On the nature of ultraluminous X-ray sources, or what a black hole should look like

We derive the luminosity-temperature relation for the accreting black holes (BHs). At the accretion rates below the Eddington, the BHs are described by the Shakura-Sunyaev model resulting in the L ~ T**4 ~ Mdot relation. At super-Eddington rates mdot=Mdot/Mdot_Edd >> 1, a strong outflow forms within the spherization radius Rsph ~ Mdot. If the angular momentum is conserved the wind occupies 50-85 per cent of the sky as viewed from the BH. The bolometric luminosity exceeds the Eddington limit by a factor 1+ln mdot and the observed luminosity is 2-7 times higher because of geometrical beaming. An edge-on observer sees the soft emission from the extended envelope, with the photosphere radius exceeding the spherization radius by orders of magnitude. The photosphere temperature follows the Tph ~ Mdot**{-3/4} or Mdot**{-1} relation depending on the velocity profile at R>Rsph. The resulting L-Tph dependence is consistent with that observed in SS 433 and V4641 Sgr. A face-on observer sees the inner hot accretion disc with Tmax a few keV. The effective temperature depends on radius as ~R**{-1/2} (up to Rsph) and the spectrum is a power-law F_E ~ E**{-1} extending from 3 Tmax down to the temperature at the Rsph: Tsph = mdot**{-1/2} keV. We associate Tmax with a few keV spectral components and Tsph with the soft, 0.1-0.2 keV components observed in the ultraluminous X-ray sources (ULX). The strong outflows combined with the large intrinsic BH luminosity explain the presence of the photoionized nebulae around ULX. An agreement between the model and the observational data on ULX strongly argues in favour of ULX being supercritically accreting, stellar-mass BHs similar to SS 433, but viewed along the symmetry axis