A. G. Zhilkin

Formation of accretion disks in close-binary systems with magnetic fields

We have developed a three-dimensional numerical model and applied it to simulate plasma flows in semi-detached binary systems whose accretor possesses a strong intrinsic magnetic field. The model is based on the assumption that the plasma dynamics are determined by the slow mean flow, which forms a backdrop for the rapid propagation of MHD waves. The equations describing the slow motion of matter were obtained by averaging over rapidly propagating pulsations. The numerical model includes the diffusion of magnetic field by current dissipation in turbulent vortices, magnetic buoyancy, and wave MHD turbulence. A modified three-dimensional, parallel, numerical code was used to simulate the flow structure in close binary systems with various accretor magnetic fields, from 105 to 108 G. The conditions for the formation of the accretion disk and the criteria distinguishing the two types of flow corresponding to intermediate polars and polars are discussed.

Magnetic-field structure in the accretion disks of semi-detached binary systems

The results of three-dimensional MHD numerical simulations are used to investigate the characteristic properties of the magnetic-field structures in the accretion disks of semi-detached binary systems. It is assumed that the intrinsic magnetic field of the accretor star is dipolar. Turbulent diffusion of the magnetic field in the disk is taken into account. The SS Cyg system is considered as an example. The results of the numerical simulations show the intense generation of a predominantly toroidal magnetic field in the accretion disk. Magnetic zones with well defined structures for the toroidal magnetic field form in the disk, which are separated by current sheets in which there ismagnetic reconnection and current dissipation. Possible observational manifestations of such structures are discussed. It is shown that the interaction of a spiral precessional wave with the accretor’s magnetosphere could lead to quasi-periodic oscillations of the accretion rate.

Impact of the magnetic field on the structure of accretion disks in semi-detached binaries

We discuss characteristic features of the magnetic gas-dynamical structure of the flows in a semi-detached binary system obtained from three-dimensional simulations, assuming that the intrinsic magnetic field of the accreting star is dipolar. The turbulent diffusion of the magnetic field is taken into account. The SS Cyg system is considered as an example. Including the magnetic field can alter the basic parameters of the accretion disk, such as the accretion rate and the characteristic density. The magnetic field in the disk is primarily toroidal.

The matter-flow structure in the SS Cyg system in its quiescent state from comparisons of observational and synthetic Doppler tomograms

Doppler tomograms are constructed for the quiescent state of the SS Cyg system based on Hβ and Hγ spectral-line observations carried out in August 2006 with the 2-m telescope at Terskol Peak. Gasdynamical simulations combined with the Doppler tomograms enable identification of the main features of the flow. Comparisons of synthetic tomograms with observations indicate that an accretion disk is present in the quiescent system. In the tomograms, the luminosity is maximum at the arms of the spiral tidal shock at the shock front due to the interaction between the gas of the circum-binary envelope and material in the stream issuing from the Lagrangian point L1 (the “hot line”), and in the region behind the bow shock due to the motion of the accretor and disk in the gas of the envelope. The contribution of this last element results in appreciable asymmetry of the tomograms.

Modeling of Protostellar Clouds and Their Observational Properties

A physical model and two-dimensional numerical method for computing the evolution and spectra of protostellar clouds are described. The physical model is based on a system of magneto-gas-dynamical equations, including ohmic and ambipolar diffusion, and a scheme for calculating the thermal and ionization structure of a cloud. The dust and gas temperatures are determined when calculating the thermal structure of the cloud. The results of computing the dynamical and thermal structure of the cloud are used to model the transfer of continuum and molecular-line radiation in the cloud. Results are presented for clouds in hydrostatic and thermal equilibrium. The evolution of a rotating magnetic protostellar cloud that is compressed starting from a quasi-static equilibrium state is also considered. Spectral maps for optically thick lines of linear molecules are analyzed. The influence of the magnetic field and rotation can lead to a redistribution of angular momentum in the cloud and the formation of a characteristic rotational-velocity structure. As a result, the distribution of the velocity centroid of the molecular lines can acquire an hourglass shape. It is planned in future to use the developed program package and a model for the chemical evolution of clouds to interpret and model in detail observed starless and protostellar cores.

The thermal structure of a protostellar envelope

A numerical hydrodynamical model for the evolution of spherically symmetric collapsing clouds, designed for the calculation of the thermal structure of these objects in both the prestellar and protostellar stages of their evolution, is presented. Distinctive features of the model include the possibility of independently describing the temperatures of the gas and dust, which is extremely important when calculating the thermal structure of prestellar and protostellar clouds, and the account of the radiation flux from the central protostar. This model is used to compare the theoretical density and temperature distributions with observations for nearby sites of star formation obtained with the Herschel Space Observatory. Application of the diffusion approximation with a flux limiter describes well the radial density and temperature distributions in protostellar clouds. However, significant differences between the model and observational density profiles were found for prestellar stages, suggesting the presence of appreciable deviations from equilibrium in the prestellar clouds. An approximate method for calculating the thermal structure of a cloud based on the adaptive τ-approximation is presented. Application of the τ-approximation yields good agreement with the diffusion approximation for the prestellar phase, but produces appreciable discrepancies for the protostellar phase, when the thermal structure of the accreting envelope is determined by the radiation of the protostar.

Full 3D MHD calculations of accretion flow structure in magnetic cataclysmic variables with strong, complex magnetic fields

We have performed three-dimensional magnetohydrodynamical calculations of stream accretion in cataclysmic variable stars for which the white dwarf primary possesses a strong, complex magnetic field. These calculations were motivated by observations of polars: cataclysmic variables containing white dwarfs with magnetic fields sufficiently strong to prevent the formation of an accretion disk. In this case, an accretion stream flows from the L1 point and impacts directly onto one or more spots on the surface of the white dwarf. Observations indicate that the white dwarfs in some binaries possess complex (non-dipolar) magnetic fields. We performed simulations of ten polars, with the only variable being the azimuthal angle of the secondary with respect to the white dwarf. These calculations are also applicable to asynchronous polars, where the spin period of the white dwarf differs by a few percent from the orbital period. Our results are equivalent to calculating the structure of one asynchronous polar at ten different spin-orbit beat phases. Our models have an aligned dipolar plus quadrupolar magnetic field centered on the whitedwarf primary. We find that, with a sufficiently strong quadrupolar component, an accretion spot arises near the magnetic equator for slightly less than half our simulations, while a polar accretion zone is active for most of the remaining simulations. For two configurations, accretion at a dominant polar region and in an equatorial zone occurs simultaneously. Most polar studies assume that the magnetic field is dipolar, especially for single-pole accretors. We demonstrate that, with the orbital parameters and magnetic-field strengths typical of polars, the accretion flow patterns can vary widely in the case of a complex magnetic field. This may make it difficult formany polars to determine observationally whether the field is pure dipolar or is more complex, but there shoulid be indications for some systems. In particular, a complex magnetic field should be suspected if there is an accretion zone near the white dwarf’s equator (assumed to be in the orbital plane) or if there are two or more accretion regions that cannot be fitted by dipolar magnetic field. Magnetic-field constraints are expected to be substantially stronger for asynchronous polars, with clearer signs of complex field geometry due to changes in the accretion flow structure as a function of azimuthal angle. These indications become clearer in asynchronous polars because each azimuthal angle corresponds to a different spin-orbit beat phase.

Reduction of mass loss by the hot Jupiter WASP-12b due to its magnetic field

The influence of the dipolar magnetic field of a “hot Jupiter” with the parameters of the object WASP-12b on the mass-loss rate from its atmosphere is investigated. The results of three-dimensional gas-dynamical and magnetohydrodynamical computations show that the presence of a magnetic moment with a strength of ~0.1 the magnetic moment of Jupiter leads to appreciable variations of the matter flow structure. For example, in the case of the exoplanet WASP-12b with its specified set of atmospheric parameters, the stream from the vicinity of the Lagrange point L1 is not stopped by the dynamical pressure of the stellar wind, and the envelope remains open. Including the effect of the magnetic field leads to a variation in this picture—the atmosphere becomes quasi-closed, with a characteristic size of order 14 planetary radii, which, in turn, substantially decreases the mass-loss rate by the exoplanet atmosphere (by~70%). This reduction of the mass-loss rate due to the influence of the magnetic fieldmakes it possible for exoplanets to form closed and quasi-closed envelopes in the presence of more strongly overflowing Roche lobes than is possible without a magnetic field.

Features of the accretion in the EX Hydrae system: Results of numerical simulation

A two-dimensional numerical model in the axisymmetric approximation that describes the flow structure in the magnetosphere of the white dwarf in the EX Hya system has been developed. Results of simulations show that the accretion in EX Hya proceeds via accretion columns, which are not closed and have curtain-like shapes. The thickness of the accretion curtains depends only weakly on the thickness of the accretion disk. This thickness developed in the simulations does not agree with observations. It is concluded that the main reason for the formation of thick accretion curtains in the model is the assumption that the magnetic field penetrates fully into the plasma of the disk. An analysis based on simple estimates shows that a diamagnetic disk that fully or partially shields the magnetic field of the star may be a more attractive explanation for the observed features of the accretion in EX Hya.

Features of the matter flows in the peculiar cataclysmic variable AE Aquarii

The structure ofmatter flows in close binary systems in which one of the components is a rapidly rotating magnetic white dwarf is studied. Themain example considered is the AEAquarii system; the period of the white dwarf’s rotation is about a factor of 1000 shorter than the orbital period, and the magnetic field on the white-dwarf surface is of order 50MG. The matter flows in this system were analyzed via numerical solution of a systemofmagnetohydrodynamical equatons. These computations show that the white dwarf’s magnetic field does not significantly influence the velocity field of the matter in its Roche lobe in the case of a laminar flow regime, so that the field does not hinder the formation of a transient disk (ring) surrounding the magnetosphere. However, the efficiency of the energy and angular-momentum exchange between the white dwarf and the surrounding matter increases considerably with the development of turbulent motions in the matter, accelerating the matter at the magnetosphere boundary and leading to a high escape rate from the system. The time scales for the system’s transition between the laminar and turbulent modes are close to those for the transition of AE Aquarii between its quiet and active phases.