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We consider the stability of a planar accelerating shock front in an exponential atmosphere, a situation that can be described by a self-similar solution. A previous linear instability analysis showed that there are three regimes, depending on the wavelength of the perturbation along the direction of the shock front: at long wavelengths the shock is unstable, at intermediate wavelengths it is overstable, and at short wavelenghts it is stable, where the characteristic length is set by the initial density scale height. We have carried out numerical simulations of such an accelerating shock front and have confirmed the results of the semianalytic linear analysis in the linear regime. In the nonlinear regime, the evolution again depends on the three wavelength domains. At long wavelengths, the instability continuously grows but the flow remains smooth, and at short wavelengths, the flow is stable. The intermediate wavelength, overstable regime shows more complex evolution. The growing linear oscillations saturate soon after entering the nonlinear regime and the oscillations continue with the same approximate period. The shock front develops moving points of intersection, which generate weak shock fronts and density and pressure structure in the immediate postshock flow. The density fluctuations, with a contrast of a factor of 2-3, become frozen into the downstream flow. The growth of the instability is slow, so substantial initial perturbations are needed; thesemay be present in Type II supernovae with red supergiant progenitor stars which have outer convective regions. The clumping in the outer supernova atmosphere may affect spectral line formation and may play a role in the formation of fast knots.

As in the case of the solar wind, the magnetic field in the wind from a magnetized, rotating star becomes increasingly toroidal with distance from the star. The strength of the magnetic field can be characterized by sigma, the ratio of toroidal magnetic energy density to kinetic energy density in the equatorial plane of the wind. A fast wind shocks against the external medium and creates a bubble whose volume is dominated by shocked gas. The toroidal magnetic field increases in the shocked bubble and can dominate the thermal pressure. Because of the low velocities in the bubble, hydrostatic equilibrium is a good approximation and allows the calculation of the thermal and magnetic pressure in the bubble, as in the model of Begelman and Li (1992) for the Crab Nebula. The structure, which is axisymmetric and extended in the polar direction, depends on two parameters: sigma nu(sub w)/w(sub 0), where nu(sub w) is the wind velocity and w(sub 0) is the shell velocity in the polar direction, and lambda = nu(sub a)/w(sub 0), where nu(sub a) is the velocity of the slow wind. For small values of lambda, there is a cusp in the shell in the equatorial plane, i.e., there is an equatorial ring. For larger values of lambda, the maximum of the surface density moves away from the equator i.e., a double ring structure. Our models should apply to planetary nebulae, if their central stars are sufficiently magnetized; the calculated shapes do resemble the observed shapes of planetaries. In all cases, our model predicts that X-ray emission from the bubble is concentrated toward the polar axis. Finally, we briefly discuss the asymmetry of the Crab Nebula and 3C 58.

The steady state structure and linear stability of spherical accretion flows onto compact objects are investigated over a wide range of accretion rates (ARs) for a variety of cooling functions as a function of the ratio of specific heats (gamma). Both radial and nonradial shock perturbations are considered. The flows become more extended as AR decreases. The cooling function has a significant effect on the extended structure of settling solutions with gamma = 5/3. In contrast, the extended structure of settling solutions with gamma = 4/3 is nearly independent of the form of the cooling function. For both gamma = 4.3 and gamma = 5.3, radial shock oscillation in the fundamental and first overtone modes are destabilized in spherically extended accretion envelopes. The application of these results to postsupernova neutron star accretion flows and to luminosity oscillations in AM Her objects are discussed.

An initial study aimed at elucidating the multidimensional aspects of the hydrodynamic instabilities in supernova remnants is presented. Self-similar solutions are found to exist for the interaction of a steep power-law density profile expanding into a relatively flat stationary power-law density profile. Consideration of the pressure and entropy profiles in the shocked 1D flows shows that the flows are subject to convective instability, by a local criterion. The growth rate for the instability becomes very large near the contact discontinuity between the two shocked regions. A linear analysis of the complete self-similar solutions shows that the solutions are unstable above a critical wavenumber and that the growth rate is greatest at the position of the contact discontinuity. The X-ray image of the remnant of SN 1572 (Tycho) shows emission from clumps of supernova ejecta, which is good evidence for instabilities in this remnant.

The present study of hypercritical accretion flows onto neutron stars considers steady-state, spherically symmetric flows whose accretion rate range is characterized by the carrying away of gravitational-accretion energy by neutrinos. The models used encompass pair production, radiation diffusion, and general relativistic effects. While pair pressure dominates throughout the accretion envelope when accretion rates above about 100 solar masses/yr, radiation diffusion becomes important when the accretion rate falls below about 0.001 solar masses/yr. At the lower accretion rates, free fall toward the neutron-star surface stops and an extended, quasi-static, radiation pressure-supported envelope emerges which is probably dynamically unstable.

The spherical collapse of a gas cloud initially in hydrostatic equilibrium is examined using self-similar solutions. It is found that the collapse of gas clouds to form galaxies can occur on a hydrodynamic time scale only if the gas dominates the gravitational field and the inflow forms a central dominant mass. The likelihood of a collisionless component and the observation of extended mass distributions in galaxies implies that the collapse of a hot protogalactic cloud is cooling-regulated. The formation of the Galaxy from an initially smooth, hot cloud is examined, showing that some nonlinear substructure must initially be present.

This paper examines the interaction of a massive star supernova with the shell created by the fast wind from a blue supergiant, either in the main-sequence phase or in a late evolutionary phase. Making a number of idealizations, the general features of shell interaction are described by semianalytical solutions. The expected properties of the supernova and its environment are discussed, and the hydrodynamics of the interaction is described. It is found that, typically, the shock traversal occurs before the energy transfer is significant. Applications of the model to observed objects are considered, with special attention given to the interaction of SN 1987A with its circumstellar shell, which is expected to occur within decades.

The observed properties of pulsars are modeled on the assumption that they evolve by emitting magnetic dipole radiation and have exponentially decaying magnetic fields. The models are constructed by using Monte Carlo techniques to generate a Galactic sample of pulsars having particular distributions of initial periods, magnetic dipole moments, and positions. By choosing a relationship between the radio luminosity L(r), the period (P), and the P derivative, it is determined which pulsars of the generated sample could be detected by one of the major pulsar surveys. Detailed account is taken of known selection effects in these surveys. Models in which the size of the pulsar emission cone is dependent on the period are considered. The properties of the detectable pulsars are compared with the properties of the observed pulsars, and the initial distributions and luminosity relation of the model are adjusted until a satisfactory agreement is obtained. A crucial point is that the observed relation between L(r) and P, P derivative is affected by selection effects and does not apply to the actual pulsar population. It is found that the best fits are obtained with models in which the pulsars are injected with relatively long periods, about 0.5 sec.

Monte Carlo techniques are used to study the energy deposition of gamma rays from the radioactive decay of Co-56 in Type Ib and Type II SN. It is found that above an electron fraction of about 0.1, direct excitations are negligible, and the line emission arises from thermal processes. The results indicate that the emission is dominated by neutral and singly ionized lines, including forbiden O I, forbidden Ca II, forbidden C I, and forbidden Si I. The late spectrum is shown to be useful as a diagnostic of the nucleosynthetic structure of the ejecta. The present model has been applied to observations of the Type Ib SN 1985F, and it is suggested that Type Ib SN come from stars of greater than 25 solar masses.

Analytic models for the spherically symmetric expansion of SN 1987 A are discussed. The SN model includes a bend in the expanded density profiles at a velocity of about 4000 km/s and employs an asymmetric initial density distribution or energy deposition on the assumption of radial flow. The calculations show that there is a tendency for the flow to become more spherical during the expansion phase, and that the sense of density asymmetry changes across the bend in the density profile.

Self-similar solutions are presented for the idealized case of a spherical galaxy with a singular isothermal gravitational potential where the ISM is built up from mass loss by stars or by accretion of external gas. For the former case, where a galaxy initially devoid of gas obtains gas from stellar evolution, steady flow only is obtained inside the cooling radius. Several possibilities occur and are discussed for flow outside the cooling radius. For the case involving infall of external gas, the nature of the flow depends on the initial density of the infalling gas. At high density, only a cold, unshocked flow is possible. At low density, the flow is accelerated inward, is heated in a shock front, approaches a hydrostatic state, passes through the cooling radius and enters a steady subsonic cooling flow, and finally passes through a sonic point. The effects of radiative cooling are discussed.

A full evolutionary calculation of ion abundances and radiative cooling has been incorporated into an accurate one-dimensional gasdynamics calculation in order to investigate the dynamics of radiative shock instability and to determine the extent to which power-law cooling models describe the situation. Radiative shocks are shown to be unstable for velocities of greater than about 140 km/s. The temperature dependence of cooling functions behind steady shocks suggests that the stability limit may depend upon the amplitude of the perturbation. Oscillation is noted in the fundamental oscillation mode.

The time-dependent behavior of a shocked spherically symmetric relativistic fluid with tangential magnetic field is investigated, considering the case where the boundaries of the shocked fluid move at constant velocity so that self-similar solutions exist. The behavior of the fluid in the ultrarelativistic regime is compared to that in the nonrelativistic regime; there is a smooth transition between these limits. If a magnetic field is present, the magnetic pressure becomes increasingly important with distance from the shock wave; the gas pressure vanishes at the contact discontinuity that bounds the flow. Analytic expressions are given which describe the flow. The solutions can be applied to the evolution of shocked relativistic pulsar winds, which are probably observed as Crab-like supernova remnants. A model for the Crab Nebula, based on the steady-state model of Kennel and Coroniti (1984), indicates that sigma = 0.0016, where sigma is twice the ratio of magnetic to particle energy in the wind as measured in the fluid frame. This is about half the value suggested by Kennel and Coroniti and is much smaller than the value that might be expected for a pulsar wind.

The evolution of a cooling flow from an initial state of hydrostatic equilibrium in a cluster of galaxies is investigated. After gas mass and energy are injected into the cluster at an early phase, the gas approaches hydrostatic equilibrium over most of the cluster and cooling becomes important in the dense central regions. As time passes, cooling strongly affects an increasing amount of gas. The effects of mass removal from the flow, the inclusion of magnetic or cosmic-ray pressure, and heat conduction are considered individually.