arXiv subjects

Motoyuki Saijo

Publications and source records attributed to Motoyuki Saijo.

24 records · Page 2Linked to original sources

arXiv2000

Possible direct method to determine the radius of a star from the spectrum of gravitational wave signals II : Spectra for various cases

We compute the spectrum and the waveform of gravitational waves generated by the inspiral of a disk or a spherical like dust body into a Kerr black hole. We investigate the effect of the radius R of the body on gravitational waves and conclude that the radius is inferred from the gravitational wave signal irrespective of (1) the form of the body (a disk or a spherical star) (2) the location where the shape of the body is determined, (3) the orbital angular momentum of the body, and (4) a black hole rotation. We find that when $R$ is much larger than the characteristic length of the quasinormal mode frequency, the spectrum has several peaks and the separation of the troughs $Δω$ is proportional to $R^{-1}$. Thus, we may directly determine the radius of a star in a coalescing binary black hole - star system from the observed spectrum of gravitational waves. For example, both trough frequency of neutron stars and white dwarfs are within the detectable frequency range of some laser interferometers and resonant type detectors so that this effect can be observed in the future. We therefore conclude that the spectrum of gravitational waves may provide us important signals in gravitational wave astronomy as in optical astronomy.

astro-ph↗

arXiv2000

Dynamical Bar Instability in Rotating Stars: Effect of General Relativity

We study the dynamical stability against bar-mode deformation of rapidly and differentially rotating stars in the first post-Newtonian approximation of general relativity. We vary the compaction of the star $M/R$ (where $M$ is the gravitational mass and $R$ the equatorial circumferential radius) between 0.01 and 0.05 to isolate the influence of relativistic gravitation on the instability. For compactions in this moderate range, the critical value of $β\equiv T/W$ for the onset of the dynamical instability (where $T$ is the rotational kinetic energy and $W$ the gravitational binding energy) slightly decreases from $\sim 0.26$ to $\sim 0.25$ with increasing compaction for our choice of the differential rotational law. Combined with our earlier findings based on simulations in full general relativity for stars with higher compaction, we conclude that relativistic gravitation {\em enhances} the dynamical bar-mode instability, i.e. the onset of instability sets in for smaller values of $β$ in relativistic gravity than in Newtonian gravity. We also find that once a triaxial structure forms after the bar-mode perturbation saturates in dynamically unstable stars, the triaxial shape is maintained, at least for several rotational periods. To check the reliability of our numerical integrations, we verify that the general relativistic Kelvin-Helmholtz circulation is well-conserved, in addition to rest-mass energy, total mass-energy, linear and angular momentum. Conservation of circulation indicates that our code is not seriously affected by numerical viscosity. We determine the amplitude and frequency of the quasi-periodic gravitational waves emitted during the bar formation process using the quadrupole formula.

astro-ph↗

arXiv2000

Gravitational waves from a spinning particle scattered by a relativistic star: Axial mode case

We study gravitational waves from a spinning test particle scattered by a relativistic star using a perturbation method. The present analysis is restricted to axial modes. By calculating the energy spectrum, the waveforms and the total energy and angular momentum of gravitational waves, we analyze the dependence of the emitted gravitational waves on a particle spin. For a normal neutron star, the energy spectrum has one broad peak whose characteristic frequency corresponds to the angular velocity at the turning point (a periastron). Since the turning point is determined by the orbital parameter, there exists the dependence of the gravitational wave on a particle spin. We find that the total energy of $l = 2$ gravitational waves gets larger as the spin increases in the anti-parallel direction to the orbital angular momentum. For an ultracompact star, in addition to such an orbital contribution, we find the quasi-normal modes exited by a scattered particle, whose excitation rate to gravitational waves depends on the particle spin. We also discuss the ratio of the total angular momentum to the total energy of gravitational waves and explain its spin dependence.

gr-qc↗

arXiv2000

Possible direct method to determine the radius of a star from the spectrum of gravitational wave signals

We computed the spectrum of gravitational waves from a dust disk star of radius R inspiraling into a Kerr black hole of mass M and specific angular momentum a. We found that when R is much larger than the wave length of the quasinormal mode, the spectrum has several peaks and the separation of peaks $Δω$ is proportional to $R^{-1}$ irrespective of M and a. This suggests that the radius of the star in coalescing binary black hole - star systems may be determined directly from the observed spectrum of gravitational wave. This also suggests that the spectrum of the radiation may give us important information in gravitational wave astronomy as in optical astronomy.

astro-ph↗

arXiv1999

Gravitational waves from a test particle scattered by a neutron star: Axial mode case

Using a metric perturbation method, we study gravitational waves from a test particle scattered by a spherically symmetric relativistic star. We calculate the energy spectrum and the waveform of gravitational waves for axial modes. Since metric perturbations in axial modes do not couple to the matter fluid of the star, emitted waves for a normal neutron star show only one peak in the spectrum, which corresponds to the orbital frequency at the turning point, where the gravitational field is strongest. However, for an ultracompact star (the radius $R \lesssim 3M$), another type of resonant periodic peak appears in the spectrum. This is just because of an excitation by a scattered particle of axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This excitation comes from the existence of the potential minimum inside of a star. We also find for an ultracompact star many small periodic peaks at the frequency region beyond the maximum of the potential, which would be due to a resonance of two waves reflected by two potential barriers (Regge-Wheeler type and one at the center of the star). Such resonant peaks appear neither for a normal neutron star nor for a Schwarzschild black hole. Consequently, even if we analyze the energy spectrum of gravitational waves only for axial modes, it would be possible to distinguish between an ultracompact star and a normal neutron star (or a Schwarzschild black hole).

gr-qc↗

arXiv1997

Gravitational Waves in Brans-Dicke Theory : Analysis by Test Particles around a Kerr Black Hole

Analyzing test particles falling into a Kerr black hole, we study gravitational waves in Brans-Dicke theory of gravity. First we consider a test particle plunging with a constant azimuthal angle into a rotating black hole and calculate the waveform and emitted energy of both scalar and tensor modes of gravitational radiation. We find that the waveform as well as the energy of the scalar gravitational waves weakly depends on the rotation parameter of black hole $a$ and on the azimuthal angle. Secondly, using a model of a non-spherical dust shell of test particles falling into a Kerr black hole, we study when the scalar modes dominate. When a black hole is rotating, the tensor modes do not vanish even for a ``spherically symmetric" shell, instead a slightly oblate shell minimizes their energy but with non-zero finite value, which depends on Kerr parameter $a$. As a result, we find that the scalar modes dominate only for highly spherical collapse, but they never exceed the tensor modes unless the Brans-Dicke parameter $ω_{BD} \lsim 750 $ for $a/M=0.99$ or unless $ω_{BD} \lsim 20,000 $ for $a/M=0.5$, where $M$ is mass of black hole. We conclude that the scalar gravitational waves with $ω_{BD} \lsim$ several thousands do not dominate except for very limited situations (observation from the face-on direction of a test particle falling into a Schwarzschild black hole or highly spherical dust shell collapse into a Kerr black hole). Therefore observation of polarization is also required when we determine the theory of gravity by the observation of gravitational waves.

gr-qc↗