Anatolii M. Cherepashchuk

The mass of the black hole in the X-ray binary M33 X-7 and the evolutionary status of M33 X-7 and IC 10 X-1

We have analyzed the observed radial-velocity curve for the X-ray binary M33 X-7 in a Roche model. We have analyzed the dependence between the component masses and the degree of filling of the optical star’s Roche lobe to obtain the ratio of the masses of the optical star and compact object. For the most probable mass of the optical star, mv = 70 M⊙, the mass of the compact object is mx = 15.55 ± 3.20 M⊙. It has been shown that black holes with masses of mx = 15 M⊙ and even higher can form in binaries. We present characteristic evolutionary tracks for binary systems passing through an evolutionary stage with properties similar to M33 X-7-type objects. According to population-synthesis analyses, such binaries should be present in galaxies with masses of at least 1011M⊙. The present number of such systems in M33 should be of the order of unity. We have also studied the evolutionary status of the X-ray binary IC 10 X-1 with a Wolf-Rayet component, which may contain a massive black hole. The final stages of the evolution of the M33 X-7 and IC 10 X-1 systems should be accompanied by the radiation of gravitational waves.

Masses of X-ray pulsars in binary systems with OB supergiants

We describe the results of a statistical approach to analyzing the combined radial-velocity curves of X-ray binaries with OB supergiants in a Roche model, both with and without allowance for the anisotropy of the stellar wind. We present new mass estimates for the X-ray pulsars in the close binary systems Cen X-3, LMC X-4, SMC X-1, 4U 1538-52, and Vela X-1.

Estimate of the Black-Hole Mass and Orbital Inclination from the Radial-Velocity Curve of the X-Ray Binary Cyg X-1

The results of a statistical approach to interpreting a master radial-velocity curve for the X-ray binary Cyg X-1 are presented. The dependence of the mass of the X-ray component mx on the mass of the optical component mv is obtained in a Roche model. A method for estimating the orbital inclination from the radial-velocity curve is described. In contrast to the situation for a pointlike optical star, both the amplitude and shape of the radial-velocity curve changes as a function of the orbital inclination i in the case of a tidally deformed star with a complex temperature distribution over its surface. Thus, high-accuracy radial-velocity curves can be used to impose constraints on the mass and orbital inclination of the black hole: i<45°. Using the information on the optical light curve, radius, and luminosity of the optical star, we estimate 31°

INTEGRAL observations of SS433: system's parameters and nutation of supercritical accretion disc

Based on multiyear INTEGRAL observations of SS433 in 2003-2011, a composite IBIS/ISGRI 18-60 keV orbital light curve is constructed around zero precessional phases psi_{pr}= 0 at the maximim accretion disk opening angle. It shows a peculiar shape with significant excess near the orbital phase phi_orb= 0.25, which is not seen in the softer 2-10 keV energy band. The 40-60 keV orbital light curve demonstrates two almost equal humps at phases \sim 0.25 and \sim 0.75, most likely due to nutation effects of the accretion disk. The nutational variability of SS433 in 15-50 keV with a period of 6.290 days is independently found from timing analysis of Swift/BAT data. The change of the off-eclipse 18-60 keV X-ray flux with the precessional phase shows a double-wave form with strong primary maximum at psi_{pr}= 0 and weak but significant secondary maximum at psi_{pr}= 0.6. A weak variability of the 18-60 keV flux in the middle of the orbital eclipse correlated with the disk precessional phase is also observed. The joint analysis of the broadband 18-60 keV orbital and precessional light curves confirms the presence of a hot extended corona in the central parts of the supercritical accretion disk and constrains the binary mass ratio in SS433 in the range 0.5>q>0.3, suggesting the black hole nature of the compact object.

Kinematics of Disk Galaxies with Known Masses of Their Supermassive Black Holes. Observations

This is the first paper in a project aimed at analyzing relations between the masses of supermassive black holes or nuclear clusters in galaxies and the kinematic features of the host galaxies. We present long-slit spectroscopic observations of galaxies obtained on the 6-m telescope of the Special Astrophysical Observatory using the SCORPIO focal reducer. Radial profiles of the line-of-sight velocities and velocity dispersions of the stellar populations were obtained for seven galaxies with known masses of their supermassive black holes (Mkn 79, Mkn 279, NGC 2787, NGC 3245, NGC 3516, NGC 7457, and NGC 7469), and also for one galaxy with a nuclear cluster (NGC 428). Velocity profiles of the emitting gas were obtained for some of these galaxies as well. We present preliminary galactic rotation curves derived from these data.

Spectroscopic monitoring of SS 433: A search for long-term variations of kinematic model parameters

Between 1994 and 2006, we obtained uniform spectroscopic observations of SS 433 in the region of Hα. We determined Doppler shifts of the moving emission lines, Hα+ and Hα−, and studied various irregularities in the profiles for the moving emission lines. The total number of Doppler shifts measured in these 13 years is 488 for Hα− and 389 for Hα+. We have also used published data to study possible long-term variations of the SS 433 system, based on 755 Doppler shifts for Hα− and 630 for Hα+ obtained over 28 years. We have derived improved kinematic model parameters for the precessing relativistic jets of S S 433 using five-and eight-parameter models. On average, the precession period was stable during the 28 years of observations (60 precession cycles), at 162.250d ± 0.003d. Phase jumps of the precession period and random variations of its length with amplitudes of ≈6% and ≈1%, respectively, were observed, but no secular changes in the precession period were detected. The nutation period, Pnut = 6.2876d ± 0.00035d, and its phase were stable during 28 years (more than 1600 nutation cycles). We find no secular variations of the nutation cycle. The ejection speed of the relativistic jets, v, was, on average, constant during the 28 years, β = v/c = 0.2561 ± 0.0157. No secular variation of β is detected. In general, S S 433 demonstrates remarkably stable long-term characteristics of its precession and nutation, as well as of the central “engine” near the relativistic object that collimates the plasma in the jets and accelerates it to v = 0.2561c. Our results support a model with a “slaved” accretion disk in S S 433, which follows the precession of the optical star’s rotation axis.

K-Corrections to radial-velocity curves of optical components in X-ray binaries. Massive systems with weak X-ray heating

The radial-velocity curves of optical components in X-ray binary systems can differ from the radial-velocity curves of their barycenters due to tidal distortion, gravitational darkening, X-ray heating, etc. This motivated us to investigate how the semi-amplitudes of the radial-velocity curves of these optical components can depend on the binary-system parameters in a Roche model. The K correction is taken to be the ratio of the radial velocity semi-amplitude for a star in the Roche model to the corresponding value for the stellar barycenter. K corrections are tabulated for the optical stars in the massive X-ray binaries Cen X-3, LMC X-4, SMC X-1, Vela X-1, and 4U 1538-52.

Supermassive black holes and galaxy kinematics

The statistical relation between the masses of supermassive black holes (SMBHs) in disk galaxies and the kinematic properties of their host galaxies is analyzed. Velocity estimates for several galaxies obtained earlier at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences and the data for other galaxies taken from the literature are used. The SMBH masses correlate well with the rotational velocities at a distance of R ≈ 1 kpc, V1, which characterize the mean density of the central region of the galaxy. The SMBH masses correlate appreciably weaker with the asymptotic velocity at large distances from the center and the angular velocity at the optical radius R25. We have found for the first time a correlation between the SMBH mass and the total mass of the galaxy within the optical radius R25, M25, which includes both baryonic and “dark” mass. The masses of the nuclear star clusters in disk galaxies (based on the catalog of Seth et al.) are also related to the dynamical mass M25; the correlations with the luminosity and rotational velocity of the disk are appreciably weaker. For a given value of M25, the masses of the central cluster are, on average, an order of magnitude higher in S0-Sbc galaxies than in late-type galaxies, or than the SMBH masses. We suggest that the growth of the SMBH occurs in the forming “classical” bulge of the galaxy over a time < 109 yr, during a monolithic collapse of gas in the central region of the protogalaxy. The central star clusters form on a different time scale, and their stellar masses continue to grow for a long time after the growth of the central black hole has ceased, if this process is not hindered by activity of the nucleus.

Light curve analysis for eclipsing systems with exoplanets. The system HD 209458

We have analyzed precision light curves for HD 209458, a binary with an exoplanet. The parameters obtained at different epochs and different wavelengths are in good mutual agreement when confidence regions are used to calculate the uncertainty intervals. We demonstrate the effectiveness and reliability of our new method for estimating the uncertainty intervals. Reliable estimates are provided for the linear and quadratic limb-darkening coefficients of the star and their confidence intervals (uncertainties). We find that the wavelength dependence for the limb-darkening coefficients at λ = 3201−9708 Å differs significantly from the corresponding theoretical relation based on thin model stellar atmospheres.

Estimation of parameter errors in inverse problems. Determining limb-darkening coefficients in classical eclipsing systems

The estimation of parameters and their errors is considered using the observed light curve of the eclipsing binary system YZ Cas as an example. The error intervals are calculated using the differential-correction and confidence-region methods. The error intervals and reliability of the methods are investigated, and the reliability of limb-darkening coefficients derived from the observed light curve analyzed. A new method for calculating parameter errors is proposed.