No Arabic abstract
The mass transfer in binaries with massive donors and compact companions, when the donors rapidly evolve after their main sequence, is one of the dominant formation channels of merging double stellar-mass black hole binaries. This mass transfer was previously postulated to be unstable and was expected to lead to a common envelope event. The common envelope event then would end with either double black hole formation, or with the merger of the two stars. We re-visit the stability of this mass transfer, and find that for a large range of the binary orbital separations this mass transfer is stable. This newly found stability allows us to reconcile the theoretical rate for double black hole binary mergers predicted by population synthesis studies, and the empirical rate obtained by LIGO. Futhermore, the stability of the mass transfer leads to the formation of ultra-luminous X-ray sources. The theoretically predicted formation rates of ultra-luminous X-ray sources powered by a stellar-mass BH, as well as the range of produced X-ray luminosity, can explain the observed bright ultra-luminous X-ray sources.
The Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) has detected direct signals of gravitational waves (GWs) from GW150914. The event was a merger of binary black holes whose masses are $36^{+5}_{-4}M_{odot}$ and $29^{+4}_{-4}M_{odot}$. 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.
Gravitational waves from the binary black hole (BH) merger GW150914 may enlighten our understanding of ultra-luminous X-ray sources (ULXs), as BHs>30Msun can reach luminosities>4x10^39 erg s^-1 without exceeding their Eddington limit. It is then important to study variations of evolutionary channels for merging BHs, which might instead form accreting BHs and become ULXs. It was recently shown that massive binaries with mass ratios close to unity and tight orbits can undergo efficient rotational mixing and evolve chemically homogeneously, resulting in a compact BH binary. We study similar systems by computing ~120000 detailed binary models with the MESA code covering a wide range of initial parameters. For initial mass ratios M2/M1~0.1-0.4, primaries >40Msun can evolve chemically homogeneously, remaining compact and forming a BH without undergoing Roche-lobe overflow. The secondary then expands and transfers mass to the BH, initiating a ULX phase. We predict that ~1 out of 10^4 massive stars evolves this way, and that in the local universe 0.13 ULXs per Msun yr^-1 of star-formation rate are observable, with a strong preference for low-metallicities. At metallicities log Z>-3, BH masses in ULXs are limited to 60Msun due to the occurrence of pair-instability supernovae which leave no remnant, resulting in an X-ray luminosity cut-off. At lower metallicities, very massive stars can avoid exploding as pair-instability supernovae and instead form BHs with masses above 130Msun, producing a gap in the ULX luminosity distribution. After the ULX phase, neutron-star-BH binaries that merge in less than a Hubble time are produced with a formation rate <0.2 Gpc^-3 yr^-1. We expect that upcoming X-ray observatories will test these predictions, which together with additional gravitational wave detections will provide strict constraints on the origin of the most massive BHs that can be produced by stars.
A calibration is made for the correlation between the X-ray Variability Amplitude (XVA) and Black Hole (BH) mass. The correlation for 21 reverberation-mapped Active Galactic Nuclei (AGN) appears very tight, with an intrinsic dispersion of 0.20 dex. The intrinsic dispersion of 0.27 dex can be obtained if BH masses are estimated from the stellar velocity dispersions. We further test the uncertainties of mass estimates from XVAs for objects which have been observed multiple times with good enough data quality. The results show that the XVAs derived from multiple observations change by a factor of 3. This means that BH mass uncertainty from a single observation is slightly worse than either reverberation-mapping or stellar velocity dispersion measurements; however BH mass estimates with X-ray data only can be more accurate if the mean XVA value from more observations is used. Applying this relation, the BH mass of RE J1034+396 is found to be $4^{+3}_{-2} times 10^6$ $M_{odot}$. The high end of the mass range follows the relationship between the 2$f_0$ frequencies of high-frequency QPO and the BH masses derived from the Galactic X-ray binaries. We also calculate the high-frequency constant $C= 2.37 M_odot$ Hz$^{-1}$ from 21 reverberation-mapped AGN. As suggested by Gierlinski et al., $M_{rm BH}=C/C_{rm M}$, where $C_{rm M}$ is the high-frequency variability derived from XVA. Given the similar shape of power-law dominated X-ray spectra in ULXs and AGN, this can be applied to BH mass estimates of ULXs. We discuss the observed QPO frequencies and BH mass estimates in the Ultra-Luminous X-ray source M82 X-1 and NGC 5408 X-1 and favor ULXs as intermediate mass BH systems (abridged).
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.
Many upcoming surveys, particularly in the radio and optical domains, are designed to probe either the temporal and/or the spatial variability of a range of astronomical objects. In the light of these high resolution surveys, we review the subject of ultra-luminous X-ray (ULX) sources, which are thought to be accreting black holes for the most part. We also discuss the sub-class of ULXs known as the hyper-luminous X-ray sources, which may be accreting intermediate mass black holes. We focus on some of the open questions that will be addressed with the new facilities, such as the mass of the black hole in ULXs, their temporal variability and the nature of the state changes, their surrounding nebulae and the nature of the region in which ULXs reside.