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تسجيل مستخدم جديدOn the Black Hole Masses In Ultra-luminous X-ray Sources
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Xin-Lin Zhou
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Ultra-luminous X-ray sources (ULXs) are off-nuclear X-ray sources in nearby galaxies with X-ray luminosities $geq$ 10$^{39}$ erg s$^{-1}$. The measurement of the black hole (BH) masses of ULXs is a long-standing problem. Here we estimate BH masses in a sample of ULXs with XMM-Newton observations using two different mass indicators, the X-ray photon index and X-ray variability amplitude based on the correlations established for active galactic nuclei (AGNs). The BH masses estimated from the two methods are compared and discussed. We find that some extreme high-luminosity ($L_{rm X} >5times10^{40}$ erg s$^{-1}$) ULXs contain the BH of 10$^{4}$-10$^{5}$ $M_odot$. The results from X-ray variability amplitude are in conflict with those from X-ray photon indices for ULXs with lower luminosities. This suggests that these ULXs generally accrete at rates different from those of X-ray luminous AGNs, or they have different power spectral densities of X-ray variability. We conclude that most of ULXs accrete at super-Eddington rate, thus harbor stellar-mass BH.
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The nature of ultra-luminous X-ray sources (ULXs), which are off-nuclear extragalactic X-ray sources that exceed the Eddington luminosity for a stellar-mass black hole, is still largely unknown. They might be black hole X-ray binaries in a super-Eddi
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odot}$. Such binary systems are expected to be directly evolved from stellar binary systems or formed by dynamical interactions of black holes in dense stellar environments. Here we derive the binary black hole merger rate based on the nearby ultra-luminous X-ray source (ULX) luminosity function (LF) under the assumption that binary black holes evolve through X-ray emitting phases. We obtain the binary black hole merger rate as $5.8 ({t}_{rm ULX}/{0.1 rm Myr})^{-1} lambda^{-0.6} exp{(-0.30lambda)} {rm Gpc^{-3} yr^{-1}}$, where $t_{rm ULX}$ is the typical duration of the ULX phase and $lambda$ is the Eddington ratio in luminosity. This is coincident with the event rate inferred from the detection of GW150914 as well as the predictions based on binary population synthesis models. Although we are currently unable to constrain the Eddington ratio of ULXs in luminosity due to the uncertainties of our models and measured binary black hole merger event rates, further X-ray and GW data will allow us to narrow down the range of the Eddington ratios of ULXs. We also find the cumulative merger rate for the mass range of $5M_odotle M_{rm BH}le100M_odot$ inferred from the ULX LF is consistent with that estimated by the aLIGO collaboration considering various astrophysical conditions such as the mass function of black holes.
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