James R. Ipser

The oscillations of rapidly rotating Newtonian stellar models. II - Dissipative effects

A method is described for determining the dissipative effects of viscosity and gravitational radiation on the modes of rapidly rotating Newtonian stellar models. Integral formulae for the dissipative imaginary parts of the frequencies (i.e., the damping or growth times) of these modes are derived. These expressions are evaluated numerically to determine the angular-velocity dependence of these dissipative effects on the l = m f-modes of uniformly rotating polytropes. The importance of the gravitational-radiation driven secular instability in limiting the rotation rate of neutron stars is estimated using these results. 13 refs.

Phase-space structure of cold dark matter halos

Abstract We discuss the extent to which the phase-space distribution of cold dark matter particles is thermalized in a galactic halo and find that there are large deviations from a thermal distribution in that the highest energy particles have discrete values of velocity. The central values and intensities of the corresponding peaks provide detailed information on the history of the Galaxy. This information becomes immediately available if a signal is found in a cavity detector of galactic halo axions.

The oscillations of rapidly rotating Newtonian stellar models

A method is described for solving the equations that govern the oscillations of rapidly rotating inhomogeneous Newtonian stellar models. A covariant reformulation of the general pulsation equations is presented, which reduces them to a single scalar equation for a single potential. From this potential, all of the properties of the normal mode may be deduced. The techniques developed to solve this complicated eigenvalue problem numerically are described, and solutions to this equation are presented for the l = m f-modes of rigidly rotating stellar models having polytropic equations of state. 26 refs.

Maximum mass of a uniformly rotating neutron star

The effect of rapid uniform rotation on the upper mass limit for neutron stars is studied under the assumption that the equation of state is subject to only a minimal set of physical constraints. For given ranges of the energy condition, microstability constraint, and causality constraint, the maximum mass of a uniformly rotating neutron star is about 24-25 percent greater than the corresponding nonrotating maximum mass. The obtained value is compared with that of the maximum mass of uniformly rotating configurations associated with the stiffest of the equations of state proposed for actual neutron-star matter. Rotation increases the upper limit on baryon mass by only about 20 percent, while the limiting moment of inertia is about twice its value for the nonrotating case. Upper limits are also found for the frequency of rotation, the frequency of frame dragging, and the maximum polar and equatorial redshifts. Discarding the causality constraint would allow the upper mass limit to increase by a given value. 16 references.

On the pulsations of relativistic accretion disks and rotating stars - The Cowling approximation

It is shown that the hydrodynamic degrees of the adiabatic pulsations of relativistic fluids (e.g., accretion disks or rotating stars) can be described by a single scalar potential. When the gravitational perturbations are neglected, the Cowling approximation, this potential is determined by a second-order (typically elliptic) partial differential equation. A variational principle is developed from which the pulsation frequencies may be evaluated in this approximation. For objects like accretion disks in which self-gravitational effects are negligible, this approximation becomes an exact description of the pulsations

Rapidly rotating relativistic stars

Within the last decade, significant progress has been made in modelling rotating stars in general relativity and in relating observable properties to the equation of state of matter at high density. A formalism describing rotating perfect fluids is presented and numerical models of neutron stars are briefly discussed, with emphasis on upper limits on mass and rotation. The equations governing small oscillations are reviewed, and a variational principle appropriate both to eulerian and lagrangian perturbations is obtained. This extends to relativity an eulerian principle used to find non-axisymmetric stability points for perfect fluids. A related eulerian approach has been recently used to obtain normal modes of rotating newtonian stars. The review concludes with an outline of this work and of the two types of instability that can restrict the range of neutron stars. In particular, current work shows that several kinds of effective viscosity limit the possible role of a non-axisymmetric instability driven by gravitational waves.

Generalizedr-modes of the Maclaurin spheroids

Analytical solutions are presented for a class of generalized r-modes of rigidly rotating uniform density stars—the Maclaurin spheroids—with arbitrary values of the angular velocity. Our analysis is based on the work of Bryan; however, we derive the solutions using slightly different coordinates that give purely real representations of the r-modes. The class of generalized r-modes is much larger than the previously studied “classical” r-modes. In particular, for each l and m we find l−m (or l−1 for the m = 0 case) distinct r-modes. Many of these previously unstudied r-modes (about 30% of those examined) are subject to a secular instability DRIVEN by gravitational radiation. The eigenfunctions of the “classical” r-modes, the l = m+1 case here, are found to have particularly simple analytical representations. These r-modes provide an interesting mathematical example of solutions to a hyperbolic eigenvalue problem.

On the adiabatic pulsations of accretion disks and rotating stars

The adiabatic pulsations of rotating Newtonian fluids, including nonbarotropic configurations, are represented completely in terms of two scalar potentials. The second-order equations that determine these potentials are more convenient to solve numerically than the standard Lagrangian-displacement form of the equations. A variational principle is derived for these equations from which estimates of the frequencies of the modes may be obtained. This analysis generalizes previous work by describing the adiabatic pulsations of fluids having any (including nonbarotropic) equation of state, any (including differential) rotation law, and self-gravitation.

Relativistic stellar pulsations with near-zone boundary conditions

A new method is presented here for evaluating approximately the pulsation modes of relativistic stellar models. This approximation relies on the fact that gravitational radiation influences these modes only on time scales that are much longer than the basic hydrodynamic time scale of the system. This makes it possible to impose the boundary conditions on the gravitational potentials at the surface of the star rather than in the asymptotic wave zone of the gravitational field. This approximation is tested here by predicting the frequencies of the outgoing nonradial hydrodynamic modes of nonrotating stars. The real parts of the frequencies are determined with an accuracy that is better than our knowledge of the exact frequencies (about

Low-Frequency Oscillations of Relativistic Accretion Disks

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