Most ultraluminous X-ray sources (ULXs) are thought to be supercritical accreting compact objects, where massive outflows are inevitable. Using the long-term monitoring data with the Swift X-ray Telescope, we identified a common feature in bright, hard ULXs: they display a quasi-periodic modulation in their hard X-ray band but not in their soft band. As a result, some sources show a bimodal distribution on the hardness intensity map. We argue that these model-independent results can be well interpreted in a picture that involves supercritical accretion with precession, where the hard X-ray emission from the central funnel is more or less beamed, while the soft X-rays may arise from the photosphere of the massive outflow and be nearly isotropic. It implies that precession may be ubiquitous in supercritical systems, such as the Galactic microquasar SS 433. How the hard X-rays are modulated can be used to constrain the angular distribution of the hard X-ray emission and the geometry of the accretion flow. We also find that two ULX pulsars (NGC 5907 ULX-1 and NGC 7793 P13) show similar behaviors but no bimodal distribution, which may imply that they have a different beaming shape or mechanism.

Ultraluminous X-ray sources (ULXs) were identified as a separate class of objects in 2000 based on data from the Chandra X-Ray Observatory. These are unique objects: their X-ray luminosities exceed the Eddington limit for a typical stellar-mass black hole. For a long time, the nature of ULXs remained unclear. However, the gradual accumulation of data, new results of X-ray and optical spectroscopy, and the study of the structure and energy of nebulae surrounding ULXs led to the understanding that most of the ultraluminous X-ray sources must be supercritical accretion disks like SS 433. The discovery of neutron stars in a number of objects only increased the confidence of the scientific community in the conclusions obtained, since the presence of neutron stars in such systems clearly indicates a supercritical accretion regime. In this review, we systematize the main facts about the observational manifestations of ULXs and SS 433 in the X-ray and optical ranges and discuss their explanation from the point of view of the supercritical accretion theory.

We study the optical counterparts of ultraluminous X-ray sources NGC 4559 X-10 and NGC 4395 ULX-1. Their absolute magnitudes, after taking the reddening into account, are M V ≈ −5.3 and M V ≈ −6.2, respectively. The spectral energy distribution of the NGC 4559 X-10 counterpart is well fitted by a spectrum of an F-type star, whereas NGC 4395 ULX-1 has a blue power-law spectrum. Optical spectroscopy of NGC 4395 ULX-1 has shown a broad and variable HeII λ4686 emission, which puts this object in line with all the other spectrally-studied ULXs. Using the Swift archival X-ray data for NGC 4395 ULX-1, we have found a period of 62.8 ± 2.3 days. The X-ray phase curve of the source is very similar to the precession curve of SS 433. The optical variation of the counterpart (between two accurate measurements) amounts to 0.10 mag. Analyzing the absolute magnitudes of 16 well-studied ULX counterparts one may suggest that as the original accretion rate decreases (but nevertheless remains supercritical), the optical luminosity of the wind becomes dimmer and the donor star dominates. However, an observational bias may also influence the distribution.

We describe a model of spectral energy distribution in supercritical accretion disks (SCAD) based on the conception by Shakura and Sunyaev. We apply this model to five ultra-luminous X-ray sources (ULXs). In this approach, the disk becomes thick at distances to the center less than the spherization radius, and the temperature dependence is T ∝ r −1/2 . In this region the disk luminosity is L bol ∼ L Edd ln(Ṁ /Ṁ Edd ), and strong wind arises forming a wind funnel above the disk. Outside the spherization radius, the disk is thin and its total luminosity is Eddington, L Edd . The thin disk heats the wind from below. From the inner side of the funnel the wind is heated by the supercritical disk. In this paper we do not consider Comptonization in the inner hot winds which must cover the deep supercritical disk regions.Our model is technically similar to the DISKIR model of Gierlinski et al. The models differ in disk type (standard supercritical) and irradiation (disk wind). We propose to distinguish between these two models in the X-ray region ∼ 0.3-1 keV, where the SCAD model has a flat νF ν spectrum, and the DISKIR model never has a flat part, as it is based on the standard α-disk. An important difference between the models can be found in their resulting black hole masses. In application to the ULX spectra, the DISKIR model yields black hole masses of a few hundred solar masses, whereas the SCAD model produces stellar-mass black holes ∼ 10 M ⊙ .

We study a stochastic variability of SS 433 in the 10 −4 − 5 × 10 −2 Hz frequency range based on RXTE data, and on simultaneous observations with RXTE and optical telescopes. We find that the cross-correlation functions and power spectra depends drastically on the precession phase of the supercritical accretion disc. When the wind funnel of the disc is maximally open to the observer, a flat part emerges in the power spectrum; a break is observed at the frequency 1.7 × 10 −3 Hz, with a power-law index β ≈ 1.67 at higher frequencies. The soft emission forming mostly in the jets, lags behind the hard and optical emission. When the observer does not see the funnel and jets (the 'edge-on' disc), the power spectrum is described by a single power-law with β ≈ 1.34 and no correlations between X-ray ranges are detected. We investigated two mechanisms to explain the observed variability at the open disc phase, 1) reflection of radiation at the funnel wall (X-rays and optical) and 2) the gas cooling in the jets (X-rays only). The X-ray variability is determined by the contribution of both mechanisms, however the contribution of the jets is much higher. We found that the funnel size is (2 − 2.5) × 10 12 cm, and the opening angle is ϑ f ∼ 50 • . X-ray jets may consist of three fractions with different densities: 8 × 10 13 , 3 × 10 13 and 5 × 10 11 cm −3 , with most of the jet's mass falling within the latter fraction. We suppose that revealed flat part in the power spectrum may be related to an abrupt change in the disc structure and viscous time-scale at the spherization radius, because the accretion disc becomes thick at this radius, h/r ∼ 1. The extent of the flat spectrum depends on the variation of viscosity at the spherization radius.