arXiv subjects

Motoyuki Saijo

Publications and source records attributed to Motoyuki Saijo.

At least 19 recordsLinked to original sources

arXiv2020

Current status of space gravitational wave antenna DECIGO and B-DECIGO

Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is the future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could be produced during the inflationary period right after the birth of the universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in the heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1,000 km. Three clusters of DECIGO will be placed far from each other, and the fourth cluster will be placed in the same position as one of the three clusters to obtain the correlation signals for the detection of the primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder of DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand the multi-messenger astronomy.

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arXiv2018

Determining the stiffness of the equation of state using low T/W dynamical instabilities in differentially rotating stars

We investigate the nature of low T/W dynamical instabilities in various ranges of the stiffness of the equation of state in differentially rotating stars. Here T is the rotational kinetic energy, while W the gravitational binding energy. We analyze these instabilities in both a linear perturbation analysis and a three-dimensional hydrodynamical simulation. An unstable normal mode of a differentially rotating star is detected by solving an eigenvalue problem along the equatorial plane of the star. The physical mechanism of low T/W dynamical instabilities is also qualitatively confirmed by a scattering of sound waves between corotation and the surface caused by the corotation barrier. Therefore, we can draw a picture of existing pulsation modes unstabilized due to an amplified reflection of sound waves from the corotation barrier. The feature in the eigenfrequency and eigenfunction of the unstable mode in the linear analysis roughly agrees with that in the three-dimensional hydrodynamical simulation in Newtonian gravity. Moreover, the nature of the eigenfunction that oscillates between corotation and the surface for an unstable star requires reinterpretation of pulsation modes in differentially rotating stars. Finally, we propose a manner by which to constrain the stiffness of the equation of state by the direct detection of mode decomposed gravitational waveforms.

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arXiv2016

On a role of corotation radius in the low $T/W$ dynamical instability of differentially rotating stars

We investigate the nature of so-called low $T/W$ dynamical instability in a differentially rotating star by focusing on the role played by the corotation radius of the unstable oscillation modes. An one dimensional model of linear perturbation, which neglects dependence of variables on the coordinate along the rotational axis of the star, is solved to obtain stable and unstable eigenmodes. A linear eigenmode having a corotation radius, at which azimuthal pattern speed of the mode coincides with the stellar angular velocity, is categorized to either a complex (growing or damping) mode or a purely real mode belonging to a continuous spectrum of frequency. We compute canonical angular momentum and its flux to study eigenmodes with corotation radius. In a dynamically unstable mode, sound wave transports its angular momentum in such a way that the absolute value of the angular momentum is increased on both sides of the corotation radius. We further evaluate growth of amplitude of reflected sound wave incident to a corotation point and find that the over-reflection of the wave and the trapping of it between the corotation radius and the surface of the star may qualitatively explain dependences of eigenfrequencies on the stellar differential rotation. The results suggest that the low $T/W$ instability may be caused by over-reflection of sound waves trapped mainly between the surface of the star and a corotation radius.

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arXiv2016

Unstable normal modes of low T/W dynamical instabilities in differentially rotating stars

We investigate the nature of low T/W dynamical instabilities in differentially rotating stars by means of linear perturbation. Here, T and W represent rotational kinetic energy and the gravitational binding energy of the star. This is the first attempt to investigate low T/W dynamical instabilities as a complete set of the eigenvalue problem. Our equilibrium configuration has "constant" specific angular momentum distribution, which potentially contains a singular solution in the perturbed enthalpy at corotation radius in linear perturbation. We find the unstable normal modes of differentially rotating stars by solving the eigenvalue problem along the equatorial plane of the star, imposing the regularity condition on the center and the vanished enthalpy at the oscillating equatorial surface. We find that the existing pulsation modes become unstable due to the existence of the corotation radius inside the star. The feature of the unstable mode eigenfrequency and its eigenfunction in the linear analysis roughly agrees with that in three-dimensional hydrodynamical simulations in Newtonian gravity. Therefore, our normal mode analysis in the equatorial motion proves valid to find the unstable equilibrium stars efficiently. Moreover, the nature of the eigenfunction that oscillates between corotation and the surface radius for unstable stars requires reinterpretation of the pulsation modes in differentially rotating stars.

astro-ph.SR↗

arXiv2011

Dynamic black holes through gravitational collapse: Analysis of multipole moment of the curvatures on the horizon

We have investigated several properties of rapidly rotating dynamic black holes generated by gravitational collapse of rotating relativistic stars. At present, numerical simulations of the binary black hole merger are able to produce a Kerr black hole of J_final / M_final^2 up to = 0.91, of gravitational collapse from uniformly rotating stars up to J_final / M_final^2 ~ 0.75, where J_final is the total angular momentum and M_final the total gravitational mass of the hole. We have succeeded in producing a dynamic black hole of spin J_final / M_final^2 ~ 0.95 through the collapse of differentially rotating relativistic stars. We have investigated those dynamic properties through diagnosing multipole moment of the horizon, and found the following two features. Firstly, two different definitions of the angular momentum of the hole, the approximated Killing vector approach and dipole moment of the current multipole approach, make no significant difference to our computational results. Secondly, dynamic hole approaches a Kerr by gravitational radiation within the order of a rotational period of an equilibrium star, although the dynamic hole at the very forming stage deviates quite far from a Kerr. We have also discussed a new phase of quasi-periodic waves in the gravitational waveform after the ringdown in terms of multipole moment of the dynamic hole.

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arXiv2009

Collapse of differentially rotating supermassive stars: Post black hole formation

We investigate the collapse of differentially rotating supermassive stars (SMSs) by means of 3+1 hydrodynamic simulations in general relativity. We particularly focus on the onset of collapse to understand the final outcome of collapsing SMSs. We find that the estimated ratio of the mass between the black hole (BH) and the surrounding disk from the equilibrium star is roughly the same as the results from numerical simulation. This suggests that the picture of axisymmetric collapse is adequate, in the absence of nonaxisymmetric instabilities, to illustrate the final state of the collapse. We also find that quasi-periodic gravitational waves continue to be emitted after the quasinormal mode frequency has decayed. We furthermore have found that when the newly formed BH is almost extreme Kerr, the amplitude of the quasi-periodic oscillation is enhanced during the late stages of the evolution. Geometrical features, shock waves, and instabilities of the fluid are suggested as a cause of this amplification behaviour. This alternative scenario for the collapse of differentially rotating SMSs might be observable by LISA.

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arXiv2008

Amplification of azimuthal modes with odd wave numbers during dynamical bar-mode growth in rotating stars

Nonlinear growth of the bar-mode deformation is studied for a differentially rotating star with supercritical rotational energy. In particular, the growth mechanism of some azimuthal modes with odd wave numbers is examined by comparing a simplified mathematical model with a realistic simulation. Mode coupling to even modes, i.e., the bar mode and higher harmonics, significantly enhances the amplitudes of odd modes, unless they are exactly zero initially. Therefore, other modes which are not axially symmetric cannot be neglected at late times in the growth of the unstable bar-mode even when starting from an almost axially symmetric state.

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arXiv2008

Faraday resonance in dynamical bar instability of differentially rotating stars

We investigate the nonlinear behaviour of the dynamically unstable rotating star for the bar mode by three-dimensional hydrodynamics in Newtonian gravity. We find that an oscillation along the rotation axis is induced throughout the growth of the unstable bar mode, and that its characteristic frequency is twice as that of the bar mode, which oscillates mainly along the equatorial plane. A possibility to observe Faraday resonance in gravitational waves is demonstrated and discussed.

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arXiv2006

Viscosity driven instability in rotating relativistic stars

We investigate the viscosity driven instability in rotating relativistic stars by means of an iterative approach. We focus on polytropic rotating equilibrium stars and impose an m=2 perturbationin the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study those effects on the value of the threshold. For a uniformly rotating star, the criterion T/W, where T is the rotational kinetic energy and W is the gravitational binding energy, mainly depends on the compactness of the star and takes values around 0.13 ~ 0.16, which differ slightly from that of Newtonian incompressible stars (~ 0.14). For differentially rotating stars, the critical value of T/W is found to span the range 0.17 - 0.25. This is significantly larger than the uniformly rotating case with the same compactness of the star. Finally we discuss a possibility of detecting gravitational waves from viscosity driven instability with ground-based interferometers.

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arXiv2006

Gravitational waves from a dust disk around a Schwarzschild black hole

We investigate gravitational waves from a dust disk around a Schwarzschild black hole to focus on whether we can extract any of its physical properties from a direct detection of gravitational waves. We adopt a black hole perturbation approach in a time domain, which is a satisfactory approximation to illustrate a dust disk in a supermassive black hole. We find that we can determine the radius of the disk by using the power spectrum of gravitational waves and that our method to extract the radius works for a disk of arbitrary density distribution. Therefore we believe a possibility exists for determining the radius of the disk from a direct observation of gravitational waves detected by the Laser Interferometer Space Antenna.

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arXiv2006

Low T/|W| dynamical instabilities in differentially rotating stars: Diagnosis with canonical angular momentum

We study the nature of non-axisymmetric dynamical instabilities in differentially rotating stars with both linear eigenmode analysis and hydrodynamic simulations in Newtonian gravity. We especially investigate the following three types of instability; the one-armed spiral instability, the low T/|W| bar instability, and the high T/|W| bar instability, where T is the rotational kinetic energy and W is the gravitational potential energy. The nature of the dynamical instabilities is clarified by using a canonical angular momentum as a diagnostic. We find that the one-armed spiral and the low T/|W| bar instabilities occur around the corotation radius, and they grow through the inflow of canonical angular momentum around the corotation radius. The result is a clear contrast to that of a classical dynamical bar instability in high T/|W|. We also discuss the feature of gravitational waves generated from these three types of instability.

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arXiv2006

Low T/|W| dynamical instability in differentially rotating stars: Diagnosis with canonical angular momentum

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arXiv2005

Dynamical bar instability in a relativistic rotational core collapse

We investigate the rotational core collapse of a rapidly rotating relativistic star by means of a 3+1 hydrodynamical simulations in conformally flat spacetime of general relativity. We concentrate our investigation to the bounce of the rotational core collapse, since potentially most of the gravitational waves from it are radiated around the core bounce. The dynamics of the star is started from a differentially rotating equilibrium star of T/W ~ 0.16 (T is the rotational kinetic energy and W is the gravitational binding energy of the equilibrium star), depleting the pressure to initiate the collapse and to exceed the threshold of dynamical bar instability. Our finding is that the collapsing star potentially forms a bar when the star has a toroidal structure due to the redistribution of the angular momentum at the core bounce. On the other hand, the collapsing star weakly forms a bar when the star has a spheroidal structure. We also find that the bar structure of the star is destroyed when the torus is destroyed in the rotational core collapse. Since the collapse of a toroidal star potentially forms a bar, it can be a promising source of gravitational waves which will be detected in advanced LIGO.

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arXiv2005

Dynamical One-Armed Spiral Instability in Differentially Rotating Stars

We investigate the dynamical one-armed spiral instability in differentially rotating stars with both eigenmode analysis and hydrodynamic simulations in Newtonian gravity. We find that the one-armed spiral mode is generated around the corotation radius of the star, and the distribution of angular momentum shifts inwards the corotation radius during the growth of one-armed spiral mode. We also find by investigating the distribution of the canonical angular momentum density that the low T/|W| dynamical instability for both m=1 and m=2 mode, where T is the rotational kinetic energy and W is the gravitational potential energy, is generated around the corotation point. Finally, we discuss the feature of gravitational waves generated from these modes.

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arXiv2004

The Collapse of Differentially Rotating Supermassive Stars: Conformally Flat Simulations

We investigate the gravitational collapse of rapidly rotating relativistic supermassive stars by means of a 3+1 hydrodynamical simulations in conformally flat spacetime of general relativity. We study the evolution of differentially rotating supermassive stars of $q \equiv J/M^{2} \sim 1$ ($J$ is the angular momentum and $M$ is the gravitational mass of the star) from the onset of radial instability at $R/M \sim 65$ ($R$ is the circumferential radius of the star) to the point where the conformally flat approximation breaks down. We find that the collapse of the star of $q \gtrsim 1$, a radially unstable differentially rotating star form a black hole of $q \lesssim 1$. The main reason to prevent formation of a black hole of $q \gtrsim 1$ is that quite a large amount of angular momentum stays at the surface. We also find that most of the mass density collapses coherently to form a supermassive black hole with no appreciable disk nor bar. In the absence of nonaxisymmetric deformation, the collapse of differentially rotating supermassive stars from the onset of radial instability are the promising sources of burst and quasinormal ringing waves in the Laser Interferometer Space Antenna.

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arXiv2003

One-Armed Spiral Instability in Differentially Rotating Stars

We investigate the dynamical instability of the one-armed spiral m=1 mode in differentially rotating stars by means of 3+1 hydrodynamical simulations in Newtonian gravitation. We find that both a soft equation of state and a high degree of differential rotation in the equilibrium star are necessary to excite a dynamical m=1 mode as the dominant instability at small values of the ratio of rotational kinetic to potential energy, T/|W|. We find that this spiral mode propagates outward from its point of origin near the maximum density at the center to the surface over several central orbital periods. An unstable m=1 mode triggers a secondary m=2 bar mode of smaller amplitude, and the bar mode can excite gravitational waves. As the spiral mode propagates to the surface it weakens, simultaneously damping the emitted gravitational wave signal. This behavior is in contrast to waves triggered by a dynamical m=2 bar instability, which persist for many rotation periods and decay only after a radiation-reaction damping timescale.

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arXiv2002

Collapse of a Rotating Supermassive Star to a Supermassive Black Hole: Post-Newtonian Simulations

We study the gravitational collapse of a rotating supermassive star (SMS) by means of a (3+1) hydrodynamical simulation in a post-Newtonian (PN) approxi- mation of general relativity. This problem is particularly challenging because of the vast dynamical range in space which must be covered in the course of col- lapse. We evolve a uniformly rotating SMS from the onset of radial instability at R_{p}/M=411, where R_{p} is the proper polar radius of the star and M is the total mass-energy, to the point at which the PN approximation breaks down. We introduce a scale factor and a "comoving" coordinate to handle the large varia- tion in radius during the collapse and focus on the central core. Since T/W, the ratio of the rotational kinetic energy to the gravitational binding energy, is nearly proportional to 1/R_{p} throughout the collapse, the imploding star may ultimately exceed the critical value of T/W for dynamical instability to bar-mode formation. However, for stars rotating uniformly at the onset of col- lapse, we do not find any unstable growth of bars prior to the termination of our simulation. We do find that the collapse is likely to form a supermassive black hole (BH) coherently, with almost all of the matter falling into the hole, leaving very little ejected matter to form a disk. In the absence of nonaxi- symmetric bar formation, the collapse of a uniformly rotating SMS does not lead to appreciable quasi-periodic gravitational wave (GW) emission by the time our integrations terminate. However, the coherent nature of the implosion suggests that rotating SMS collapse will be a promising source of GW bursts. We also expect that, following BH formation, long wavelength quasi-periodic waves will result from quasi-normal ringing. These waves may be detectable by LISA.

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arXiv2001

Dynamical Bar Instability in Relativistic Rotating Stars

We study by computational means the dynamical stability against bar-mode deformation of rapidly and differentially rotating stars in a 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 $β= T/W$ 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 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 and 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.

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