Том 62, № 4 (2018)

Most of the energy released in the gravitational collapse of the cores of massive stars is carried away by neutrinos. Neutrinos play a pivotal role in explaining core-collape supernovae. Currently, mathematical models of the gravitational collapse are based on multi-dimensional gas dynamics and thermonuclear reactions, while neutrino transport is considered in a simplified way. Multidimensional gas dynamics is used with neutrino transport in the flux-limited diffusion approximation to study the role of multi-dimensional effects. The possibility of large-scale convection is discussed, which is interesting both for explaining SN II and for setting up observations to register possible high-energy (≳10MeV) neutrinos from the supernova. A new multi-dimensional, multi-temperature gas dynamics method with neutrino transport is presented.

The photometric variability of the uniqueMdwarf flare star GJ 1243 (KIC 9726699) is investigated using the most complete set of observationalmaterial obtained with the Kepler Space Telescope. The analysis is based on 49 487 individual brightness measurements obtained during an interval of 1460 days (nearly four years). The periodicity of the brightness variations with the period P_phot = 0.59261 ± 0.00060^d is confirmed. The temperature inhomogeneities on the stellar surface reconstructed from the light curve are used to drive maps of these surface-temperature inhomogeneities (of the filling factor f). The resulting maps are used to determine the positions of active regions. Analysis of the surface-temperature maps for GJ 1243 led to the conclusion that the positions of spots on the stellar surface displayed appreciable evolution during the analyzed time interval. The maximum value for the lower limit on the differentialrotation parameter ΔΩ is 0.0022 rad/day. This more accurate estimate of ΔΩ is lower than the values presented earlier by Davenport et al. [1] (0.0058 and 0.0036 rad/day), due to the more accurate account of variations in the positions of the most active longitude in the current study. However, the differentialrotation estimate obtained in [1] using a method based on fitting the evolution of spots using twodimensional Gaussian functions essentially coincides with the new estimate presented here. The fractional area of the total spotted surface S of the star during the observing interval considered varied from 7 to 2%. The amplitude of the brightness variability of the star slowly decreased, varying in the range 1.6−0.5%. Overall, the position of GJ 1243 in spottedness–age, spottedness–rotation period, and spottedness–Rossby number diagrams agrees very well with the general character of the dependences displayed in earlier studies of M dwarfs.

The motion of a zero-mass point under the action of gravitation toward a central body and a perturbing acceleration P is considered. The magnitude of P is taken to be small compared to the main acceleration due to the gravitation of the central body, and the components of the vector P are taken to be constant in a reference frame with its origin at the central body and its axes directed along the velocity vector, normal to the velocity vector in the plane of the osculating orbit, and along the binormal. The equations in the mean elements were obtained in an earlier study. The algorithm used to solve these equations is given in this study. This algorithm is analogous to one constructed earlier for the case when P is constant in a reference frame tied to the radius vector. The properties of the solutions are similar. The main difference is that, in the most important cases, the quadratures to which the solution reduces lead to non-elementary functions. However, they can be expressed as series in powers of the eccentricity e that converge for e < 1, and often also for e = 1.

The Editor-in-Chief is retracting this article [1] because data from the RFC catalog, http://astrogeo.org/rfc, were used without permission from the copyright holder. The author admitted the decision to retract.