Stellar wind models with Alfvén waves

It is known that stellar winds from late type stars are of mixed thermal and magnetic origin. The stellar wind model presented in this work uses the hydrodynamic equations of mass and momentum conservation and closes the system of equations with a detailed energy equation. Both momentum and energy equations have terms due to the effects of Alfvén waves. A smooth transition between the two regimes for Alfvén wave propagation, the undamped and the damped modes, is achieved by considering the geometrical mean of both wave amplitudes. It will be shown that the initial push on the plasma is provided by the mechanical heating input, and that further out the Alfvén waves take over energetically.     

The emergence of a spherical magnetogasdynamic shock wave at the surface of a star

The propagation of a magnetogasdynamic shock wave originating in a stellar interior, is ocnsidered when it approaches the surfaces of the star. The flow behind the shock wave is assumed isothermal rather than adiabatic to stimulate the conditions of large radiative transfer near the stellar surface. The product solution of McVittie has been used to obtain exact solution of the problem. It has been obtained that velocity, density, pressure and magnetic field increases as we move from shock surface towards the nucleus of the star.     

The nth-order stellar hydrodynamic equation: transfer of comoving moments and pressures

The exact mathematical expression for an arbitrary n th-order stellar hydrodynamic equation is explicitly obtained depending on the central moments of the velocity distribution. In such a form the equations are physically meaningful, since they can be compared with the ordinary hydrodynamic equations of compressible, viscous fluids. The equations are deduced without any particular assumptions about symmetries, steadiness or particular kinematic behaviours, so that they can be used in their complete form, and for any order, in future works with improved observational data. Also, in order to work with a finite number of equations and unknowns, which would provide a dynamic model for the stellar system, the n th-order equation is needed to investigate in a more general way the closure conditions, which may be expressed in terms of velocity distribution statistics. A case example for a Schwarzschild distribution shows how the infinite hierarchy of hydrodynamic equations is reduced to the equations of orders   n = 0, 1, 2, 3  , owing to the recurrent form of the central moments and to the equations of order   n = 2  and 3, which become closure conditions for higher even- and odd-order equations, respectively. The closure example is generalized to a quadratic function in the peculiar velocities, so that the equivalence between moment equations and the system of equations that Chandrasekhar had obtained working from the collisionless Boltzmann equation is borne out.     

On the initial phase of interaction between expanding stellar envelopes and surrounding medium

The initial stages of deceleration in the circumstellar medium of a stellar envelope, thrown off by a shock wave, are investigated. The equations of spherical-symmetric adiabatic hydrodynamics are shown to have a similarity solution in the case of the density of the expanding envelope being approximated by a reasonable power law. The overall flow pattern has such a form that the stellar material is decelerated in the internal shock wave while another shock propagates through the circumstellar matter. Between the shocks there is a contact discontinuity separating the circumstellar and stellar matter. The characteristics of the similarity solution are calculated for various exponents in the density laws of an expanding envelope and circumstellar matter and for two values of the adiabatic index (=5/3, 4/3). Some parts of the flow exhibit Rayleigh-Taylor instability.Special attention is paid to the validity of the hydrodynamics. In full agreement with D'yachenkoet al. (1969), we conclude that the kinetic and collisionless processes are of great importance if the initial stages of stellar envelope deceleration are to be properly monitored.The results obtained can also be employed to describe the interaction between the exploding core of a red giant star and its rarefied envelope. This is of interest for explosive nucleosynthesis.The similarity solution is applied to the envelopes expelled both by type-II supernovae and by rapid novae. In particular, the thermalization time-scale of circumstellar plasma is estimated. For SNii this time-scale proves to be of the order of 60 yr. This confirms with the observational data on the moment of the maximum radio-emission of young SNRs. In the case of rapid novae, this time is less by a factor of 10. Therefore, the peak radio and X-ray (2 keV) lumnosity may occur several years after the rapid nova outburst. The explosion of a degenerate carbon core is found to result in the heating of the hydrogen-helium envelope of a red giant star up to 3×10⁶ K.     

The structure of a shock front in atomic hydrogen

We examine the problem of a shock wave propagating in a gravitational field in the presence of pressure and density gradients by attacking the non-linear equations of fluid flow. Our approach is analytical rather than numerical, and we analyze the characteristic equations of a fluid in the presence of gravity with radiative dissipation. Because the radiation field enters the fluid equations in the form of an integral, radiative dissipation may be considered an inhomogeneity which does not affect the characteristic directions. The fluid equations remain hyperbolic and thus are amenable to solution by the standard techniques of gas analysis.We give an equation of path for a shock wave and we enumerate the physical conditions which lead to stability or instability. We find that shock waves are generally unstable in most stellar atmospheres unless they are very weak. The form of the instability is that of a spicule deformation similar to that observed in the upper solar chromosphere.This work was carried out at the Smithsonian-Harvard Astrophysical Observatory and was presented in a thesis to Brandeis University, May 1963.     

Polygonal structures in a gaseous disk: Numerical simulations

The results of numerical simulations of a gaseous disk in the potential of a stellar spiral density wave are presented. The conditions under which straightened spiral arm segments (rows) form in the gas component are studied. These features of the spiral structure were identified in a series of works by A.D. Chernin with coauthors. Gas-dynamic simulations have been performed for a wide range of model parameters: the pitch angle of the spiral pattern, the amplitude of the stellar spiral density wave, the disk rotation speed, and the temperature of the gas component. The results of 2D- and 3D-disk simulations are compared. The rows in the numerical simulations are shown to be an essentially nonstationary phenomenon. A statistical analysis of the distribution of geometric parameters for spiral patterns with rows in the observed galaxies and the constructed hydrodynamic models shows good agreement. In particular, the numerical simulations and observations of galaxies give 〈α〉 }~ 120° for the average angles between straight segments.     

Analytical Solution for Stellar Density in Globular Clusters

In this paper, four parameters analytical solution will be established for the stellar density function in globular clusters. The solution could be used for any arbitrary order of outward decrease of the cluster’s density.     

Hydrodynamic equations of differentially rotating stellar systems and the velocity ellipsoid

Anisotropic hydrodynamic equations for differentially rotating collisionless stellar systems are derived. These equations can describe the evolution of the systems in a time span longer than their rotation periods.As a by-product of derivation of hydrodynamic equations, the well-known relation that the ratio of the principal axes of the velocity ellipse in a differentially rotating stellar disk is [B/(B-A)]^1/2 is re-found if the system is in a purely circular rotation, whereA andB are the Oort's constants. In addition, we find a systematic mean motion superposed on a purely circular differential rotation makes the directions of axes of the velocity ellipse deviate from the radial and the transverse direction. The observed deviation of directions of axes in our neighbourhood in the Galaxy can be explained if in the mean motion superposed on a purely circular differential rotatin the gas of stars near us is compressed in the radial direction or rarefied in the transverse directions, with irregularities of the order of 5 km/sec in amplitude of velocity and 1 kpc in size. These magnitudes of irregularities agree with those actually observed or with those anticipated from other theoretical considerations.     

Strong spherical magnetogasdynamic shock with radiation near the surface of a star

The propagation of a shock-wave, originating in a stellar interior, is considered when it approaches the surface of the star. The flow behind the magnetogasdynamic shock wave is assumed to be spatially isothermal rather than adiabatic to stimulate the conditions of large radiative transfer near the stellar surface. The exact shock-propagation laws obtained by solving the equations in similarity variables, for different values of the parameter δ in the undisturbed density law, ρ₀ ∝ γ^δ     

Equatorially trapped Rossby waves in radiative stars

Observations by recent space missions reported the detection of Rossby waves (r-modes) in light curves of many stars (mostly A, B, and F spectral types) with outer radiative envelope. This article aims to study the theoretical dynamics of Rossby-type waves in such stars. Hydrodynamic equations in a rotating frame were split into horizontal and vertical parts connected by a separation constant (or an equivalent depth). Vertical equations were solved analytically for a linear temperature profile and the equivalent depth was derived through free surface boundary condition. It is found that the vertical modes are concentrated in the near-surface layer with a thickness of several tens of surface density scale height. Then with the equivalent width, horizontal structure equations were solved, and the corresponding dispersion relation for Rossby, Rossby-gravity, and inertia-gravity waves was obtained. The solutions were found to be confined around the equator, leading to the equatorially trapped waves. It was shown that the wave frequency depends on the vertical temperature gradient as well as on stellar rotation. Therefore, observations of wave frequency in light curves of stars with known parameters (radius, surface gravity, rotation period) could be used to estimate the temperature gradient in stellar outer layers. Consequently, the Rossby mode may be considered as an additional tool in asteroseismology apart from acoustic and gravity modes.     

A solution of linearized Einstein field equations in vacuum used for the detection of the stochastic background of gravitational waves

A solution of linearized Einstein field equations in vacuum is given and discussed. First it is shown that, computing from our particular metric the linearized connections, the linearized Riemann tensor and the linearized Ricci tensor, the linearized Ricci tensor results equal to zero. Then the effect on test masses of our solution, which is a gravitational wave, is discussed. In our solution test masses have an apparent motion in the direction of propagation of the wave, while in the transverse direction they appear at rest. In this way it is possible to think that gravitational waves would be longitudinal waves, but, from careful investigation of this solution, it is shown that the tidal forces associated with gravitational waves act along the directions orthogonal to the direction of propagation of waves. The computation is first made in the long wavelengths approximation (wavelength much larger than the linear distances between test masses), then the analysis is generalized to all gravitational waves.

In the last sections of this paper it is shown that the frequency dependent angular pattern of interferometers can be obtained from our solution and the total signal seen from an interferometer for the stochastic background of gravitational waves is computed.     

Modeling the emission of an H II region containing a bubble-like structure

The influence of a bubble-like structure around a starburst within the H II regions on the shape of the ionizing spectrum and the generation of the observed emission lines was studied using multicomponent photoionization modeling. The distributions of density and other physical parameters in such bubble-like structures were determined by Weaver et al. in 1977. The first two components represent the region of the stellar wind from the central starburst region. The gas density and electron temperature distributions in these components were described by the solution of the system of equations of continuity and energy transfer with account for the heat conductivity. The third component represents a thin layer of gas with a high density that emerges due to the passage of a normal shock wave of the stellar wind. The fourth component represents a “typical” H II region. The ionizing radiation spectra were set from the calculated evolutionary models whose free parameters determine the physical conditions within the “bubble.” The influence of the stellar wind bubble on the shape of the ionizing radiation spectrum and the generation of fluxes in important emission lines was analyzed.     

The appropriate dyadic applicable to the lower region of the ionospheric plasma

An expression for the susceptibility dyadic appropriate to the lower regions of the atmospheric plasma is derived using Maxwell's field equations and the equation of conservation of momentum. The contributions due to viscous effect and convection current density are incorporated in the physical processes within the stated medium. Utilizing the approximation of linearized equations, second order coupled wave equations have been derived through the dyadic.     

Alfvén-magnetosonic waves interaction in the solar corona

The nonlinear propagation of the Alfvén and magnetosonic waves in the solar corona is investigated in terms of model equations. Due to viscous effects taken into account the propagation of the fast wave itself is governed by Burgers type equations possessing both expansion and compression shock solutions. Numerical simulations show that both parallely and perpendicularly propagating fast waves can steepen into shocks if their amplitudes are in excess of some sizeable fraction of the Alfvén velocity. However, if the magnetic field changes linearly in the perpendicular direction, then formation of perpendicular shocks can be hindered. The Alfvén waves exhibit a tendency to drive both the slow and fast magnetosonic waves whose propagation is described by linearized Boussinesq type equations with ponderomotive terms due to the Alfvén wave. The limits of the slow and fast waves are investigated.     

Interplanetary disturbances in the solar wind produced by density,temperature, or velocity pulses at 0.08 AU

Time-dependent solutions of a one-fluid model of the interplanetary medium are investigated. This set of unsteady hydrodynamic equations has been written in conservation form in order to apply the Lax-Wendroff method for the solution of this problem. The initial disturbance is specified by a pulse at 0.08 AU (astronomical units). Physically, this pulse can be interpreted as having been caused by a solar flare, surge, or any other solar disturbance. The equilibrium condition is determined to be the steady solution of the governing equations and represents the quiet solar wind. The results are presented in terms of density, temperature, and velocity profiles of the interplanetary gas flow at heliocentric distances up to 6 AU at several times. Also, the trajectories of disturbances for various initial pulses are shown. Finally, we have used some June 1972 interplanetary observational data to compare with these theoretical calculations. On the basis of these results, the effects of solar disturbances on the interplanetary environment (such as the generation of large non-linear wave trains in the shocks' wakes) can be inferred.     

非平衡动力学中恒星结构稳定性研究

采用非平衡动力学方法研究由CNO循环决定的恒星结构稳定性,本文得出:CNO循环自身是稳定的;扩散效应不会改变处于稳定的恒星结构稳定性;对流效应对其稳定性有重要影响,波数小的扰动更容易激发不稳定性;巨大的温度梯度也能激发不稳定性。本文给出了稳定性条件和恒星结构保持稳定所允许的最小扰动波数。     

Stellar wind for non-negligible gravitational potential of the atmosphere

We consider a spherically symmetric, isothermal and stationary stellar atmosphere whose gravitational potential cannot be neglected. If , the ratio of the density on the base of the corona to the mean density of the star is not zero, the density vanishes at infinity for any solution of the hydrodynamic equations. We deduce the maximum mass loss depending on two dimensionless parameters, the ratio of the gravitational to the thermal energy and . This mass loss has itself a maximum for =1/3.     

Self-similar expansion of white dwarfs

Properties of plasma expansion that propagates in an electron-positron-ion dense plasma are investigated. Suitable hydrodynamic equations for the ions and ultrarelativistic degenerate electrons and positrons are used. Using self-similar transformation, the basic set of nonlinear equations is solved numerically. Typical values of white dwarf stars are used to estimate the behavior of the ion number density and ion fluid velocity. The positive ions are found to initially slowly escape with high velocity when the ion-to-electron density ratio increases. For higher values of the electron number density, the self-similar solution validity domain decreases. The relevance of the results to white dwarf expansion and collapse is highlight.     

Relativistic hydrodynamics of a free expansion and a shock wave in one-dimension

Dynamical evolution of a relativistic explosion resulting from a large amount of energy release in a homogenous medium is studied using the Khalatnikov equation describing relativistic, hydrodynamic, planar flow. The early phase of the explosion is idealized to two stages: a free expansion and a shock wave stage. By the hodograph transformation inverting the dependent and independent variables, the hydrodynamic equations for the relativistic flow are reduced to second-order linear equations in a velocity-enthalpy space and they are solved by the method of Laplace transformation. The propagation laws and flow structures of the relativistic expansion are obtained at each stage. In the free expansion stage, the flow with a sufficiently high sound velocity forms a thin shell of the energy density in the comoving frame at the front and accelerates the front. In the shock wave stage, the Lorentz factor of the shock front decreases logarithmically with time. The transition time from a free expansion to a shock wave stage suggests that the super-light expansion observed in extragalactic radio sources has no spherical geometry but must be confined to a narrow cone.