Acoustic modes of pulsating axion stars: Nonradial oscillations

We compute the lowest frequency nonradial oscillation modes of dilute axion stars. The effective potential that enters into the Schrödinger-like equation, several associated eigenfunctions and the large as well as the small frequency separations are shown as well.

NEUTRON STAR MATTER EQUATION OF STATE AND GRAVITATIONAL WAVE EMISSION

The EOS of strongly interacting matter at densities ten to fifteen orders of magnitude larger than the typical density of terrestrial macroscopic objects determines a number of neutron star properties, including the pattern of gravitational waves emitted following the excitation of nonradial oscillation modes. This paper reviews some of the approaches employed to model neutron star matter, as well as the prospects for obtaining new insights from the experimental study of gravitational waves emitted by neutron stars.

Forced Nonradial Oscillations in Early-Type Rotating Stars

A method of calculating nonradial oscillations in rotating stars is presented. Using this method, we are able to calculate the spectrum of g-, f- and p-mode eigenfunctions of a star for different stellar rotation speeds, and also the spectrum of rotational r modes. Stability of the modes as a function of stellar rotation speed can be investigated. By regarding the response of a star which undergoes periodic deformations due to the gravitational force of an orbiting companion as a forced nonradial oscillation, the problem of determining the eigenfrequencies of the star becomes one of finding resonances with the forcing potential. Expanding the potential of the orbiting (point mass) companion in terms of the usual spherical functions, the response of the star to each tidal term , with l and m fixed, can be calculated separately. By varying the forcing frequency σ we are then able to calculate the stellar spectrum. To calculate the response of the star we numerically solve the fully non-adiabatic, but linearised hydrodynamical equations for the star, in which the Coriolis forces due to stellar rotation are fully taken into account. To this end we utilise an implicit 2D finite difference scheme which solves the equations on an (r, ϑ) grid. A calculated solution describes the steady state in which the power σT due to the external driving force is in equilibrium with the internal damping. For results and more references see Witte & Savonije (1999).

CCD Studies of δ Scuti Stars in Open Clusters

Asteroseismology on δ Scuti stars has until now produced very few convincing results – if we aim at doing strong tests of details of stellar modelling. The main reason for the lack of success is probably that these stars often rotate, which split nonradial oscillation frequencies into many more frequencies. These many frequencies and the fact that the more evolved δ Scuti stars contain a strong chemical composition gradient at the edge of the convective core, produce a very complicated eigenfrequency spectrum. In contrast to this, we expect, in principle, seismological studies of δ Scuti stars to be a very simple task: One has to compare theoretical oscillations in model stars with the observed oscillations. However, in order to produce convincing asteroseismological results, we need to do three things: (1) Detect as many eigenfrequencies as possible at high precision, (2) identify the eigenmodes and (3) improve the theoretical models. By observing δ Scuti stars in open clusters using CCDs, we have a possibility to improve on (1) and (2) as well as providing an opening for an improvement in the theoretical models by doing accurate calibrations of the basic cluster properties. In this paper I shall describe some of the results from CCD studies of δ Scuti stars in open clusters and identify some future prospects for this technique.

Quadratic and Cubic Couplings of Oscillation Modes of Stars

The strength of nonlinear interactions of oscillation modes of stars is determined by the amplitudes as well as by the eigenfunctions of the oscillation modes. The intrinsic couplings of modes through their eigenfunctions can be described by coupling coefficients. Here, we concentrate on quadratic and cubic coupling coefficients that describe the nonlinear coupling of modes with itself and are called self-coupling coefficients.We considered radial and nonradial oscillation modes of polytropic models with degrees of central condensation that correspond to central condensations of main sequence stars to highly condensed evolved stars. We study the influence of the radial order and the degree of the oscillation mode on the self- coupling coefficients.

Discontinuity Modes in Polytropes

In the calculation of linear nonradial oscillation modes in composite polytropes with a small density discontinuity, a discontinuity mode may occur. This mode consists of a wave propagating along the discontinuity interface with a large amplitude that declines exponentially away from the interface. The period P of this mode is well-estimated (to within 10%) bywhere Δρ/<ρ> is the fractional density discontinuity and k is the horizontal wavenumber (c.f. Gabriel and Scuflaire 1980, in Nonradial and Nonlinear Stellar Pulsation, eds. H. Hill and W. Dziembowski, Springer-Verlag). For a 12 solar-mass polytrope with a radius of 4.27 R⊙, a 3% density discontinuity at fractional radius 0.15 produces a discontinuity mode with a period of 7.329 hours. As the density discontinuity increases the period P decreases, resulting in avoided crossings with the normal g-mode spectrum. Between these avoided crossings, the discontinuity mode has an unusually large amplitude at the location of the discontinuity.