22 research outputs found
Importance of Perturbed Gravitational Potentials in Differentially Rotating Newtonian Stars
It is usually believed that the Cowling approximation can give satisfactory
solutions if the stars %are highly compressible have soft equations of state
and/or if the strongly general relativistic stars are treated in the case of
rigid rotation. Since, however, there have been no systematic studies about the
accuracy of the Cowling approximation for differentially rotating compressible
stars, we investigate eigenfrequencies and eigenfunctions of the oscillation
modes in {\it rapidly} and {\it differentially} rotating compressible stars by
employing the exact method including full-perturbations and the Cowling
approximation.
We have found that the Cowling approximation for f-mode oscillations is not a
good approximation in rapidly and differentially rotating stars, although rapid
rotation makes this approximation better for rigidly rotating stars. This
result suggests that we must be careful when we apply the Cowling approximation
to differentially rotating stars even in the framework of general relativity.
On the other hand, the approximation will work well for r-modes even if the
star is rotating differentially. Therefore, the Cowling approximation can be
used as a strong tool for the investigation of r-mode oscillations in the
general relativistic framework that it is difficult to compute including the
perturbations of gravity.Comment: 7 pages, 10 figures, accepted to MNRA
Funnel-flow accretion onto highly magnetized neutron stars and shock generation
In this paper, we initiate a new study of steady funnel-flow accretion onto
strongly magnetized neutron stars, including a full treatment of shock
generation. As a first step, we adopt a simplified model considering the flow
within Newtonian theory and neglecting radiative pressure and cooling. The flow
is taken to start from an accretion disc and then to follow magnetic field
lines, forming a transonic funnel flow onto the magnetic poles. A standing
shock occurs at a certain point in the flow and beyond this material accretes
subsonically onto the star with high pressure and density. We calculate the
location of the standing shock and all other features of the flow within the
assumptions of our model. Applications to observed X-ray pulsars are discussed.Comment: 18 pages, 5 figs, accepted to Progress of Theoretical Physic
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