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 a model for a super-Eddington accretion disc around a magnetized neutron star taking into account advection of heat and the mass loss by the wind. The model is semi-analytical and predicts radial profiles of all basic physical characteristics of the accretion disc. The magnetospheric radius is found as an eigenvalue of the problem. When the inner disc is in radiation-pressuredominated regime but does not reach its local Eddington limit, advection is mild, and the radius of the magnetosphere depends weakly on the accretion rate. Once approaching the local Eddington limit, the disc becomes advection-dominated, and the scaling for the magnetospheric radius with the mass accretion rate is similar to the classical Alfvén relation. Allowing for the mass loss in a wind leads to an increase of the magnetospheric radius. Our model may be applied to a large variety of magnetized neutron stars accreting close to or above their Eddington limits: ultra-luminous X-ray pulsars, Be/X-ray binaries in outbursts, and other systems. In the context of our model we discuss the observational properties of NGC 5907 X-1, the brightest ultra-luminous pulsar known so far, and NGC 300 ULX-1 which is apparently a Be/X-ray binary experiencing a very bright super-Eddington outburst.

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Aims. We address the task of modeling soft X-ray and optical light curves of X-ray novae in the high/soft state. Methods. The analytic model of viscous evolution of an externally truncated accretion α-disk is used. Relativistic effects near a Kerr black hole and self-irradiation of an accretion disk are taken into account. Results. The model is applied to the outbursts of X-ray nova Monocerotis 1975 (A 0620−00) and X-ray nova Muscae 1991 (GRS 1124−68). Comparison of observational data with the model yields constraints on the angular momentum (the Kerr parameter) of the black holes in A 0620−00 and GRS 1124−68: 0.3−0.6 and ≤0.4, and on the viscosity parameter α of the disks: 0.7−0.95 and 0.55−0.75. We also conclude that the accretion disks should have an effective geometrical thickness 1.5−2 times greater than the theoretical value of the distance between the photometric layers.