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Probing Supercritical Accretion in Ultraluminous X-ray Source M82 X-1 by means of X-ray Spectral Evolution Analysis

We analyze the spectral evolution of ultraluminous X-ray source (ULX) M82 X-1 by means of spectral fitting. We use selected Swift/XRT data in 2014 and 2015. The flux of M82 X-1 increased by a factor of 2-3 from 2014 to 2015. Most of the data in 2015 show greater dominance of hard component than those of 2014. Due to moderate signal-to-noise ratio, we only fit each spectrum with power-law and disk blackbody model separately. The data in 2014 are better fitted with powerlaw model based on the value of reduced-chi squared. On the other hand, both powerlaw and diskbb models showed comparable reduced chi-squared value for the data in 2015. We found that the range of spectral index for 2014 data is 1.65 < Γ < 2.08 and for 2015 data is 1.02 < Γ < 1.95 from the powerlaw model, resembling the range for that of black hole binary system at low mass accretion rate. We obtained higher innermost disk temperature from the disk blackbody model, 1.20 keV < Tin < 3.63 keV, compared to that of black hole binary system in the thermal state. The calculated innermost radius of the disk, Rin, varies between 0.99 to 4.89 RS assuming 10 M black hole which indicates that the spectral state is not in thermal dominant state but rather we suspect that M82 X-1 exhibits greater mass accretion rate than that of the thermal dominant state.


Introduction
Ultraluminous X-ray sources (ULXs) are defined as point-like X-ray sources located outside the center of galaxies with luminosities exceeding 3 × 10 39 erg s -1 [3]. These apparent luminosities, assuming isotropic emission, are above the Eddington limit of a 20 M black hole. Despite the fact of being very luminous, ULXs cannot be explained by the collections of many sources with each luminosity less than the Eddington limit because many ULXs exhibit significant time variabilities [6]. One reasonable assumption is that the ULXs are single compact objects powered by accretion. If the Eddington limit applies to these objects, then ULXs is one of the best candidates for an intermediate-mass black hole (IMBH). Alternatively, ULXs may represent a class of super-Eddington emitters and probes to a regime in which the accretion rate is much higher than that seen in Galactic black hole binaries (e.g. Brightman et al. 2020) [2]. The reality is probably more complex, with some ULXs being possibly more massive than stellar-mass black holes (M ULX > 100 M ), but still experiencing the super-Eddington accretion rate. M82 X-1 is one of the brightest ULXs, which can reach L X ∼ 10 41 erg s -1 at the distance of 3.4 Mpc [4]. Its high luminosity, makes it one of the best intermediate-mass black-hole (IMBH) candidates, assuming Eddington-limited accretion. Detection of twin-peaked QPOs at 3.3 and 5.1Hz lead to a mass estimate using scaling laws between the QPOs frequencies and mass of 428 ± 105 M [8]. However, the mass estimates for M82 X-1 using different methods vary considerably and have large uncertainties. Therefore its status as an IMBH has not been firmly established. For instance, modelling of the accretion disk emission shows that M82 X-1 can be explained by a ∼ 30 M stellar remnant black hole radiating at several times its Eddington limit [7].
Here, we report our X-ray spectral analysis using Swift/XRT observations. We aim to investigate the variability of the X-ray spectra and estimate the mass of the black hole in M82 X-1. In Section 2, we describe the X-ray data which we used in the this study, including the details of data reduction and fitting methods. In Section 3, fitting results are presented, together with their implications on the black hole mass. We conclude our work in Section 4.

Data
We use Swift/XRT data for our study due to its frequent observations during 2014 and 2015.  [1], the flux of M82 X-1 is found to increase during May to July in 2015. Therefore, we have added 18 observations data during May to July 2015. Table 1 provides a description of the observational data.

Data Reduction and Fitting Methods
We extracted the source counts from a circular region with a radius of ∼ 49" and the background events were extracted from a nearby circular region of the same size ( Figure 1). The hardness ratio is defined as the ratio between the count rate in 1.5-10 keV to that of 0.3-1.5 keV. Figure 2 shows the 0.3-10 keV count rate of each observation (light curve) and the corresponding hardness ratio. The hardness ratio shows that 2015 data are more dominated by the hard X-ray component than those of 2014. On the bottom panel, the light curve shows that the flux increases of about 2 to 3 times from 2014 to 2015. This shows a spectral evolution that is different from that of Galactic black hole binary, in which the softer component increases as the source brightened. The spectra were grouped with a minimum of one count per bin. The C-statistic was used for spectral fitting. The spectra were fitted in the range 0.3-10 keV with two different model, powerlaw and disk black body (diskbb).

Spectral Analysis
Not all of the data can be fitted by single powerlaw or diskbb model. Table 2   result is plotted in Figure 3. Powerlaw fittings show the range of spectral index, 1.02 to 2.08, which is similar to the range of spectral index for that of black hole binary system at low mass accretion rate. The range of T in values obtained from diskbb model is 1.20 to 3.63 keV, which is higher than typical innermost temperatures of thermal state in non-rotating BHB, but 35% of the well-fitted data gives a comparable value compared with temperatures of maximally rotating BHB. We calculated the X-ray luminosity of M82 X-1 using the flux from fitting and assuming the distance of M82 X-1 is 3.4 Mpc. Using the innermost temperature from fitting result and luminosity that has been calculated before, we calculated the innermost radius of the disk,  R in , assuming the radiation is dominated by black body radiation. We used κ ∼ 1.7 [5] which is the spectral hardening factor, and ξ = 0.412 to correct R in . Then the mass is calculated using M/M = R in /8.86β with a β value 1 for non-rotating and 1/6 for maximally rotating black hole.   hole is assumed in the data points without star symbol while maximally rotating black hole is assumed for data with star symbol. This plot shows that the obtained black hole masses varied due to the non-constant values of innermost disk radius, which cannot be physical, but instead reveal the limitation of mass estimate based on spectral fitting when the standard disk assumption cannot be justified.

Conclusion
We have used Swift/XRT data to show that the spectral variability of M82 X-1 does not resemble that of BHB. The increasing domination of hard component of the spectra as the intensity increase does not necessarily mean that the non-thermal component predominates the spectra, but may imply a higher inner disk temperature which support supercritical accretion, assuming a constant spin of the black hole. The choice of spectrum used to determine black hole mass, must be done carefully. Despite this limitation, all data used in this study indicate a black hole mass less than 100 solar mass. Based on the obtained range of black hole mass, we conclude that M82 X-1 requires a higher accretion rate to explain the different spectrum  transitions compared to BHB at sub-Eddington accretion rates. We therefore conclude that M82 X-1 is a super-Eddington accretor.