9 research outputs found
Non-axisymmetric oscillations of rapidly rotating relativistic stars by conformal flatness approximation
We present a new numerical code to compute non-axisymmetric eigenmodes of
rapidly rotating relativistic stars by adopting spatially conformally flat
approximation of general relativity. The approximation suppresses the radiative
degree of freedom of relativistic gravity and the field equations are cast into
a set of elliptic equations. The code is tested against the low-order f- and
p-modes of slowly rotating stars for which a good agreement is observed in
frequencies computed by our new code and those computed by the full theory.
Entire sequences of the low order counter-rotating f-modes are computed, which
are susceptible to an instability driven by gravitational radiation.Comment: 3 figures. To appear in Phys.Rev.
R-mode oscillations of differentially and rapidly rotating Newtonian polytropic stars
For the analysis of the r-mode oscillation of hot young neutron stars, it is
necessary to consider the effect of it differential rotation, because viscosity
is not strong enough for differentially rotating young neutron stars to be lead
to uniformly rotating configurations on a very short time scale after their
birth. In this paper, we have developed a numerical scheme to solve r-mode
oscillations of differentially rotating polytropic inviscid stars. This is the
extended version of the method which was applied to compute r-mode oscillations
of uniformly rotating Newtonian polytropic stars. By using this new method, we
have succeeded in obtaining eigenvalues and eigenfunctions of r-mode
oscillations of differentially rotating polytropic stars. Our numerical results
show that as the degree of differential rotation is increased, it becomes more
difficult to solve r-mode oscillations for slightly deformed configurations
from sphere compared to solving r-mode oscillations of considerably deformed
stars. One reason for it seems that for slightly deformed stars corotation
points appear near the surface region if the degree of differential rotation is
strong enough. This is similar to the situation that the perturbational
approach of r-mode oscillations for it slowly rotating stars in general
relativity results in a singular eigenvalue problem.Comment: including 7 figures. submitted to PR
R-mode oscillations of rapidly rotating Newtonian stars - A new numerical scheme and its application to the spin evolution of neutron stars
We have developed a new numerical scheme to solve r-mode oscillations of {\it
rapidly rotating polytropic stars} in Newtonian gravity. In this scheme, Euler
perturbations of the density, three components of the velocity are treated as
four unknown quantities together with the oscillation frequency. For the basic
equations of oscillations, the compatibility equations are used instead of the
linearized equations of motion.
By using this scheme, we have solved the classical r-mode oscillations of
rotational equilibrium sequences of polytropes with the polytropic indices and 1.5 for and 4 modes. Here is the rank of the
spherical harmonics . These results have been applied to investigate
evolution of uniformly rotating hot young neutron stars by considering the
effect of gravitational radiation and viscosity. We have found that the maximum
angular velocities of neutron stars are around 10-20% of the Keplerian angular
velocity irrespective of the softness of matter. This confirms the results
obtained from the analysis of r-modes with the slow rotation approximation
employed by many authors.Comment: LaTeX 12 pages with 19 figures, to be published in PR