Insight-HXMT discovery of the highest energy CRSF from the first Galactic ultra-luminous X-ray pulsar Swift J0243.6+6124

Ultraluminous X-ray (ULX) sources are bright X-ray sources with apparent luminosity $>10^{39}$ erg s^-1, which is above the Eddington limit of a $10$ $M_{\odot}$ black hole (BH) (Kaaret et al., 2017). X-ray pulsations detected in ULX sources such as M82 X-2 (Bachetti et al., 2014), NGC 7793 P13 (Fürst et al., 2016; Israel et al., 2017a), NGC 5907 ULX1 (Israel et al., 2017b), NGC 300 ULX1 (Carpano et al., 2018), and RX J0209.6-7427 (Chandra et al., 2020) indicate that some, or even most ULXs are accreting neutron stars (NSs) with a strong magnetic field. A potential detection of a proton CRSF at $4.5$ keV in the ULX source M51 ULX-8 implies a magnetar-like field $\sim 10^{15}$ G (Brightman et al., 2018). Such a strong dipole magnetic field prevents the spherization by radiation in its accretion disk even at luminosities $>10^{41}$ erg s^-1 (Basko & Sunyaev, 1976).

Alternative estimations of the dipole magnetic fields of NSs can be made from the accretion torque which has a close connection with the inner edge of the accretion disk influenced by the NS’s magnetosphere. However, different accretion torque models might give large measurement disparities of magnetic fields in the range of $10^{10-15}$ G (Chen et al., 2021). The estimated lower values ($<10^{13}$ G) in these pulsating ULXs will make them essentially indistinguishable from Be X-ray pulsars, with the exception of their higher luminosities which has been proposed to be a consequence of the strong beaming effect by the disk outflow, when the disk is spherized by radiation pressure (King et al., 2001; King, 2009; King & Lasota, 2016; King et al., 2017; Koliopanos et al., 2017; King & Lasota, 2019, 2020). From the relationship between the magnetic field and maximum luminosity (see Figure 5 in Mushtukov et al. (2015a)), it can be seen that only when the dipole magnetic field is greater than 10¹³ G, the maximum accretion luminosity of magnetized pulsars can be significantly greater than $10^{39}$ erg s^-1. However, from the first discovery of CRSF in Her X-1 to the present (Truemper et al., 1978; Staubert et al., 2019), a direct measurement of such a strong magnetic field has not been possible by observing the expected electron CRSF because of the relatively low cutoff energy of the non-thermal emission from NS ULX systems, and the lack of sensitive hard X-ray coverage above about 80 keV of contemporary X-ray telescopes. Fortunately, the launch of Insight-HXMT in 2017 (Zhang et al., 2014; Zhang et al., 2020), which has a broad energy coverage and a large detection area at energies above 100 keV changed the situation. The two previous records of the highest energy detection of CRSFs with higher than $5\ \sigma$ significance were also both set by Insight-HXMT: the $\sim$90 keV fundamental CRSF from GRO J1008-57 (Ge et al., 2020) and the $\sim$100 keV first harmonic of a CRSF from 1A 0535+262 (Kong et al., 2021; Kong et al., 2022) proving that Insight-HXMT has a strong advantage in detecting high-energy CRSFs.

The transient X-ray source Swift J0243.6+6124 was discovered on October 3 2017 by the Swift/BAT telescope at a flux level of $\sim$ 80 mCrab before it entered into a giant outburst from 2017 to 2018 (Cenko et al., 2017; Kennea et al., 2017). A 9.8 s period pulsation was detected in X-ray observations by Swift/XRT and an eccentric binary system with a $\sim$ 28-day orbital period was revealed by Fermi-GBM (Bahramian et al., 2017; Kennea et al., 2017; Ge et al., 2017; Doroshenko et al., 2018). Optical observations assigned a Be star as the companion (Kouroubatzakis et al., 2017; Kennea et al., 2017; Stanek et al., 2017; Yamanaka et al., 2017). A distance of 6.8 kpc as reported in Bailer-Jones et al. (2018) based on Gaia DR2 parallax measurements of the companion star implies that the source is the first Galactic pulsing ultraluminous X-ray source (pULX).

The magnetic field of Swift J0243.6+6124 was estimated in various manners, yet no consensus has been reached on its surface magnetic field strength. The pure timing analyses based on Insight-HXMT’s high cadence observations reveal two typical luminosities, around which the source is believed to have experienced transitions of different emission modes at the magnetic pole and different accretion modes on the disk (Doroshenko et al., 2020b), implying a dipole surface magnetic field of $\sim 10^{12-13}$ G and non-transition to the propeller state in quiescence. In particular, the non-detection of the transition allowed Tsygankov et al. (2018) to put an upper limit of $\sim 6\times 10^{12}$ G assuming propeller transition below $\sim 6\times 10^{35}$ erg s^-1, which was further reduced to $\leq 3\times 10^{12}$ G by Doroshenko et al., 2020b based on NuSTAR detection of the pulsations down to luminosities $\sim 6\times 10^{33}$ erg s^-1. As discussed by Doroshenko et al. (2020b), such a low dipole magnetic field allows for a coherent interpretation of the observed spin evolution of the source during the outburst, observed power spectral density, and spectral transition to correspond to the transition of the accretion disk to the radiatively dominated state. On the other hand, the estimated critical luminosity corresponding to the onset of an accretion column appeared to be more consistent with a much stronger surface magnetic field $\sim 10^{13}$  G (Kong et al., 2020; Liu et al., 2022). Doroshenko et al. (2020b), suggesting that it could be associated with either a smaller than expected magnetospheric radius (for a given field), or the presence of strong multipole components dominating the area close to the surface of the neutron star. Here we report our very statistically significant detection of a CRSF during the 2017 outburst of Swift J0243.6+6124 observed with Insight-HXMT, when the outburst peaked at a luminosity around $2\times 10^{39}$ erg s^-1 which unambigously supports the latter scenario. We also perform detailed phase-resolved spectral analyses, given that the appearance of CRSFs can be closely phased dependent (Harding & Daugherty, 1991; Nishimura, 2015).

Section 2 introduces the observations and methods of data reduction. Section 3 shows the details of the timing and spectral results. In Section 4, we discuss our results. The summary and conclusions are presented in Section 5.

The Hard X-ray Modulation Telescope (Zhang et al., 2014; Zhang et al., 2020), named Insight-HXMT, was launched on June 15, 2017. The scientific payload includes three collimated telescopes that allow observations in a broad energy band ($1-250$ keV) and with a large effective area at high energies: the High Energy X-ray Telescope (HE: 5000 $\rm cm^{2}$/20-250 keV, Liu et al., 2020), the Medium Energy X-ray Telescope (ME: 952 $\rm cm^{2}$/5-30 keV, Cao et al., 2020), and the Low Energy X-ray Telescope (LE: 384 $\rm cm^{2}$/1-10 keV, Chen et al., 2020. The main Fields of View (FoVs) are $1.6^{\circ}\times 6^{\circ}$, $1^{\circ}\times 4^{\circ}$, and $1.1^{\circ}\times 5.7^{\circ}$ for LE, ME and HE, respectively. Ascribed to the characteristics of the three detectors, Insight-HXMT possesses a broad-band capability ($1-250$ keV), with a large collection area at high energy and without pile-up for bright sources.

Insight-HXMT was triggered with 122 pointing exposures from Oct 7, 2017 (MJD 58033) to Feb 21, 2018 (MJD 58170) which sampled the entire outburst of Swift J0243.6+6124. The Insight-HXMT Data Analysis Software (HXMTDAS) v2.04, together with the calibration model v2.05, are used for the whole process of data reduction following the recommended screening conditions by the Insight-HXMT team. In particular, data with elevation angle (ELV) larger than $10^{\circ}$, geometric cutoff rigidity (COR) larger than 8 GeV, and offset for the point position smaller than $0.04^{\circ}$ are used. In addition, data taken within 300 s of the South Atlantic Anomaly (SAA) passage outside of good time intervals identified by onboard software have been rejected. In view of the conditions of in-flight calibration (Li et al., 2020), the energy bands considered for spectral analysis are: $2-10$ keV for LE, $10-40$ keV for ME, and $30-250$ keV for HE. The backgrounds are estimated with the tools provided by the Insight-HXMT team: LEBKGMAP, MEBKGMAP, and HEBKGMAP, version 2.0.9 based on the current standard Insight-HXMT background models (Liao et al., 2020a; Guo et al., 2020; Liao et al., 2020b). We note that the uncertain calibration of an Ag emission line at $\sim 22$ keV in the ME band will leave a narrow emission line in the phase-averaged spectrum (see the left panel in Figure 2), but it fades out due to lower statistics in the phase-resolved spectrum (see the right panel in Figure 2). Considering the current accuracy of the instrument calibration and appropriate $\chi^{2}$, we include 1$\%$, 0.5$\%$, and 0.5% systematic errors for spectral analysis for LE, ME, and HE, respectively. The uncertainties of the spectral parameters are computed using the Markov Chain Monte Carlo (MCMC) method with a length of 10,000 and are reported at a 90% confidence level. The XSPEC v12.12.0 software package (Arnaud, 1996) corresponding to heasoft v6.29 is used to perform the spectral fitting and error estimation. We utilize the ftool grppha to improve the counting statistic of the spectrum (with group minimum counts of 200) by combining ten exposures from Nov 03 to Nov 08 in 2017 with the addspec and addrmf tasks. The flux, pulse profile, and continuum spectral shape in these ten exposures keep stable at the outburst peak (Kong et al., 2020); it is therefore reasonable to combine them in order to search for any high energy CRSF with the best statistics. For the HE detector, the background dominates in the high energy band, and 200 counts per bin will ensure high confidence for the net spectrum. In Figure 2 and Figure 4, we use “setplot rebin 30 5” for a better visual display, which does not affect the fitting result.

We have analyzed the data from the high cadence and broad band Insight-HXMT observations of the 2017-2018 outburst of the first Galactic ULX Swift J0243.6+6124. A CRSF is discovered with high statistical significance at energies around $120-146$ keV, in a period when the source stayed at a luminosity around $2\times 10^{39}$ erg s^-1, far beyond the super-critical luminosity of the accretion column and the Eddington luminosity of the accreting NS. The energy of this newly detected CRSF is much higher than both the $\sim 90$ keV fundamental CRSF of GRO J1008-57 (Ge et al., 2020) and the $\sim 100$ keV first harmonic CRSF of 1A 0526+261 (Kong et al., 2021, 2022); both were the previous high energy records of CRSF detection, whose existence was firmly established for the first time by Insight-HXMT with a significance much higher than $5\ \sigma$. We note that a marginal detection (absorption depth unconstrained) of the possible third CRSF harmonic at $\sim$128 keV was reported in the spectrum of MAXI J1409-619 (Orlandini et al., 2012). The discovery of the CRSF from Swift J 0243.6+6124 reported here thus serves as the highest energy CRSF detected so far from a NS harbored in an accreting X-ray binary system. The strength of the magnetic field can be calculated with the following relation:

where $B_{12}$ is the magnetic field strength in units of $10^{12}$ G, and $z=(1-2GM/r_{\rm cyc}c^{2})^{-1/2}-1$ is the gravitational redshift due to the NS mass and height of the line forming region ($r_{\rm cyc}$). $n$ is the number of the Landau level involved: e.g., $n\ =\ 1$ for the fundamental line and $n\ \geq\ 2$ for its harmonics. The above equation assumes that the absorption takes place at the NS surface. However, in reality the absorption can only happen somewhere above the NS surface, and the higher the energy, the closer the absorption takes place to the NS surface. We thus take $E_{\rm cyc}\sim 146$ keV and $z=0.25$ for the emission from the surface of a typical NS ($M=1.4M_{\odot}$ and $R=10$ km) in the equation and obtain a lower limit of magnetic field $B\sim 1.6\times 10^{13}$ G. This is the strongest surface magnetic field of a NS measured directly with an electron CRSF. Here, we also consider the attenuation of the magnetic field with height, for the dipole magnetic field $B\varpropto r^{-3}$, and for the quadrupole magnetic field $B\varpropto r^{-4}$. We find that compared with the influence of redshift on cyclotron energy, the influence of height change on CRSF energy is more significant, which further shows that $B\sim 1.6\times 10^{13}$ G represents a lower limit of the magnetic field on the NS’s surface.

Our result appears to be at odds with the comparatively small magnetospheric radius estimated for the source by several authors independently based on completely different observables (Jaisawal et al., 2019; Tao et al., 2019; van den Eijnden et al., 2019; Doroshenko et al., 2020b). In particular, the non-transition of the source to a “propeller” state in quiescence implies an upper limit on the dipole field of $\leq 3\times 10^{12}$ G, i.e. an order of magnitude lower that given by the CRSF measurement. It is, therefore, necessary to discuss the origin of this discrepancy. First of all, it is important to emphasize that the evidence for the transition of the accretion disk to the radiative-pressure dominated state close to the peak of the outburst appears to be unambiguously supported by several arguments, and requires that the magnetosphere remains comparatively compact (Doroshenko et al., 2020b). In fact, as discussed in the latter paper, standard scaling of the magnetosphere size with flux implies a good agreement between estimates obtained at the peak and at the very end of the outburst, i.e. within the range of over five orders of magnitude in luminosity. It is, therefore, reasonable to assume that the magnetosphere is indeed rather compact. On the other hand, as discussed by Doroshenko et al. (2020b), the field implied by such a compact magnetosphere ($\sim 2\times 10^{7}$ cm close to the peak of the outburst) is lower than required to explain a dramatic change of the pulse profile around either $L_{x}\sim 1.5\times 10^{38}$ erg s^-1 interpreted by Doroshenko et al. (2020b), or around $L_{x}\sim 4.4\times 10^{38}$ erg s^-1 interpreted by Kong et al. (2020) as the onset of the accretion column.

Indeed, the critical luminosity for a NS XRB system corresponding to such transition and switch of the emission pattern from “pencil” to “fan” beams is connected to the magnetic field in the following way with typical NS parameters of M = 1.4 $M_{\odot}$, R = 10 km, $\Lambda$ = 0.1, and $\omega$ = 1 (Becker et al., 2012):

where $L_{37}$ is the luminosity in units of $10^{37}$ erg s^-1. Here for Swift J0243.6+6124, a critical luminosity of $L_{\rm crit}=2.9\times 10^{38}$ erg s^-1 would be expected under a magnetic field of $1.6\times 10^{13}$ G, i.e. in perfect agreement with our estimate based on the observed CRSF energy, and significantly higher than could be expected for a $\sim 10^{12}$ G field implied by other estimates. This fact was actually noted by Doroshenko et al. (2020b) who argued that this discrepancy can be explained either by a small value of the scaling factor $k=R_{m}/R_{A}$ (where $R_{A}$ is standard equation for Alfven radius), or the presence of the strong multipole components. Our detection of the CRSF thus strongly implies that the latter scenario is indeed correct, which is the first unambiguous evidence for the presence of the multipole fields in accreting neutron stars.

We note that a similar scenario has been invoked for several other pulsing ultraluminous X-ray sources (pULXs) including SMC X-3 (Tsygankov et al., 2017), GRO J1744-28 (Doroshenko et al., 2020a), ULX M82 X-2 (Brice et al., 2021), M51 ULX-8 (Middleton et al., 2019), and others (Brice et al., 2021). Our result unambiguously confirms that this scenario is indeed viable and certainly realized in at least one pulsating ULX (i.e., Swift J0243.6+6124).

We report the phase-resolved analysis of the data of the first Galactic NS ULX Swift J0243.6+6124 observed by Insight-HXMT during its 2017-2018 outburst. The 120 to 146 keV CRSF is robustly detected in a spin phase region of $0.6-1.0$ at a significance level of $6-18\ \sigma$, when the source was at a luminosity of $\sim 2\times 10^{39}$ erg s^-1, far above its critical luminosity for the transition from a “pencil” to a “fan” emission pattern. This serves as the first unambiguous measurement of a CRSF from ULXs, and also the highest CRSF energy discovered so far from all neutron star X-ray binary systems. The measured surface magnetic field of $\sim 1.6\times 10^{13}$ G for Swift J0243.6+6124 is the strongest for all known neutron stars with detected electron CRSFs, and also the strongest for all NS ULXs, unless the cases of marginal detection of possible proton CRSFs are confirmed with future instruments of a much larger effective area than the current instruments at 1-30 keV, e.g., the enhanced X-ray Timing and Polarimetry (eXTP) observatory to be launched in around 2027 (Zhang et al., 2019).

Considering that several independent estimates previously constrained the dipole component of the magnetic field in Swift J0243.6+6124 to be an order of magnitude weaker, we conclude that the observed CRSF traces the multipole component of the field which, therefore, dominates the field in the vicinity of the neutron star’s surface. The presence of multipole field components has been previously argued for several other pULXs based on various arguments, however, our result represents the first and the unambiguous confirmation of this scenario. We emphasize that the detection of a CRSF at such a high energy has only been made possible by the large effective area of HXMT in a hard X-ray band, and of course, a lucky coincidence that the mission was launched in time to observe the first and only giant outburst of Swift J0243.6+6124. Our results are highly relevant for pULXs in general and allow us to settle several inconsistencies in the interpretation of pULX’s phenomenology. In particular, the inconsistency between estimates arguing for a low field based on the spin-up rate and the fact that strong winds are apparently launched by most pULXs which would be impossible in the presence of magnetar fields (King & Lasota, 2019), and those arguing for ultra-strong fields based on the fact that only low plasma opacity realized in ultra-magnetized plasma might explain their observed luminosities (Mushtukov et al., 2015b).