8 research outputs found
r-modes in Relativistic Superfluid Stars
We discuss the modal properties of the -modes of relativistic superfluid
neutron stars, taking account of the entrainment effects between superfluids.
In this paper, the neutron stars are assumed to be filled with neutron and
proton superfluids and the strength of the entrainment effects between the
superfluids are represented by a single parameter . We find that the
basic properties of the -modes in a relativistic superfluid star are very
similar to those found for a Newtonian superfluid star. The -modes of a
relativistic superfluid star are split into two families, ordinary fluid-like
-modes (-mode) and superfluid-like -modes (-mode). The two
superfluids counter-move for the -modes, while they co-move for the
-modes. For the -modes, the quantity is
almost independent of the entrainment parameter , where and
are the azimuthal wave number and the oscillation frequency observed by an
inertial observer at spatial infinity, respectively. For the -modes, on
the other hand, almost linearly increases with increasing . It
is also found that the radiation driven instability due to the -modes is
much weaker than that of the -modes because the matter current associated
with the axial parity perturbations almost completely vanishes.Comment: 14 pages, 4 figures. To appear in Physical Review
R-mode Instability of Slowly Rotating Non-isentropic Relativistic Stars
We investigate properties of -mode instability in slowly rotating
relativistic polytropes. Inside the star slow rotation and low frequency
formalism that was mainly developed by Kojima is employed to study axial
oscillations restored by Coriolis force. At the stellar surface, in order to
take account of gravitational radiation reaction effect, we use a near-zone
boundary condition instead of the usually imposed boundary condition for
asymptotically flat spacetime. Due to the boundary condition, complex
frequencies whose imaginary part represents secular instability are obtained
for discrete -mode oscillations in some polytropic models. It is found that
such discrete -mode solutions can be obtained only for some restricted
polytropic models. Basic properties of the solutions are similar to those
obtained by imposing the boundary condition for asymptotically flat spacetime.
Our results suggest that existence of a continuous part of spectrum cannot be
avoided even when its frequency becomes complex due to the emission of
gravitational radiation.Comment: 10 pages, 4 figures, accepted for publlication in PR
The rotational modes of relativistic stars: Numerical results
We study the inertial modes of slowly rotating, fully relativistic compact
stars. The equations that govern perturbations of both barotropic and
non-barotropic models are discussed, but we present numerical results only for
the barotropic case. For barotropic stars all inertial modes are a hybrid
mixture of axial and polar perturbations. We use a spectral method to solve for
such modes of various polytropic models. Our main attention is on modes that
can be driven unstable by the emission of gravitational waves. Hence, we
calculate the gravitational-wave growth timescale for these unstable modes and
compare the results to previous estimates obtained in Newtonian gravity (i.e.
using post-Newtonian radiation formulas). We find that the inertial modes are
slightly stabilized by relativistic effects, but that previous conclusions
concerning eg. the unstable r-modes remain essentially unaltered when the
problem is studied in full general relativity.Comment: RevTeX, 29 pages, 31 eps figure
Physical interpretation of gauge invariant perturbations of spherically symmetric space-times
By calculating the Newman-Penrose Weyl tensor components of a perturbed
spherically symmetric space-time with respect to invariantly defined classes of
null tetrads, we give a physical interpretation, in terms of gravitational
radiation, of odd parity gauge invariant metric perturbations. We point out how
these gauge invariants may be used in setting boundary and/or initial
conditions in perturbation theory.Comment: 6 pages. To appear in PR
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