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Register a new userA Determination of the Spin of the Black Hole Primary in LMC X-1
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Lijun Gou
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The first extragalactic X-ray binary, LMC X-1, was discovered in 1969. In the 1980s, its compact primary was established as the fourth dynamical black-hole candidate. Recently, we published accurate values for the mass of the black hole and the orbital inclination angle of the binary system. Building on these results, we have analyzed 53 X-ray spectra obtained by RXTE and, using a selected sample of 18 of these spectra, we have determined the dimensionless spin parameter of the black hole to be a* = 0.92(-0.07,+0.05). This result takes into account all sources of observational and model-parameter uncertainties. The standard deviation around the mean value of a* for these 18 X-ray spectra, which were obtained over a span of several years, is only 0.02. When we consider our complete sample of 53 RXTE spectra, we find a somewhat higher value of the spin parameter and a larger standard deviation. Finally, we show that our results based on RXTE data are confirmed by our analyses of selected X-ray spectra obtained by the XMM-Newton, BeppoSAX and Ginga missions.
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The compact primary in the X-ray binary Cygnus X-1 was the first black hole to be established via dynamical observations. We have recently determined accurate values for its mass and distance, and for the orbital inclination angle of the binary. Building on these results, which are based on our favored (asynchronous) dynamical model, we have measured the radius of the inner edge of the black holes accretion disk by fitting its thermal continuum spectrum to a fully relativistic model of a thin accretion disk. Assuming that the spin axis of the black hole is aligned with the orbital angular momentum vector, we have determined that Cygnus X-1 contains a near-extreme Kerr black hole with a spin parameter a/M>0.95 (3sigma). For a less probable (synchronous) dynamical model, we find a/M>0.92 (3sigma). In our analysis, we include the uncertainties in black hole mass, orbital inclination angle and distance, and we also include the uncertainty in the calibration of the absolute flux via the Crab. These four sources of uncertainty totally dominate the error budget. The uncertainties introduced by the thin-disk model we employ are particularly small in this case given the extreme spin of the black hole and the disks low luminosity.
Cygnus X-1 is a well-studied persistent black hole X-ray binary. Recently, the three parameters needed to estimate the black hole spin of this system, namely the black hole mass $M$, the orbital inclination $i$ and the source distance $D$, have been updated. In this work we redetermine the spin parameter using the continuum-fitting technique for those updated parameter values. Based on the assumption that the spin axis of the black hole is aligned with the orbital plane, we fit the thermal disk component to a fully relativistic thin accretion disk model. The error in the spin estimate arising from the combined observational uncertainties is obtained via Monte Carlo (MC) simulations. We demonstrate that, without considering the counteracting torque effect, the new spin parameter is constrained to be a$_* > 0.9985$ (3$sigma$), which confirms that the spin of the black hole in Cygnus X-1 is extreme.
We present the first results of extragalactic black hole X-ray binaries LMC X-1 and LMC X-3 using all the archival and legacy observations by AstroSat during the period of $2016-2020$. Broadband energy spectra ($0.5-20$ keV) of both sources obtained from the SXT and LAXPC on-board AstroSat are characterized by strong thermal disc blackbody component ($kT_{in}sim1$keV, $f_{disc}>79%$) along with a steep power-law ($Gammasim2.4-3.2$). Bolometric luminosity of LMC X-1 varies from $7-10%$ of Eddington luminosity ($L_{Edd}$) and for LMC X-3 is in the range $7-13%$ of $L_{Edd}$. We study the long-term variation of the light curve using MAXI data and find the fractional variance to be $sim25%$ for LMC X-1 and $sim53%$ for LMC X-3. We examine the temporal properties of both sources and obtain fractional rms variability of PDS in the frequency range $0.002-10$ Hz to be $sim9%-17%$ for LMC X-1, and $sim7%-11%$ for LMC X-3. The `spectro-temporal properties indicate both sources are in thermally dominated soft state. By modelling the spectra with relativistic accretion disc model, we determine the mass of LMC X-1 and LMC X-3 in the range $7.64-10.00$ $M_{odot}$ and $5.35-6.22$ $M_{odot}$ respectively. We also constrain the spin of LMC X-1 to be in the range $0.82-0.92$ and that of LMC X-3 in $0.22-0.41$ with 90% confidence. We discuss the implications of our results in the context of accretion dynamics around the black hole binaries and compare it with the previous findings of both sources.
We present results from 170ksec long RXTE observations of LMC X-1 and LMC X-3, taken in 1996 December, where their spectra can be described by a disc black body plus an additional soft (Gamma~2.8) high-energy power-law (detected up to 50keV in LMC X-3). These observations, as well as archival ASCA observations, constrain any narrow Fe line present in the spectra to have an equivalent width <90eV, broad lines (~150eV EW, sigma ~ 1keV) are permitted. We also study the variability of LMC X-1. Its X-ray power spectral density (PSD) is approximately f^{-1} between 10^{-3} and 0.3Hz with a rms variability of ~7%. Above 5keV the PSD shows evidence of a break at f > 0.2Hz, possibly indicating an outer disc radius of ~1000GM/c^2 in this likely wind-fed system. Furthermore, the coherence function between variability in the > 5keV band and variablity in the lower energy bands is extremely low. We discuss the implications of these observations for the mechanisms.
We present a dynamical model of the high mass X-ray binary LMC X-1 based on high-resolution optical spectroscopy and extensive optical and near-infrared photometry. From our new optical data we find an orbital period of P=3.90917 +/- 0.00005 days. We present a refined analysis of the All Sky Monitor data from RXTE and find an X-ray period of P=3.9094 +/- 0.0008 days, which is consistent with the optical period. A simple model of Thomson scattering in the stellar wind can account for the modulation seen in the X-ray light curves. The V-K color of the star (1.17 +/- 0.05) implies A_V = 2.28 +/- 0.06, which is much larger than previously assumed. For the secondary star, we measure a radius of R_2 = 17.0 +/- 0.8 solar radii and a projected rotational velocity of V_rot*sin(i) = 129.9 +/- 2.2 km/s. Using these measured properties to constrain the dynamical model, we find an inclination of i = 36.38 +/- 1.92 deg, a secondary star mass of M_2 = 31.79 +/- 3.48 solar masses, and a black hole mass of 10.91 +/- 1.41 solar masses. The present location of the secondary star in a temperature-luminosity diagram is consistent with that of a star with an initial mass of 35 solar masses that is 5 Myr past the zero-age main sequence. The star nearly fills its Roche lobe (~90% or more), and owing to the rapid change in radius with time in its present evolutionary state, it will encounter its Roche lobe and begin rapid and possibly unstable mass transfer on a timescale of a few hundred thousand years.
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