Propeller effect during magnetocentrifugal plasma acceleration

We study the effect of magnetic-field axial asymmetry on the magnetocentrifugal acceleration of plasma when it flows in a source’s rotating magnetosphere (propeller effect). For an axisymmetric steady plasma flow, the first corrections to the energy that arise when the source rotates slowly are proportional to Ω⁴, suggesting a highly inefficient plasma acceleration. Magnetic-field axial asymmetry is shown to substantially modify the acceleration. The first corrections arise even in the first order in Ω. The plasma acceleration turns out to be considerably more efficient in a nonaxisymmetric magnetic field.     

The possibility of emersion of the outer layers in a massive star simultaneously with iron-core collapse: A hydrodynamic model

We analyze the behavior of the outer envelope in a massive star during and after the collapse of its iron core into a protoneutron star (PNS) in terms of the equations of one-dimensional spherically symmetric ideal hydrodynamics. The profiles obtained in the studies of the evolution of massive stars up to the final stages of their existence, immediately before a supernova explosion (Boyes et al. 1999), are used as the initial data for the distribution of thermodynamic quantities in the envelope. We use a complex equation of state for matter with allowances made for arbitrary electron degeneracy and relativity, the appearance of electron-positron pairs, the presence of radiation, and the possibility of iron nuclei dissociating into free nucleons and helium nuclei. We performed calculations with the help of a numerical scheme based on Godunov's method. These calculations allowed us to ascertain whether the emersion of the outer envelope in a massive star is possible through the following two mechanisms: first, the decrease in the gravitational mass of the central PNS through neutrino-signal emission and, second, the effect of hot nucleon bubbles, which are most likely formed in the PNS corona, on the envelope emersion. We show that the second mechanism is highly efficient in the range of acceptable masses of the nucleon bubbles (≤0.01M _⊙) simulated in our hydrodynamic calculations in a rough, spherically symmetric approximation.     

The toroidal iron atmosphere of a protoneutron star: Numerical solution

A numerical method presented by Imshennik et al. (2002) is used to solve the two-dimensional axisymmetric hydrodynamic problem on the formation of a toroidal atmosphere during the collapse of an iron stellar core and outer stellar layers. An evolutionary model from Boyes et al. (1999) with a total mass of 25M_⊙ is used as the initial data for the distribution of thermodynamic quantities in the outer shells of a high-mass star. Our computational region includes the outer part of the iron core (without its central part with a mass of 1M_⊙ that forms the embryo of a protoneutron star at the preceding stage of the collapse) and the silicon and carbon-oxygen shells with a total mass of (1.8–2.5)M_⊙. We analyze in detail the results of three calculations in which the difference mesh and the location of the inner boundary of the computational region are varied. In the initial data, we roughly specify an angular velocity distribution that is actually justified by the final result—the formation of a hydrostatic equilibrium toroidal atmosphere with reasonable total mass, M^tot=(0.117–0.122)M_⊙, and total angular momentum, J^tot=(0.445–0.472)×10⁵⁰ erg s, for the two main calculations. We compare the numerical solution with our previous analytical solution in the form of toroidal atmospheres (Imshennik and Manukovskii 2000). This comparison indicates that they are identical if we take into account the more general and complex equation of state with a nonzero temperature and self-gravitation effects in the atmosphere. Our numerical calculations, first, prove the stability of toroidal atmospheres on characteristic hydrodynamic time scales and, second, show the possibility of sporadic fragmentation of these atmospheres even after a hydrodynamic equilibrium is established. The calculations were carried out under the assumption of equatorial symmetry of the problem and up to relatively long time scales (～10 s).     

A hydrodynamic model for asymmetric explosions of rapidly rotating collapsing supernovae with a toroidal atmosphere

We numerically solved the two-dimensional axisymmetric hydrodynamic problem of the explosion of a low-mass neutron star in a circular orbit. In the initial conditions, we assumed a nonuniform density distribution in the space surrounding the collapsed iron core in the form of a stationary toroidal atmosphere that was previously predicted analytically and computed numerically. The configuration of the exploded neutron star itself was modeled by a torus with a circular cross section whose central line almost coincided with its circular orbit. Using an equation of state for the stellar matter and the toroidal atmosphere in which the nuclear statistical equilibrium conditions were satisfied, we performed a series of numerical calculations that showed the propagation of a strong divergent shock wave with a total energy of ～0.2×10⁵¹ erg at initial explosion energy release of ～1.0×10⁵¹ erg. In our calculations, we rigorously took into account the gravitational interaction, including the attraction from a higher-mass (1.9M_⊙) neutron star located at the coordinate origin, in accordance with the rotational explosion mechanism for collapsing supernovae. We compared in detail our results with previous similar results of asymmetric supernova explosion simulations and concluded that we found a lower limit for the total explosion energy.     

The Crab Nebula: Interpretation of Chandra observations

We interpret the observed X-ray morphology of the central part of the Crab Nebula (torus + jets) in terms of the standard theory by Kennel and Coroniti (1984). The only new element is the inclusion of anisotropy in the energy flux from the pulsar in the theory. In the standard theory of relativistic winds, the Lorentz factor of the particles in front of the shock that terminates the pulsar relativistic wind depends on the polar angle as γ = γ₀ + γ _m sin² θ, where γ₀∼200 and γ_m∼4.5×10⁶. The plasma flow in the wind is isotropic. After the passage of the pulsar wind through the shock, the flow becomes subsonic with a roughly constant (over the plerion volume) pressure P=1/3;n∈ where n is the plasma particle density and ∈ is the mean particle energy. Since ∈∼γmc ², a low-density region filled with the most energetic electrons is formed near the equator. A bright torus of synchrotron radiation develops here. Jet-like regions are formed along the pulsar rotation axis, where the particle density is almost four orders of magnitude higher than that in the equatorial plane, because the particle energy there is four orders of magnitude lower. The energy of these particles is too low to produce detectable synchrotron radiation. However, these quasijets become comparable in brightness to the torus if additional particle acceleration takes place in the plerion. We also present the results of our study of the hydrodynamic interaction between an anisotropic wind and the interstellar medium. We compare the calculated and observed distributions of the volume emissivity of X-ray radiation.     

Shock waves with large energy losses by direct radiation from the front

Highly nonadiabatic shock waves are formed at an early stage of a supernova explosion inside a stellar wind because of the large energy losses by direct radiation from the front. The properties of such waves are considered for velocities of (5?25)×10³km s^?1 and gas densities of 10^?17?10^?10 g cm^?3. A critical energy flux going to “infinity” that separates two modes is shown to exist. If the flux is lower than the critical one, then energy losses cause even an increase in the post-shock temperature. An excess of the flux over its critical value results in an abrupt cooling and in a strong compression of the gas. For the flux equal to the critical one, the post-shock gas velocity matches the isothermal speed of sound. Approximate formulas are given for estimating the degree of gas compression and the post-shock radiation-to-gas pressure ratio at energy losses equal to the critical ones and for the limiting compression.     

Prominence height and vertical gradient in magnetic field

The existence of a critical height for quiescent prominences and its relationship to parameters of the magnetic field of photospheric sources are discussed. In the inverse-polarity model, stable equilibrium of a filament with a current is possible only in the region where the external field decreases with height no faster than ～1/h. Calculations of the potential magnetic field above the polarity-inversion line are compared with the observed prominence height. The prominence height is shown to actually depend on the vertical field gradient and does not exceed the level at which the exponent of field decrease is equal to unity.     

On the origin of energetic particles in the foreshock region of the Earth’s bow shock

We consider the processes related to the formation of the so-called foreshock region upstream of the Earth’s bow shock. We suggest a model based on the surfing of pick-up ions in the bow shock front in terms of which the ion acceleration mechanism in the front can be explained. We ascertain the physical conditions under which the accelerated ions lie upstream of the shock front and determine the direction of motion of the energetic ions. We conclude that it is this population of energetic ions (longitudinal beams) that plays a major role in forming the ion foreshock boundary.     

Spectra and light curves of GRB afterglows

We performed accurate numerical calculations of angle-, time-, and frequency-dependent radiative transfer for the relativistic motion of matter in gamma-ray burst (GRB) models. Our technique for solving the transfer equation, which is based on the method of characteristics, can be applied to the motion of matter with a Lorentz factor up to 1000. The effect of synchrotron self-absorption is taken into account. We computed the spectra and light curves from electrons with a power-law energy distribution in an expanding relativistic shock and compare them with available analytic estimates. The behavior of the optical afterglows from GRB 990510 and GRB 000301c is discussed qualitatively.     

Peculiarities of entropy and magnetosonic waves in optically thin cosmic plasma

The stability problem for small magnetohydrodynamic (MHD) perturbations in an optically thin, perfectly conducting uniform plasma with a cosmic abundance of elements is solved in the linear approximation. The electron heat conduction along the magnetic field and the proton heat conduction across the field are taken into account. We have shown for the first time that the entropy waves can grow exponentially, while the magnetosonic waves are damped in a wide range of physical conditions closest to the conditions in stellar coronae with the proper allowance for radiative losses. Slow magnetosonic waves are damped particularly rapidly. For the solar corona, the calculated damping decrement of slow magnetosonic waves agrees well with the averaged one in 11 quasi-periodic events observed from the TRACE satellite in extreme ultraviolet radiation. Other possible astrophysical applications of the results obtained are briefly discussed.     

Dynamics of the flows accreting onto a magnetized neutron star

We investigate the unsteady column accretion of material at a rate \(10^{15} g s^{ - 1} \leqslant \dot M \leqslant 10^{16} g s^{ - 1}\) onto the surface of a magnetized neutron star using a modified first-order Godunov method with splitting. We study the dynamics of the formation and evolution of a shock in an accretion column near the surface of a star with a magnetic field 5×10¹¹≤B≤10¹³ G. An effective transformation of the accretion flow energy into cyclotron radiation is shown to be possible for unsteady accretion with a collisionless shock whose front executes damped oscillations. The collisionless deceleration of the accreting material admits the conservation of a fraction of the heavy nuclei that have not been destroyed in spallation reactions. The fraction of the CNO nuclei that reach the stellar atmosphere is shown to depend on the magnetic field strength of the star.     

A self-similar solution for spherically symmetric gravitational collapse

A model of gas-dynamical flow during gravitational collapse is analyzed mathematically by assuming its spherical symmetry and self-similarity. A shock wave diverging from the center emerges in this model. The physical requirements imposed on the post-shock flow at the center for the specified parameters at infinity unambiguously determine the shock front and the flow behind it.     

Supersonic steady accretion of a rotating cold “Iron Gas” onto a neutron star after gravitational collapse

We analytically generalize the well-known solution of steady supersonic spherically symmetric gas accretion onto a star (Bondi 1952) for an iron atmosphere with completely degenerate electrons with an arbitrary degree of relativity. This solution is used for typical physical conditions in the vicinity of protoneutron stars produced by gravitational collapse with masses M ₀=(1.4?1.8)M _⊙ and over a wide range of nonzero “iron gas” densities at infinity, ρ_∞=(10⁴?5×10⁶)g cm^?3. Under these conditions, we determine all accretion parameters, including the accretion rate, whose value is ～(10?50)M _⊙s^?1 at M ₀=1.8M _⊙ (it is a factor of 1.7 lower for M ₀=1.4M _⊙, because the accretion rate is exactly ∝M ₀ ² ). We take into account the effect of accreting-gas rotation in a quasi-one-dimensional approximation, which has generally proved to be marginal with respect to the accretion rate.     

The role of a magnetic field in the formation of jet-like features in the crab nebula

The toroidal magnetic field frozen in the relativistic plasma ejected by pulsars must play a significant role in the formation of jet-like features observed in the central parts of plerions. We performed a semiquantitative analysis and calculations of the plasma flow in a plerion using the perturbation theory. We show that for the latitudinal magnetic-field distribution expected during the interaction of the pulsar wind with the interstellar medium, the magnetic field will have an appreciable effect on the flow primarily near the rotation axis. In the equatorial region, the effect of the magnetic field is negligible up to distances of 7r_sh.     

Effects of boundary conditions and viscous energy dissipation on carbon burning in thermonuclear supernova models

Based on a one-dimensional hydrodynamic model, we investigate carbon burning in a thermonuclear type-Ia supernova in the approximation of unsteady convection. The relatively broad range of convective parameters, 1×10^?3≤α_c≤2×10^?3, in which delayed detonation from the edge takes place was found to be preserved only for cases with a low boundary temperature at the presupernova stage, T _b ^(PS) = 6.4 × 10⁶ K, and with a high envelope mass, m_ex ? 2 × 10^?3M_⊙. In cases with a more realistic temperature, T _b ^(PS) = 2 × 10⁸ K, which corresponds to helium burning in the shell source, and with a lower mass m_ex, delayed detonation from the edge takes place only at α_c = 2 × 10^?3, while at α_c = 1 × 10^?3, numerous model pulsations occur during t?500 s. Artificial viscosity is shown to give a determining contribution to the increase in entropy in outer model shells, which is caused by the generation of weak shock waves during pulsations. We also show that the entropies calculated by two independent methods are equal.     

A nonlinear theory of stellar wind with allowance for the influence of relativistic particles

We solve the nonlinear problem of the dynamics of a steady-state, spherically symmetric stellar wind by taking into account particle acceleration to relativistic energies near the shock front. The particles are assumed to be accelerated through the Fermi mechanism, interacting with stellar-wind turbulence and crossing many times the shock front that separates the supersonic and subsonic stellar-wind regions. We take into account the influence of the accelerated particles on hydrodynamic plasma-flow parameters. Our method allows all hydrodynamic parameters of the shock front and plasma in the supersonic region to be determined in a self-consistent way and the accelerated-particle energy spectrum to be calculated. Our numerical and analytic calculations show that the plasma compression ratio at the shock front increases compared to the case where there are no relativistic particles and that the velocity profile in the supersonic region acquires a characteristic kink. The shape of the energy spectrum for the accelerated particles and their pressure near the front are essentially determined by the presumed dependence of the diffusion coefficient on particle energy, which, in turn, depends on the scale distribution of turbulent pulsations and other stellar-wind inhomogeneities.     

Studying the influence of turbulent mixing on thermonuclear burning regimes during X-ray bursts of neutron stars using the <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">ε</Emphasis></Subscript> model

We study the influence of turbulent mixing on the development of thermonuclear flashes in the surface layers of neutron stars. A simple K _ε model that includes various physical processes is used to describe the turbulent processes. In contrast to the widespread mixing-length theory, the K _ε model does not require using additional dimensional parameters, traces the development of turbulence in dynamics, describes the various turbulence development scenarios (gravitational and shear instabilities, convection, semiconvection, etc.) in a unified way, and can be used in multidimensional numerical simulations. Empirical constants of the model are chosen on the basis of experimental data and direct numerical simulations of typical processes. We have used the Era and Tigr-3T software packages to numerically simulate thermonuclear flashes in the accretion-renewable atmospheres of neutron stars. Turbulence is shown to accelerate significantly the transport of released energy to the stellar surface. Mixing equalizes the concentrations of matter components throughout the burning layer and increases the amount of matter involved in the thermonuclear burning during a flash.     

A two-dimensional hydrostatically equilibrium atmosphere of a neutron star with given differential rotation

An analytic solution has been found in the Roche approximation for the axially symmetric structure of a hydrostatically equilibrium atmosphere of a neutron star produced by collapse. A hydrodynamic (quasione-dimensional) model for the collapse of a rotating iron core in a massive star gives rise to a heterogeneous rotating protoneutron star with an extended atmosphere composed of matter from the outer part of the iron core with differential rotation (Imshennik and Nadyozhin, 1992). The equation of state of a completely degenerate iron gas with an arbitrary degree of relativity is taken for the atmospheric matter. We construct a family of toroidal model atmospheres with total masses M≈ 0.1?2M _⊙ and total angular momenta J≈(1?5.5)×⁴⁹ erg s, which are acceptable for the outer part of the collapsed iron core, in accordance with the hydrodynamic model, as a function of constant parameters ω₀ and r ₀ of the specified differential rotation law Ω=ω₀exp[?(rsinθ)²/r ₀ ² ] in spherical coordinates. The assumed rotation law is also qualitatively consistent with the hydrodynamic model for the collapse of an iron core.     

New generation mechanisms for X-ray quasi-periodic oscillations in accreting neutron stars

We propose three mechanisms for the generation of quasi-periodic oscillations (QPOs) in X-ray binaries. Two of them are based on an analogy with nonlinear oscillations of gaseous cavities in a fluid. The first mechanism, called magnetocavitation, implies that X-ray QPOs are produced by radial oscillations of the neutron-star magnetosphere interacting with accreted plasma. The photon-cavitation mechanism is considered when studying X-ray QPOs in neutron stars with critical (Eddington) luminosities. In this case, X-ray QPOs are generated by radial oscillations of photon cavities in the fully ionized hydrogen plasma that settles in the accretion column of a compact object. The mechanism according to which X-ray QPOs result from nonlinear oscillations of current sheets originating in accretion disks is suggested to explain QPOs in X-ray binaries with black holes and in cataclysmic variables. The calculated values of basic physical parameters of QPOs, such as the characteristic frequency, the dependences of QPO frequency and amplitude on X-ray flux, photon energy, and QPO lag time between photons at different energies are in good agreement with observational data.