Evolution of Massive Black Hole Binaries

We present the result of large-scale N-body simulations of the stellar-dynamical evolution of a massive black-hole binary at the center of a spherical galaxy. We focus on the dependence of the hardening rate on the relaxation timescale of the parent galaxy. A simple theoretical argument predicts that a binary black hole creates the ``loss cone'' around it. Once the loss cone is formed, the hardening rate is determined by the rate at which field stars diffuse into the loss cone. Therefore the hardening timescale becomes proportional to the relaxation timescale. Recent N-body simulations, however, have failed to confirm this theory and various explanations have been proposed. By performing simulations with sufficiently large N (up to $10^6$) for sufficiently long time, we found that the hardening rate does depend on N. Our result is consistent with the simple theoretical prediction that the hardening timescale is proportional to the relaxation timescale. This dependence implies that most massive black hole binaries are unlikely to merge within the Hubble time through interaction with field stars and gravitational wave radiation alone.Comment: Reviced version accepted for publication in ApJ. Scheduled to appear in the February 10, 2004 issu

Non-Poissonian level spacing statistics of classically integrable quantum systems based on the Berry-Robnik approach

Along the line of thoughts of Berry and Robnik\cite{[1]}, we investigated the gap distribution function of systems with infinitely many independent components, and discussed the level-spacing distribution of classically integrable quantum systems. The level spacing distribution is classified into three cases: Case 1: Poissonian if $\bar{\mu}(+\infty)=0$, Case 2: Poissonian for large $S$, but possibly not for small $S$ if $0<\bar{\mu}(+\infty)< 1$, and Case 3: sub-Poissonian if $\bar{\mu}(+\infty)=1$. Thus, even when the energy levels of individual components are statistically independent, non-Poisson level spacing distributions are possible.Comment: 5 pages, 0 figur

Long-Range Spectral Statistics of Classically Integrable Systems --Investigation along the Line of the Berry-Robnik Approach--

Extending the argument of Ref.\citen{[4]} to the long-range spectral statistics of classically integrable quantum systems, we examine the level number variance, spectral rigidity and two-level cluster function. These observables are obtained by applying the approach of Berry and Robnik\cite{[0]} and the mathematical framework of Pandey \cite{[2]} to systems with infinitely many components, and they are parameterized by a single function $\bar{c}$, where $\bar{c}=0$ corresponds to Poisson statistics, and $\bar{c}\not=0$ indicates deviations from Poisson statistics. This implies that even when the spectral components are statistically independent, non-Poissonian spectral statistics are possible.Comment: 13 pages, 4 figure

Long-Term Evolution of Massive Black Hole Binaries. II. Binary Evolution in Low-Density Galaxies

We use direct-summation N-body integrations to follow the evolution of binary black holes at the centers of galaxy models with large, constant-density cores. Particle numbers as large as 400K are considered. The results are compared with the predictions of loss-cone theory, under the assumption that the supply of stars to the binary is limited by the rate at which they can be scattered into the binary's influence sphere by gravitational encounters. The agreement between theory and simulation is quite good; in particular, we are able to quantitatively explain the observed dependence of binary hardening rate on N. We do not verify the recent claim of Chatterjee, Hernquist & Loeb (2003) that the hardening rate of the binary stabilizes when N exceeds a particular value, or that Brownian wandering of the binary has a significant effect on its evolution. When scaled to real galaxies, our results suggest that massive black hole binaries in gas-poor nuclei would be unlikely to reach gravitational-wave coalescence in a Hubble time.Comment: 13 pages, 8 figure

Time-Symmetrized Kustaanheimo-Stiefel Regularization

In this paper we describe a new algorithm for the long-term numerical integration of the two-body problem, in which two particles interact under a Newtonian gravitational potential. Although analytical solutions exist in the unperturbed and weakly perturbed cases, numerical integration is necessary in situations where the perturbation is relatively strong. Kustaanheimo--Stiefel (KS) regularization is widely used to remove the singularity in the equations of motion, making it possible to integrate orbits having very high eccentricity. However, even with KS regularization, long-term integration is difficult, simply because the required accuracy is usually very high. We present a new time-integration algorithm which has no secular error in either the binding energy or the eccentricity, while allowing variable stepsize. The basic approach is to take a time-symmetric algorithm, then apply an implicit criterion for the stepsize to ensure strict time reversibility. We describe the algorithm in detail and present the results of numerical tests involving long-term integration of binaries and hierarchical triples. In all cases studied, we found no systematic error in either the energy or the angular momentum. We also found that its calculation cost does not become higher than those of existing algorithms. By contrast, the stabilization technique, which has been widely used in the field of collisional stellar dynamics, conserves energy very well but does not conserve angular momentum.Comment: figures are available at http://grape.c.u-tokyo.ac.jp/~funato/; To appear in Astronomical Journal (July, 1996

A general framework for online audio source separation

We consider the problem of online audio source separation. Existing algorithms adopt either a sliding block approach or a stochastic gradient approach, which is faster but less accurate. Also, they rely either on spatial cues or on spectral cues and cannot separate certain mixtures. In this paper, we design a general online audio source separation framework that combines both approaches and both types of cues. The model parameters are estimated in the Maximum Likelihood (ML) sense using a Generalised Expectation Maximisation (GEM) algorithm with multiplicative updates. The separation performance is evaluated as a function of the block size and the step size and compared to that of an offline algorithm.Comment: International conference on Latente Variable Analysis and Signal Separation (2012

Biosynthesis, structure, and biological activities of envelope protein gp65 of murine coronavirus.

We have previously shown that gp65 (E3) is a virion structural protein which varies widely in quantity among different strains of mouse hepatitis virus (MHV). In this study, the biosynthetic pathway and possible biological activities of this protein were examined. The glycosylation of gp65 in virus-infected cells was inhibited by tunicamycin but not by monensin, suggesting that it contains an N-glycosidic linkage. Glycosylation is cotranslational and appears to be complete before the glycoprotein reaches the Golgi complex. Pulse-chase experiments showed that this protein decreased in size after 30 min of chase, suggesting that the carbohydrate chains of gp65 undergo trimming during its transport across the Golgi. This interpretation is supported by the endoglycosidase treatment of gp65, which showed that the peptide backbone of gp65 did not decrease in size after pulse-chase periods. This maturation pathway is distinct from that of the E1 or E2 glycoproteins. Partial endoglycosidase treatment indicated that gp65 contains 9 to 10 carbohydrate side chains; thus, almost all of the potential glycosylation sites of gp65 were glycosylated. In vitro translation studies coupled with protease digestion suggest that gp65 is an integral membrane protein. The presence of gp65 in the virion is correlated with the presence of an acetylesterase activity. No hemagglutinin activity was detected

Gallium concentration dependence of room-temperature near-bandedge luminescence in n-type ZnO:Ga

We investigated the optical properties of epitaxial \textit{n}-type ZnO films grown on lattice-matched ScAlMgO$_4$ substrates. As the Ga doping concentration increased up to $6 \times 10^{20}$ cm$^{-3}$, the absorption edge showed a systematic blueshift, consistent with the Burstein-Moss effect. A bright near-bandedge photoluminescence (PL) could be observed even at room temperature, the intensity of which increased monotonically as the doping concentration was increased except for the highest doping level. It indicates that nonradiative transitions dominate at a low doping density. Both a Stokes shift and broadening in the PL band are monotonically increasing functions of donor concentration, which was explained in terms of potential fluctuations caused by the random distribution of donor impurities.Comment: accepted for publication for Applied Physics Letters 4 figure