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Shijun Yoshida

Publications and source records attributed to Shijun Yoshida.

50 records · Page 3Linked to original sources
arXiv2003

r-modes in Relativistic Superfluid Stars

We discuss the modal properties of the $r$-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 $η$. We find that the basic properties of the $r$-modes in a relativistic superfluid star are very similar to those found for a Newtonian superfluid star. The $r$-modes of a relativistic superfluid star are split into two families, ordinary fluid-like $r$-modes ($r^o$-mode) and superfluid-like $r$-modes ($r^s$-mode). The two superfluids counter-move for the $r^s$-modes, while they co-move for the $r^o$-modes. For the $r^o$-modes, the quantity $κ\equivσ/Ω+m$ is almost independent of the entrainment parameter $η$, where $m$ and $σ$ are the azimuthal wave number and the oscillation frequency observed by an inertial observer at spatial infinity, respectively. For the $r^s$-modes, on the other hand, $κ$ almost linearly increases with increasing $η$. It is also found that the radiation driven instability due to the $r^s$-modes is much weaker than that of the $r^o$-modes because the matter current associated with the axial parity perturbations almost completely vanishes.

gr-qc↗
arXiv2002

R-modes of neutron stars with the superfluid core

We investigate the modal properties of the $r$-modes of rotating neutron stars with the core filled with neutron and proton superfluids, taking account of entrainment effects between the superfluids. The stability of the $r$-modes against gravitational radiation reaction is also examined considering viscous dissipation due to shear and a damping mechanism called mutual friction between the superfluids in the core. We find the $r$-modes in the superfluid core are split into ordinary $r$-modes and superfluid $r$-modes, which we call, respectively, $r^o$- and $r^s$-modes. The two superfluids in the core flow together for the $r^o$-modes, while they counter-move for the $r^s$-modes. For the $r^o$-modes, the coefficient $κ_0\equiv\lim_{Ω\to 0}ω/Ω$ is equal to $2m/[l^\prime(l^\prime+1)]$, almost independent of the parameter $η$ that parameterizes the entrainment effects between the superfluids, where $Ω$ is the angular frequency of rotation, $ω$ the oscillation frequency observed in the corotating frame of the star, and $l^\prime$ and $m$ are the indices of the spherical harmonic function representing the angular dependence of the $r$-modes. For the $r^s$-modes, on the other hand, $κ_0$ is equal to $2m/[l^\prime(l^\prime+1)]$ at $η=0$ (no entrainment), and it almost linearly increases as $η$ is increased from $η=0$. The mutual friction in the superfluid core is found ineffective to stabilize the $r$-mode instability caused by the $r^o$-mode except in a few narrow regions of $η$. The $r$-mode instability caused by the $r^s$-modes, on the other hand, is extremely weak and easily damped by dissipative processes in the star.

astro-ph↗
arXiv2002

Nonradial Oscillations of Neutron Stars with a Solid Crust -- Analysis in the Relativistic Cowling Approximation--

Nonradial oscillations of relativistic neutron stars with a solid crust are computed in the relativistic Cowling approximation, in which all metric perturbations are ignored. For the modal analysis, we employ three-component relativistic neutron star models with a solid crust, a fluid core, and a fluid ocean. As a measure for the relativistic effects on the oscillation modes, we calculate the relative frequency difference defined as $δσ/σ\equiv(σ_{GR}-σ_N)/σ_{GR}$, where $σ_{GR}$ and $σ_R$ are, respectively, the relativistic and the Newtonian oscillation frequencies. The relative difference $δσ/σ$ takes various values for different oscillation modes of the neutron star model, and the value of $δσ/σ$ for a given mode depends on the physical properties of the models. We find that $|δσ/σ|$ is less than $\sim0.1$ for most of the oscillation modes we calculate, although there are a few exceptions such as the fundamental (nodeless) toroidal torsional modes in the crust, the surface gravity modes confined in the surface ocean, and the core gravity modes trapped in the fluid core. We also find that the modal properties, represented by the eigenfunctions, are not strongly affected by introducing general relativity. It is however shown that the mode characters of the two interfacial modes, associated with the core/crust and crust/ocean interfaces, have been interchanged between the two through an avoided crossing when we move from Newtonian dynamics to general relativistic dynamics.

astro-ph↗
arXiv2001

Relativistic r-modes in Slowly Rotating Neutron Stars: Numerical Analysis in the Cowling Approximation

We investigate the properties of relativistic $r$-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the influence of the Coriolis like force on the stellar oscillations, but ignore the effects of the centrifugal like force. For three neutron star models, we calculated the fundamental $r$-modes with $l'=m=2$ and 3. We found that the oscillation frequency $\barσ$ of the fundamental $r$-mode is in a good approximation given by $\barσ\approx κ_0 Ω$, where $\barσ$ is defined in the corotating frame at the spatial infinity, and $Ω$ is the angular frequency of rotation of the star. The proportional coefficient $κ_0$ is only weakly dependent on $Ω$, but it strongly depends on the relativistic parameter $GM/c^2R$, where $M$ and $R$ are the mass and the radius of the star. All the fundamental $r$-modes with $l'=m$ computed in this study are discrete modes with distinct regular eigenfunctions, and they all fall in the continuous part of the frequency spectrum associated with Kojima's equation (Kojima 1998). These relativistic $r$-modes are obtained by including the effects of rotation higher than the first order of $Ω$ so that the buoyant force plays a role, the situation of which is quite similar to that for the Newtonian $r$-modes.

gr-qc↗
arXiv2001

R-mode Instability of Slowly Rotating Non-isentropic Relativistic Stars

We investigate properties of $r$-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 $r$-mode oscillations in some polytropic models. It is found that such discrete $r$-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.

gr-qc↗
arXiv2001

r-modes of slowly rotating non-isentropic relativistic stars

We investigate properties of r-modes characterized by regular eigenvalue problem in slowly rotating relativistic polytropes. Our numerical results suggest that discrete r-mode solutions for the regular eigenvalue problem exist only for restricted polytropic models. In particular the r-mode associated with l=m=2, which is considered to be the most important for gravitational radiation driven instability, do not have a discrete mode as solutions of the regular eigenvalue problem for polytropes having the polytropic index N > 1.18 even in the post-Newtonian order. Furthermore for a N=1 polytrope, which is employed as a typical neutron star model, discrete r-mode solutions for regular eigenvalue problem do not exist for stars whose relativistic factor M/R is larger than about 0.1. Here M and R are stellar mass and stellar radius, respectively.

gr-qc↗
arXiv2001

Possible measurement of Quintessence and density parameter using strong gravitational lensing events

We propose a possible measurement of the time variability of the vacuum energy using strong gravitational lensing events. As an example we take an Einstein cross lens HST 14176+5226 and demonstrate that the measurement of the velocity dispersion with the accuracy of $\pm$ 5 km/sec will have a chance to determine the time dependence of the vacuum energy as well as the density parameter with the accuracy of order 0.1 if one fixes the lens model.

gr-qc↗
arXiv2000

R-modes of neutron stars with a solid crust

We investigate the properties of $r$-mode oscillations of a slowly rotating neutron star with a solid crust, by taking account of the effects of the Coriolis force. For the modal analysis we employ three-component neutron star models that are composed of a fluid core, a solid crust and a surface fluid ocean. For the three-component models, we find that there exist two kinds of $r$-modes, that is, those confined in the surface fluid ocean and those confined in the fluid core, which are most important for the $r$-mode instability. The $r$-modes do not have any appreciable amplitudes in the solid crust if rotation rate of the star is sufficiently small. We find that the core $r$-modes are strongly affected by mode coupling with the crustal torsional (toroidal) modes and lose their simple properties of the eigenfunction and eigenfrequency as functions of the angular rotation velocity $Ω$. This indicates that the extrapolation formula, which is obtained in the limit of $Ω\to 0$, cannot be used to examine the $r$-mode instability of rapidly rotating neutron stars with a solid crust unless the effects of mode coupling with the crustal torsional modes are correctly taken into account.

astro-ph↗
arXiv2000

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.

astro-ph↗
arXiv2000

A numerical study of the r-mode instability of rapidly rotating nascent neutron stars

The first results of numerical analysis of classical r-modes of {\it rapidly} rotating compressible stellar models are reported. The full set of linear perturbation equations of rotating stars in Newtonian gravity are numerically solved without the slow rotation approximation. A critical curve of gravitational wave emission induced instability which restricts the rotational frequencies of hot young neutron stars is obtained. Taking the standard cooling mechanisms of neutron stars into account, we also show the `evolutionary curves' along which neutron stars are supposed to evolve as cooling and spinning-down proceed. Rotational frequencies of $1.4M_{\odot}$ stars suffering from this instability decrease to around 100Hz when the standard cooling mechanism of neutron stars is employed. This result confirms the results of other authors who adopted the slow rotation approximation.

astro-ph↗
arXiv2000

Rotational modes of non-isentropic stars and the gravitational radiation driven instability

We investigate the properties of r-mode and inertial mode of slowly rotating, non-isentropic, Newtonian stars, by taking account of the effects of the Coriolis force and the centrifugal force. For the non-isentropic models we consider only two cases, that is, the models with the stable fluid stratification in the whole interior and the models that are fully convective. For simplicity we call these two kinds of models "radiative" and "convective" models in this paper. For both cases, we assume the deviation of the models from isentropic structure is small. Examining the dissipation timescales due to the gravitational radiation and several viscous processes for the polytropic neutron star models, we find that the gravitational radiation driven instability of the r-modes remains strong even in the non-isentropic models. Calculating the rotational modes of the radiative models as functions of the angular rotation frequency $Ω$, we find that the inertial modes are strongly modified by the buoyant force at small $Ω$, where the buoyant force as a dominant restoring force becomes comparable with or stronger than the Coriolis force. Because of this property we obtain the mode sequences in which the inertial modes at large $Ω$ are identified as g-modes or the r-modes with l=|m| at small $Ω$. We also note that as $Ω$ increases from $Ω=0$ the retrograde g-modes become retrograde inertial modes, which are unstable against the gravitational radiation reaction.

astro-ph↗
arXiv1999

Inertial modes of slowly rotating isentropic stars

We investigate inertial mode oscillations of slowly and uniformly rotating, isentropic, Newtonian stars. Inertial mode oscillations are induced by the Coriolis force due to the star's rotation, and their characteristic frequencies are comparable with the rotation frequency $Ω$ of the star. So called r-mode oscillations form a sub-class of the inertial modes. In this paper, we use the term ``r-modes'' to denote the inertial modes for which the toroidal motion dominates the spheroidal motion, and the term ``inertial modes'' to denote the inertial modes for which the toroidal and spheroidal motions have comparable amplitude to each other. Using the slow rotation approximation consistent up to the order of $Ω^3$, we study the properties of the inertial modes and r-modes, by taking account of the effect of the rotational deformation of the equilibrium on the eigenfrequencies and eigenfunctions. The eigenfrequencies of the r-modes and inertial modes calculated in this paper are in excellent agreement with those obtained by Lindblom et al (1999) and Lockitch & Friedman (1998). We also estimate the dissipation timescales due to the gravitational radiation and several viscous processes for polytropic neutron star models. We find that for the inertial modes, the mass multipole gravitational radiation dominates the current multipole radiation, which is dominating in the case of the r-modes. It is also found that the inertial mode instability is more unstable than previously reported by Lockitch & Friedman (1998), and survives the viscous damping processes relevant in neutron stars.

astro-ph↗
arXiv1997

Accuracy of the relativistic Cowling approximation in slowly rotating stars

We have calculated the non-radial oscillation in slowly rotating relativistic stars with the Cowling approximation. The frequencies are compared with those based on the complete linearized equations of general relativity. It is found that the results with the approximation differ by less than about $20 %$ for typical relativistic stellar models. The approximation is more accurate for higher-order modes as in the Newtonian case.

gr-qc↗