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 $N = 0.5, 1.0$ and 1.5 for $m = 2, 3$ and 4 modes. Here $m$ is the rank of the spherical harmonics $Y_l^m$. 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