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Hiroko Koyama

Publications and source records attributed to Hiroko Koyama.

At least 19 recordsLinked to original sources
arXiv2010

The Dynamics of Three-Planet Systems: an Approach from Dynamical System

We study in detail the motions of three planets interacting with each other under the influence of a central star. It is known that the system with more than two planets becomes unstable after remaining quasi-stable for long times, leading to highly eccentric orbital motions or ejections of some of the planets. In this paper, we are concerned with the underlying physics for this quasi-stability as well as the subsequent instability and advocate the so-called "stagnant motion" in the phase space, which has been explored in the field of dynamical system. We employ the Lyapunov exponent, the power spectra of orbital elements and the distribution of the durations of quasi-stable motions to analyze the phase space structure of the three-planet system, the simplest and hopefully representative one that shows the instability. We find from the Lyapunov exponent that the system is almost non-chaotic in the initial quasi-stable state whereas it becomes intermittently chaotic thereafter. The non-chaotic motions produce the horizontal dense band in the action-angle plot whereas the voids correspond to the chaotic motions. We obtain power laws for the power spectra of orbital eccentricities. Power-law distributions are also found for the durations of quasi-stable states. All these results combined together, we may reach the following picture: the phase space consists of the so-called KAM tori surrounded by satellite tori and imbedded in the chaotic sea. The satellite tori have a self-similar distribution and are responsible for the scale-free power-law distributions of the duration times. The system is trapped around one of the KAM torus and the satellites for a long time (the stagnant motion) and moves to another KAM torus with its own satellites from time to time, corresponding to the intermittent chaotic behaviors.

astro-ph.EP↗
arXiv2008

Dynamical response to supernova-induced gas removal in spiral galaxies with dark matter halo

We investigate the dynamical response, in terms of disc size and rotation velocity, to mass loss by supernovae in the evolution of spiral galaxies. A thin baryonic disc having the Kuzmin density profile embedded in a spherical dark matter halo having a density profile proposed by Navarro, Frenk & White is considered. For a purpose of comparison, we also consider the homogeneous and $r^{-1}$ profiles for dark matter in a truncated spherical halo. Assuming for simplicity that the dark matter distribution is not affected by mass loss from discs and the change of baryonic disc matter distribution is homologous, we evaluate the effects of dynamical response in the resulting discs. We found that the dynamical response only for an adiabatic approximation of mass loss can simultaneously account for the rotation velocity and disc size as observed particularly in dwarf spiral galaxies, thus reproducing the Tully-Fisher relation and the size versus magnitude relation over the full range of magnitude. Furthermore, we found that the mean specific angular momentum in discs after the mass loss becomes larger than that before the mass loss, suggesting that the mass loss would occur most likely from the central disc region where the specific angular momentum is low.

astro-ph↗
arXiv2008

Chaotic motion of Charged Particles in an Electromagnetic Field Surrounding a Rotating Black Hole

The observational data from some black hole candidates suggest the importance of electromagnetic fields in the vicinity of a black hole. Highly magnetized disk accretion may play an importance rule, and large scale magnetic field may be formed above the disk surface. Then, we expect that the nature of the black hole spacetime would be reveiled by magnetic phenomena near the black hole. We will start to investigate the motion of a charged particle which depends on the initial parameter setting in the black hole dipole magnetic field. Specially, we study the spin effects of a rotating black hole on the motion of the charged particle trapped in magnetic field lines. We make detailed analysis for the particle's trajectories by using the Poincaré map method, and show the chaotic properties that depend on the black hole spin. We find that the dragging effects of the spacetime by a rotating black hole weaken the chaotic properties and generate regular trajectories for some sets of initial parameters, while the chaotic properties dominate on the trajectories for slowly rotating black hole cases. The dragging effects can generate the fourth adiabatic invariant on the particle motion approximately.

astro-ph↗
arXiv2007

Gravitational Wave Signals from Chaotic System: A Point Mass with A Disk

We study gravitational waves from a particle moving around a system of a point mass with a disk in Newtonian gravitational theory. A particle motion in this system can be chaotic when the gravitational contribution from a surface density of a disk is comparable with that from a point mass. In such an orbit, we sometimes find that there appears a phase of the orbit in which particle motion becomes to be nearly regular (the so-called ``stagnant motion'') for a finite time interval between more strongly chaotic phases. To study how these different chaotic behaviours affect on observation of gravitational waves, we investigate a correlation of the particle motion and the waves. We find that such a difference in chaotic motions reflects on the wave forms and energy spectra. The character of the waves in the stagnant motion is quite different from that either in a regular motion or in a more strongly chaotic motion. This suggests that we may make a distinction between different chaotic behaviours of the orbit via the gravitational waves.

gr-qc↗
arXiv2007

1/f fluctuations in spinning-particle motions around Schwarzschild black hole

We study the properties of chaos in the motions of a spinning test particle in Schwarzschild spacetime. We characterize the chaos using the power spectrum of the time series of $z$ components of the particle's position. It is found that the pattern of the power spectrum shows not only white noise but also $1/f$-type fluctuation, depending on the value of the total angular momentum $J$ and the spin $S$ of the test particle. Therefore we succeed in classifying the chaotic motions, which have been classified as simply chaotic ones in former works, into the two distinct types. One is $1/f$, and the other is white noise. Based on this classification, we plot, in the two-dimensional parameter space $(J,S)$, the phase diagram for the properties of the chaos. This phase diagram enables us in principle to guess the properties of the system $(J,S)$ by observing the dynamics of the test particle, even if the motion is chaotic. Furthermore, we detect that the origin of the $1/f$ fluctuation is that the particle motion stagnates around regular orbits (tori), while traveling back and forth between them, which is called ``stagnant motion'' or ``sticky motion'' in Hamiltonian dynamical systems. The point is that the difference of the property of the chaos or the power spectra is due to the topological structure of the phase space, which in turn is governed by the physical parameter set $(J,S)$ of the system. From this point of view, the chaos we found in this system is not always merely random.

gr-qc↗
arXiv2006

Clusters die hard: Time-correlated excitation in the Hamiltonian Mean Field model

The Hamiltonian Mean Field (HMF) model has a low-energy phase where $N$ particles are trapped inside a cluster. Here, we investigate some properties of the trapping/untrapping mechanism of a single particle into/outside the cluster. Since the single particle dynamics of the HMF model resembles the one of a simple pendulum, each particle can be identified as a high-energy particle (HEP) or a low-energy particle (LEP), depending on whether its energy is above or below the separatrix energy. We then define the trapping ratio as the ratio of the number of LEP to the total number of particles and the ``fully-clustered'' and ``excited'' dynamical states as having either no HEP or at least one HEP. We analytically compute the phase-space average of the trapping ratio by using the Boltzmann-Gibbs stable stationary solution of the Vlasov equation associated with the $N \to \infty$ limit of the HMF model. The same quantity, obtained numerically as a time average, is shown to be in very good agreement with the analytical calculation. Another important feature of the dynamical behavior of the system is that the dynamical state changes transitionally: the ``fully-clustered'' and ``excited'' states appear in turn. We find that the distribution of the lifetime of the ``fully-clustered'' state obeys a power law. This means that clusters die hard, and that the excitation of a particle from the cluster is not a Poisson process and might be controlled by some type of collective motion with long memory. Such behavior should not be specific of the HMF model and appear also in systems where {\it itinerancy} among different ``quasi-stationary'' states has been observed. It is also possible that it could mimick the behavior of transient motion in molecular clusters or some observed deterministic features of chemical reactions.

nlin.CD↗
arXiv2005

Formation of fractal structure in many-body systems with attractive power-law potentials

We study the formation of fractal structure in one-dimensional many-body systems with attractive power-law potentials. Numerical analysis shows that the range of the index of the power for which fractal structure emerges is limited. Dependence of the growth rate on wavenumber and power-index is obtained by linear analysis of the collisionless Boltzmann equation, which supports the numerical results.

nlin.PS↗
arXiv2005

The relation between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime

The connection between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime is studied. Under a scaling hypothesis, we find that the three-point correlation function, $ζ$, obeys the scaling law $ζ\propto ξ^{\frac{3m+4w-2ε}{2m+2w}}$ in the nonlinear regime, where $ξ$, $m$, $w$, and $ε$ are the two-point correlation function, the power index of the power spectrum in the nonlinear regime, the number of spatial dimensions, and the power index of the phase correlations, respectively. The new formula reveals the origin of the power index of the three-point correlation function. We also obtain the theoretical condition for which the ``hierarchical form'' $ζ\proptoξ^2$ is reproduced.

astro-ph↗
arXiv2004

Construction and enlargement of traversable wormholes from Schwarzschild black holes

Analytic solutions are presented which describe the construction of a traversable wormhole from a Schwarzschild black hole, and the enlargement of such a wormhole, in Einstein gravity. The matter model is pure radiation which may have negative energy density (phantom or ghost radiation) and the idealization of impulsive radiation (infinitesimally thin null shells) is employed.

gr-qc↗
arXiv2004

How to make a traversable wormhole from a Schwarzschild black hole

The theoretical construction of a traversable wormhole from a Schwarzschild black hole is described, using analytic solutions in Einstein gravity. The matter model is pure phantom radiation (pure radiation with negative energy density) and the idealization of impulsive radiation is employed.

gr-qc↗
arXiv2003

Universality in the distribution of caustics in the expanding Universe

We numerically investigate the long--time evolution of density perturbations after the first appearance of caustics in an expanding cosmological model with one--dimensional `single--wave' initial conditions. Focussing on the time--intervals of caustic appearances and the spatial distribution of caustics at subsequent times, we find that the time--intervals of caustic appearances approach a constant, i.e., their time--subsequent ratio converges to 1; it is also found that the spatial distribution of caustics at a given time features some universality rules, e.g., the ratio between the position of the nearest caustic from the center and that of the second nearest caustic from the center approaches a constant. Furthermore we find some rules for the mass distribution for each caustic. Using these universality constants we are in the position to predict the spatial distribution of caustics at an arbitrary time in order to give an estimate for the power spectral index in the fully--developed non--dissipative turbulent (`virialized') regime.

astro-ph↗
arXiv2002

Construction and enlargement of dilatonic wormholes by impulsive radiation

The dynamical behavior of traversable wormholes and black holes under impulsive radiation is studied in an exactly soluble dilaton gravity model. Simple solutions are presented where a traversable wormhole is constructed from a black hole, or the throat of a wormhole is stably enlarged or reduced. These solutions illustrate the basic operating principles needed to construct similar analytic solutions in full Einstein gravity.

gr-qc↗
arXiv2002

Slowly decaying tails of massive scalar fields in spherically symmetric spacetimes

We study the dominant late-time behaviors of massive scalar fields in static and spherically symmetric spacetimes. Considering the field evolution in the far zone where the gravitational field is weak, we show under which conditions the massive field oscillates with an amplitude that decays slowly as $t^{-5/6}$ at very late times, as previously found in (say) the Schwarzschild case. Our conclusion is that this long-lived oscillating tail is generally observed at timelike infinity in black hole spacetimes, while it may not be able to survive if the central object is a normal star. We also discuss that such a remarkable backscattering effect is absent for the field near the null cone at larger spatial distances.

gr-qc↗
arXiv2001

Asymptotic tails of massive scalar fields in Schwarzschild background

We investigate the asymptotic tail behavior of massive scalar fields in Schwarzschild background. It is shown that the oscillatory tail of the scalar field has the decay rate of $t^{-5/6}$ at asymptotically late times, and the oscillation with the period $2π/m$ for the field mass $m$ is modulated by the long-term phase shift. These behaviors are qualitatively similar to those found in nearly extreme Reissner-Nordström background, which are discussed in terms of a resonant backscattering due to the space-time curvature.

gr-qc↗
arXiv2000

Asymptotic power-law tails of massive scalar fields in Reissner-Nordström background

We investigate dominant late-time tail behaviors of massive scalar fields in nearly extreme Reissner-Nordström background. It is shown that the oscillatory tail of the scalar fields has the decay rate of $t^{-5/6}$ at asymptotically late times. The physical mechanism by which the asymptotic $t^{-5/6}$ tail yields and the relation between the field mass and the time scale when the tail begins to dominate, are discussed in terms of resonance backscattering due to spacetime curvature.

gr-qc↗