Masa-aki Sakagami

Long-Term Evolution of Stellar Self-Gravitating Systems Away from Thermal Equilibrium: Connection with Nonextensive Statistics

With particular attention to the recently postulated introduction of a nonextensive generalization of Boltzmann-Gibbs statistics, we study the long-term stellar dynamical evolution of self-gravitating systems on time scales much longer than the two-body relaxation time. In a self-gravitating N-body system confined in an adiabatic wall, we show that the quasiequilibrium sequence arising from the Tsallis entropy, so-called stellar polytropes, plays an important role in characterizing the transient states away from the Boltzmann-Gibbs equilibrium state.

NUMERICAL MODELING OF THE COAGULATION AND POROSITY EVOLUTION OF DUST AGGREGATES

Porosity evolution of dust aggregates is crucial in understanding dust evolution in protoplanetary disks. In this study, we present useful tools to study the coagulation and porosity evolution of dust aggregates. First, we present a new numerical method for simulating dust coagulation and porosity evolution as an extension of the conventional Smoluchowski equation. This method follows the evolution of the mean porosity for each aggregate mass simultaneously with the evolution of the mass distribution function. This method reproduces the results of previous Monte Carlo simulations with much less computational expense. Second, we propose a new collision model for porous dust aggregates on the basis of our N-body experiments on aggregate collisions. As the first step, we focus on hit-and-stick collisions, which involve neither compression nor fragmentation of aggregates. We first obtain empirical data on porosity changes between the classical limits of ballistic cluster-cluster and particle-cluster aggregation. Using the data, we construct a recipe for the porosity change due to general hit-and-stick collisions as well as formulae for the aerodynamical and collisional cross sections. Our collision model is thus more realistic than a previous model of Ormel et al. based on the classical aggregation limits only. Simple coagulation simulations using the extended Smoluchowski method show that our collision model explains the fractal dimensions of porous aggregates observed in a full N-body simulation and a laboratory experiment. By contrast, similar simulations using the collision model of Ormel et al. result in much less porous aggregates, meaning that this model underestimates the porosity increase upon unequal-sized collisions. Besides, we discover that aggregates at the high-mass end of the distribution can have a considerably small aerodynamical cross section per unit mass compared with aggregates of lower masses. This occurs when aggregates drift under uniform acceleration (e.g., gravity) and their collision is induced by the difference in their terminal velocities. We point out an important implication of this discovery for dust growth in protoplanetary disks.

Gravothermal catastrophe and Tsallis’ generalized entropy of self-gravitating systems

We present a first physical application of Tsallis’ generalized entropy to the thermodynamics of self-gravitating systems. The stellar system confined in a spherical cavity of radius re exhibits an instability, so-called gravothermal catastrophe, which has been originally investigated by Antonov (Vestn. Leningrad Gros. Univ. 7 (1962) 135) and Lynden-Bell and Wood (Mon. Not. R. Astron. Soc. 138 (1968) 495) on the basis of the maximum entropy principle for the phase-space distribution function. In contrast to previous analyses using the Boltzmann–Gibbs entropy, we apply the Tsallis-type generalized entropy to seek the equilibrium criteria. Then the distribution function of Vlassov–Poisson system can be reduced to the stellar polytrope system. Evaluating the second variation of Tsallis entropy and solving the zero eigenvalue problem explicitly, we find that the gravothermal instability appears in cases with polytrope index n>5. The critical point characterizing the onset of instability are obtained, which exactly matches with the results derived from the standard turning-point analysis. The results give an important suggestion that the Tsallis’ generalized entropy is indeed applicable and viable to the long-range nature of the self-gravitating system.

Instability of 1-loop superstring cosmology

Abstract A stability analysis is made in the context of the previously discovered non-singular cosmological solution from 1-loop corrected superstring effective action. We found that this solution has an instability in graviton mode, which is shown to have a close relation to the avoidance of initial singularity via energy condition. We also estimate the condition for the breakdown of the background solution due to the overdominance of the graviton.

ELECTROSTATIC BARRIER AGAINST DUST GROWTH IN PROTOPLANETARY DISKS. I. CLASSIFYING THE EVOLUTION OF SIZE DISTRIBUTION

Collisional growth of submicron-sized dust grains into macroscopic aggregates is the first step of planet formation in protoplanetary disks. These grains are expected to carry nonzero negative charges in the weakly ionized disks, but its effect on their collisional growth has not been fully understood so far. In this paper, we investigate how the charging affects the evolution of the dust size distribution properly taking into account the charging mechanism in a weakly ionized gas as well as porosity evolution through low-energy collisions. To clarify the role of the size distribution, we divide our analysis into two steps. First, we analyze the collisional growth of charged aggregates assuming a monodisperse (i.e., narrow) size distribution. We show that the monodisperse growth stalls due to the electrostatic repulsion when a certain condition is met, as was already expected in our previous work. Second, we numerically simulate dust coagulation using Smoluchowskis method to see how the outcome changes when the size distribution is allowed to freely evolve. We find that, under certain conditions, the dust undergoes bimodal growth where only a limited number of aggregates continue to grow, carrying a major part of the dust mass in the system. This occurs because remaining small aggregates efficiently sweep up free electrons to prevent the larger aggregates from being strongly charged. We obtain a set of simple criteria that allows us to predict how the size distribution evolves for a given condition. In Paper II, we apply these criteria to dust growth in protoplanetary disks.

Gravothermal catastrophe and Tsallis’ generalized entropy of self-gravitating systems. (III). Quasi-equilibrium structure using normalized q-values

We revisit the issues on the thermodynamic property of stellar self-gravitating system arising from Tsallis’ non-extensive entropy. Previous papers (Physica A 307 (2002) 185; ibid. 318 (2003) 387) have revealed that the extremum-state of Tsallis entropy, the so-called stellar polytrope, has consistent thermodynamic structure, which predicts the thermodynamic instability due to the negative specific heat. However, their analyses heavily relies on the old Tsallis formalism using standard linear mean values. In this paper, extending our previous study, we focus on the quasi-equilibrium structure based on the standard framework by means of the normalized q-expectation values. It then turns out that the new extremum-state of Tsallis entropy essentially remains unchanged from the previous result, i.e., the stellar quasi-equilibrium distribution can be described by the stellar polytrope. While the thermodynamic stability for a system confined in an adiabatic wall completely agrees with the previous study and thereby the stability/instability criterion remains unchanged, the stability analysis reveals a new equilibrium property for the system surrounded by a thermal bath. In any case, the stability/instability criteria are consistently explained from the presence of negative specific heat and within the formalism, the stellar polytrope is characterized as a plausible non-extensive meta-equilibrium state.

Massive quasi-normal mode

This paper proposes to study quasi-normal modes due to massive scalar fields. We, in particular, investigate the dependence of quasi-normal mode (QNM) frequencies on the field mass. From this research, we find that there are quasi-normal modes with arbitrarily long life when the field mass has specific values. It is also found that QNM may disappear when the field mass exceeds these values.

Probing nontensorial polarizations of stochastic gravitational-wave backgrounds with ground-based laser interferometers

In a general metric theory of gravitation in four dimensions, six polarizations of a gravitational wave are allowed: two scalar and two vector modes, in addition to two tensor modes in general relativity. Such additional polarization modes appear due to additional degrees of freedom in modified theories of gravitation or theories with extra dimensions. Thus, observations of gravitational waves can be utilized to constrain the extended models of gravitation. In this paper, we investigate detectability of additional polarization modes of gravitational waves, particularly focusing on a stochastic gravitational-wave background, with laser-interferometric detectors on the Earth. We found that more than three detectors can separate the mixture of polarization modes in detector outputs, and that they have almost the same sensitivity to each polarization mode of stochastic gravitational-wave background.

Laser-interferometric Detectors for Gravitational Wave Backgrounds at 100 MHz : Detector Design and Sensitivity

Recently, observational searches for gravitational wave background (GWB) have been developed and given direct and indirect constraints on the energy density of GWB in a broad range of frequencies. These constraints have already rejected some theoretical models of large GWB spectra. However, at 100 MHz, there is no strict upper limit from direct observation, though the indirect limit by

Self-gravitating stellar systems and non-extensive thermostatistics

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