We derive the luminosity–temperature relation for the supercritically accreting black holes (BHs) and compare it to the data on ultraluminous X‐ray sources (ULXs). At super‐Eddington accretion rates, an outflow forms within the spherization radius. We construct the accretion disc model accounting for the advection and the outflow, and compute characteristic disc temperatures. The bolometric luminosity exceeds the Eddington luminosity LEdd by a logarithmic factor (where is the accretion rate in Eddington units) and the wind kinetic luminosity is close to LEdd. The apparent luminosity for the face‐on observer is 2–7 times higher because of geometrical beaming. Such an observer has a direct view of the inner hot accretion disc, which has a peak temperature Tmax of a few keV in stellar mass BHs. The emitted spectrum extends as a power law FE∝E−1 down to the temperature at the spherization radius . We associate Tmax with a few keV spectral components and Tsp with the soft, 0.1–0.2 keV components observed in ULXs. An edge‐on observer sees only the soft emission from the extended envelope, with the photosphere radius exceeding the spherization radius by orders of magnitude. The dependence of the photosphere temperature on luminosity is consistent with that observed in the super‐Eddington accreting BHs SS 433 and V4641 Sgr. Strong outflows combined with the large intrinsic X‐ray luminosity of the central BH explain naturally the presence of the photoionized nebulae around ULXs. An excellent agreement between the model and the observational data strongly argues in favour of ULXs being supercritically accreting, stellar mass BHs similar to SS 433, but viewed close to the symmetric axis.

We present X-ray/gamma-ray spectra of Cyg X-1 observed during the transition from the hard to the soft state and in the soft state by ASCA, RXTE and OSSE in 1996 May and June. The spectra consist of a dominant soft component below ~2 keV and a power-law-like continuum extending to at least ~800 keV. We interpret them as emission from an optically-thick, cold accretion disc and from an optically-thin, non-thermal corona above the disc. A fraction f ~ 0.6 of total available power is dissipated in the corona. We model the soft component by multi-colour blackbody disc emission taking into account the torque-free inner-boundary condition. If the disc extends down to the minimum stable orbit, the ASCA/RXTE data yield the most probable black hole mass of about 10 solar masses and an accretion rate about 0.5 L_E/c^2, locating Cyg X-1 in the soft state in the upper part of the stable, gas-pressure dominated, accretion-disc solution branch. The spectrum of the corona is well modelled by repeated Compton scattering of seed photons from the disc off electrons with a hybrid, thermal/non-thermal distribution. The electron distribution can be characterized by a Maxwellian with an equilibrium temperature of kT ~ 30--50 keV and a Thomson optical depth of ~0.3 and a quasi-power-law tail. The compactness of the corona is between 2 and 7, and a presence of a significant population of electron-positron pairs is ruled out. We find strong signatures of Compton reflection from a cold and ionized medium, presumably an accretion disc, with an apparent reflector solid angle ~0.5--0.7. The reflected continuum is accompanied by a broad iron K-alpha line.Comment: 18 pages, 12 figures, 2 landscape tables in a separate file. Accepted to MNRA

We consider two phase accretion disk-corona models for active galactic nuclei and some X-ray binaries. We describe in detail how one can exactly solve the polarized radiative transfer and Comptonization using the iterative scattering method, while simultaneously solving the energy and pair balance equation for both the cold and hot phases. We take into account Compton scattering, photon-photon pair production, pair annihilation, bremsstrahlung, and double Compton scattering, as well as exact reflection from the cold disk. We consider coronae having slab geometry as well as coronae consisting of one or more well separated active regions of cylinder or hemisphere geometry.The method is useful for determining the spectral intensity and the polarization emerging in different directions from disk-corona systems. The code is tested against a Monte-Carlo code. We also compare with earlier, less accurate, work. The method is more than an order of magnitude faster than applying Monte Carlo methods to the same problem and has the potential of being used in spectral fitting software such as XSPEC.