the neutron star transferred into the spin-up pro-cess again.In addition, we also have studied the evolution ofpulse profiles of GRO J1008-57 in the di ff erent energy4 S p i n P e r i od ( s ) MJD (D)
Figure 2: The spin period of the neutron star in GRO J1008-57 from2017 to 2020 determined by Insight-HXMT. From August 2017 toFeb 2018, the neutron star continue to spin up, but after Feb 2018,the accretion torque of the neutron star changed and the neutron starbecame to spin down. During the outburst in 2020, GRO J1008-57turned into the spin-up. ranges from 2017 – 2020. We used efold tasks to obtainpulse profiles in three energy bands: 3 –10 keV; 10 –26keV; 26 – 120 keV. The pulse profile of GRO J1008-57had a double-peaked structure between 3–10 keV in allobservations of four outbursts from 2017 – 2020. Above10 keV, the pulse profiles became a nearly single peakfeature, but there are still the di ff erences for the pulsefeatures around the pulse phase 0.2 in four di ff erent out-bursts (see Figures 3). In the type II outbursts of 2017and 2020, there existed a mini second peak around thepulse phase 0.2 from 10– 26 keV, and above 26 keV,the mini second peak was not obvious. For the twoType I outbursts in 2018 and 2019, the pulse profilesin the ranges of 10 –26 keV and 26 –120 keV showedthe purely single peak features.
4. Spectral properties of GRO J1008-57 in outbursts
In this section, we will carry out the spectral analy-sis for GRO J1008-57 during the four outbursts, check-ing the possible spectral variations during the epochs ofthe accretion torque reversal. We have used the spectrafrom three detectors, covering the energy bands as 3 –10 keV (LE), 10 – 26 keV (ME) and 26 – 120 keV (HE)respectively. We have used the Xspec package version12.10.1 in the following spectral analysis work. TheX-ray spectrum of a neutron star X-ray binary can begenerally described by a power-law model plus a highenergy cuto ff ( power*highecut ): KE − Γ when E ≤ E cut , Table 3: The X-ray spectral parameters of GRO J1008-57 in four out-bursts. X-ray flux from 3–100 keV is given in units of erg cm − s − . Parameter 2017 2018 2019 2020kT (keV) 1 . ± .
06 1.74 ± .
02 1.77 ± .
04 2 . ± . Γ . ± .
06 0 . ± .
02 0 . ± .
07 0.48 ± . E cut (keV) 5 . ± .
64 6 . ± .
36 4 . ± .
53 4.21 ± . E f (keV) 16 . ± .
67 15 . ± .
23 14 . ± .
52 14 . ± . E fe (keV) 6 . ± .
13 6 . ± .
13 6 . ± .
14 6 . ± . σ (keV) 0.08 ± .
06 0.01 (fixed) 0 . ± .
06 0.17 ± . E cycl (keV) 76.6 ± . . ± . W cycl (keV) 4.3 ± . . ± . D cycl . ± . . ± . × − × − × − × − χ / d . o . f KE − Γ exp − [( E − E cut ) / E f ] when E ≥ E cut , where Γ is the photon index of the power law, E cut is the cut-o ff energy in keV, E f is the e-folding energy in keV.When we fit the spectra of GRO J1008-57 from 3–120 keV observed by Insight-HXMT, there existed thecount excesses below 6 keV, we add the thermal com-ponent ( bbody ) to fit the soft X-ray band. We also triedother possible spectral models (i.e. bmc, CompTT ) tofit the continuum spectra, however, the fittings were notgood (reduced χ significantly larger 1). For the typeI outbursts in 2018 and 2019, the spectra can be fit-ted with the continuum model, there were no signifi-cant absorption features in the range of 70 – 90 keV.While for the type II outbursts in 2017 and 2020, afterthe spectral fittings with the continuum model bbody + power*highecut , there were the absorption features inthe energy range of 70 −
90 keV, which should be the cy-clotron resonant scattering features. We have used theline model cyclabs to fit the cyclotron absorption line.In addition, around the energy of 6–7 keV, the iron linefeature were also found in the residuals, thus we add thegaussian emission line to fit the Fe K α line.In Figure 4, we showed the X-ray spectral examplesof GRO J1008-57 in four outbursts. The all fitted pa-rameters of these spectra are collected in Table 3. In the2007 outburst, the significant absorption feature around80 keV was confirmed, which was attributed to the cy-clotron resonant scattering feature (also see Ge et al.2020). This cyclotron resonant scattering feature wasalso detected during the peak epoch of the 2020 out-burst. During the type I outbursts in 2018 and 2019, thecyclotron absorption lines around 70-90 keV cannot bedetected with Insight-HXMT. The continuum spectralproperties did not change with the di ff erent outburstsand luminosity levels.We can calculated the value of the magnetic field ofthe neutron star in GRO J1008-57 by using the formula[ B / G] = [ E cycl / . + z ) , (1)where E cycl is the energy of the fundamental line, here5 Figure 3: Spin pulse profiles of GRO J1008-57 in di ff erent epochs of the four outbursts: (Top) MJD 57976, MJD 57983 and MJD 57985 in August2017; (Middle-1) MJD 58151, MJD 58158, MJD 58164 in February 2018; (Middle-2) MJD 58656, MJD 58660, MJD 58663 in July 2019; (Bottom)MJD 59001, MJD 59006, MJD 59013 in June 2020. The pulse profiles are presented in three energy bands: 26–120 keV, 10–26 keV and 3– 10keV.
017 20182019 2020
Figure 4: The X-ray spectra of GRO J1008-57 obtained by Insight-HXMT in four outbursts: August 2017 (with the cyclotron absorption line), Feb2018, June 2019, June 2020 (with the cyclotron absorption line). cycl =
80 keV, and z is the gravitational redshift nearthe surface of the neutron star. For a canonical neutronstar of 1.4 M (cid:12) with a radius of 10 km, we can find z ∼ . ∼ × G for the neutron star in GRO J1008-57.
5. Discussion and conclusion
With the Insight-HXMT data, we studied the tem-poral properties of the neutron star in GRO J1008-57from August 2017 to June 2020, revealing the accretiontorque reversals occurring around February 2018 andJune 2020. As mentioned in the previous articles (e.g.,Wang 2014), the neutron star in GRO J1008-57 showeda long time evolution of the spin period. GRO J1008-57 experienced a spin-down process from 1993 to 2009,and its mean spin-down rate was (3 . ± . × − s / d,and it might change from spin-down to spin-up processafter 2009 (Wang 2014). Combined with the work ofthe previous articles, the evolution of the spin period inGRO J1008-57 from 1993 to 2020 has be displayed inFig. 5.From the present observations, we confirmed the spinup trend of the neutron star after 2009, and inferred aspin-up rate of − (2 . ± . × − s / d from 2009to 2018. Furthermore, after the type I outburst in Feb2018, the accreting torque of the neutron star in GROJ1008-57 changed, the neutron star turned into the spin-down process, with a spin-down rate of (6 . ± . × − s / d from 2018 to 2019. During the torque reversal, thepulse profiles of X-ray pulsar in GRO J1008-57 did notvary with di ff erent time. In addition, we also com-pared the X-ray spectra of GRO J1008-57, the contin-uum spectral properties of the outbursts from 2017 –2019 did not change significantly, while the cyclotronabsorption line features can not be detected in two out-bursts of 2018 and 2019. During the recent type II out-burst in 2020, neutron star in GRO J1008-57 showed thefast spin-up process again with a rate of ∼ − × − s / d. The cyclotron line absorption feature around 80keV was detected during the peak of the 2020 outburst. Spin up process from 2009 – 2018
Interactions between the strongly magnetized neutronstars and surrounding accretion disk are thought to bethe dominant mechanism to drive the spin evolutionsof the neutron stars. The classical torque model pro-posed by Ghosh & Lamb (1979) suggested that the mag-netic field lines were threaded in the Keplerian accre-tion disk in a broad transition zone, which will derivethe torque acting on the neutron star. The torque fromthe inner accretion matter flow into the neutron star will S p i n P e r i od ( s ) MJD (Day)3.5x10 -5 s/d -2.1x10 -4 s/d6.7x10 -5 s/d Figure 5: The spin period evolution of the neutron star in GRO J1008-57 from 1993 to 2020 collected from di ff erent observations includingthe new Insight-HXMT observations. drive the spin up process. The magnetic torque due tothe magnetosphere interacting with the matter will re-sult in the spin down of the neutron star. The positiveor negative torque would depend on a so-called fast-ness parameter (Ghosh & Lamb 1979, Wang 1995): ω = Ω NS / Ω = ( R / R c ) / , where Ω NS is the angularvelocity of the star and Ω is the the Keplerian angularvelocity at the inner radius R of the disk. The inner ra-dius R is generally thought to be in the same order ofthe Alfv´en radius R A , here they can be expressed in theform of R = ξ R A , where R A = µ / ˙ M − / (2 GM ) − / inthe case of spherical accretion, and µ = BR , B is thesurface dipole magnetic field of neutron star, M is themass of neutron star, ˙ M is the accretion rate.The neutron star of GRO J1008-57 undergone thelong-term spin-up process from 2009 to 2018. Basedon the accreting torque model and the observed spin-up rate, we could estimate the surface magnetic fieldof GRO J1008-57. The spin-up rate during the accret-ing state can be expressed as (Joss & Rappaport 1984;Wang 1996): − ˙ PP = ˙ M ( GMR ) / n ( ω ) I Ω NS , (2)where I ∼ MR NS / − ˙ PP (cid:39) . × − s − ω / n ( ω ) L P / ( M . M (cid:12) ) − / R − . (3) L is the X-ray luminosity of the X-ray pulsar in unitsof 10 erg cm − s − , R is the radius of the neutron star8n units of 10 cm. n ω is a dimensionless torque functiongiven by (Wang 1995): n ( ω ) = (7 / − (4 / ω + (1 / ω − ω . (4)Thus we can deduce the dipole magnetic field momentof the star: µ ∼ . ξ − / ω / L / P / ( M . M (cid:12) ) / R / , (5)where µ is the dipole moment of the star in units of10 G cm .In the case of GRO J1008-57, the spin period of theneutron star is 93.3 s. The mean accretion rate is un-certain. The X-ray luminosities in several type II out-bursts (e.g. March, 2009, November 2012, November2014, January 2015, August 2017) are in the range of ∼ − × erg s − (Wang 2014; Yamamoto etal. 2014; Bellm et al. 2014; Ge et al. 2020). Morefrequent Type I bursts have the mean luminosity around10 erg / s (K¨uhnel et al. 2017). For the quiescent state,the system has a mean luminosity of ∼ erg / s orhigher (Tsygankov et al. 2017). During the spin-upstage from 2009 - 2017, we take the mean accretion lu-minosity of 10 erg / s. Then we derived the ”fastnessparameter” ω (cid:39) .
95, furthermore determined the sur-face magnetic field of the neutron star in GRO J1008-57as B (cid:39) × ξ − / G. If the inner radius of the ac-cretion disk is near the Alfv´en radius, i.e., ξ ∼
1, onewill derive the strong magnetic field in GRO J1008-57,which is higher than that obtained from the cyclotronline measurement. The similar results were obtained byShi et al. (2015) that the surface magnetic fields of mostneutron stars in known Be / X-ray pulsars are higher than10 G estimated by spin equilibrium using the accre-tion torque and magnetosphere models (Dai & Li 2006).There still exist some uncertainties in estimating themagnetic field, like the inner radius of the accretiondisk. If we assume that the magnetic field determinedby the cyclotron line centroid energy is the real valueof the surface magnetic field in GRO J1008-57, thenwe find ξ ∼ .
2. Thus the inner radius of the accre-tion disk is larger than the Alfv´en radius in the case ofGRO J1008-57. It could be possible for X-ray pulsars inBe / X-ray binaries. In some Be / X-ray pulsars, the quasi-periodic oscillations were observed (Roy et al. 2019,Takeshima et al. 1994, and references therein). Usingthe beat frequency model, Takeshima et al. (1994) di-rectly determined the inner radius of these X-ray pulsarwhich was about 1 –3.5 times of the Alfv´en radius.Here it should be pointed out that we have used thetorque function based on the work by Wang (1995). This model predicts the critical fastness parameter inthe range of 0.88 - 0.95 near the spin equilibrium. Someother models give the lower values of the critical fast-ness parameter, e.g., 0.7 - 0.9 suggested by Li & Wang(1996, 1999), 0.4 - 0.6 by Li & Wickramasinghe (1997),and ∼ .
35 based on Ghosh & Lamb (1979). If we con-sider the smaller values of the critical fastness parame-ter (i.e., ω ∼ . B ∼ . × ξ − / G. Thusby comparing the magnetic field value from the CRSFmeasurement, we can find ξ ∼
1, the inner disk radiuswould be close to the Alfv´en radius in GRO J1008-57,which is also consistent with the conclusion by Li &Wang (1999).
Spin down process from 2018 – 2019
After February 2018, the X-ray pulsar in GRO J1008-57 transferred to the spin-down process. Similar to thelong-term spin-down trend observed from 1993– 2009,these spin down processes might be the evidence for thepropeller phase in which the angular momentum of theneutron star is removed by the interaction between mat-ter and the magnetosphere (Illarionov & Sunyaev 1975).The other possibility is that the neutron star has not goneinto the propeller phase yet, but the spin-up torque fromthe accretion flows is smaller than the magnetic torque,then the neutron star in GRO J1008-57 showed the spin-down behavior. In Fig. 3, the pulse X-ray emissionsin GRO J1008-57 during 2018 – 2019 can be clearlydetected, suggesting that the accretion still occurred onthe surface of neutron star. Thus we think that the latterpossibility may better describe the spin-down process inGRO J1008-57.If we neglected the spin-up torque from accretionflow during the spin-down process, we can estimate thelow limit of the magnetic field strength of the neutronstar. The magnetic torque should be a little larger thanthe observed spin-down torque of the system, i.e., µ / R c ≥ I | ˙ ω | , (6)where R c = ( GMP / π ) / is the corotation radius ofthe neutron star. Given the observed mean spin-downrate from 2018 – 2019, ˙ P = . × − s day − , the de-rived surface magnetic field is B ≥ × G, which isconsistent with the strength measured by the cyclotronabsorption lines (this work, also see Ge et al. 2020).
Acknowledgements
We are grateful to the referee for the suggestions toimprove the manuscript. This work made use of thedata from the Insight-HXMT mission, a project fundedby China National Space Administration (CNSA) andthe Chinese Academy of Sciences (CAS). The au-thors thank the support by the National Programon Key Research and Development Project (Grants9o. 2016YFA0400803) and the NSFC (U1838103,11622326, U1838201 and U1838202).
ReferencesReferences