Cosmological Implications of Number Counts of Clusters of Galaxies: logN-logS in X-Ray and Submm Bands

We compute the number counts of clusters of galaxies, the logN-logS relation, in several X-ray and submm bands on the basis of the Press-Schechter theory. We pay particular attention to a set of theoretical models which well reproduce the ROSAT 0.5-2 keV band logN-logS, and explore possibilities to further constrain the models from future observations with ASCA and/or at submm bands. The latter is closely related to the European PLANCK mission and the Japanese Large Millimeter and Submillimeter Array (LMSA) project. We exhibit that one can break the degeneracy in an acceptable parameter region on the $\Omega_0 - \sigma_8$ plane by combining the ROSAT logN-logS and the submm number counts. Models which reproduce the ROSAT band logN-logS will have $N(>S) \sim (150-300) (S/10^{-12} erg cm^{-2} s^{-1})^{-1.3}$ str$^{-1}$ at $S > 10^{-12} erg cm^{-2} s^{-1}$ in the ASCA 2-10 keV band, and $N(>S_\nu) \sim (10^2-10^4) (S_\nu/100 mJy)^{-1.5} str^{-1}$ at $S_\nu > 100 mJy$ in the submm (0.85mm) band. The amplitude of the logN-logS is very sensitive to the model parameters in the submm band. We also compute the redshift evolution of the cluster number counts and compare with that of the X-ray brightest Abell-type clusters. The results, although still preliminary, point to low density ($\Omega_0\sim 0.3$) universes. The contribution of clusters to the X-ray and submm background radiations is shown to be insignificant in any model compatible with the ROSAT logN-logS.Comment: 18 pages, 6 figures and 1 table. Figures revised. Accepted for publication in PAS

Gravitational Radiation Reaction to a Particle Motion

In this paper, we discuss the leading order correction to the equation of motion of the particle, which presumably describes the effect of gravitational radiation reaction. We derive the equation of motion in two different ways. The first one is an extension of the well-known formalism by DeWitt and Brehme developed for deriving the equation of motion of an electrically charged particle. In contrast to the electromagnetic case, in which there are two different charges, i.e., the electric charge and the mass, the gravitational counterpart has only one charge. This fact prevents us from using the same renormalization scheme that was used in the electromagnetic case. To make clear the subtlety in the first approach, we then consider the asymptotic matching of two different schemes, i.e., the internal scheme in which the small particle is represented by a spherically symmetric black hole with tidal perturbations and the external scheme in which the metric is given by small perturbations on the given background geometry. The equation of motion is obtained from the consistency condition of the matching. We find that in both ways the same equation of motion is obtained. The resulting equation of motion is analogous to that derived in the electromagnetic case. We discuss implications of this equation of motion.Comment: 25 pages revtex fil

Monte-Carlo Modeling of Non-Gravitational Heating Processes in Galaxy Clusters

We consider non-gravitational heating effects on galaxy clusters on the basis of the Monte-Carlo modeling of merging trees of dark matter halos combined with the thermal evolution of gas inside each halo. Under the assumption of hydrostatic equilibrium and the isothermal gas profiles, our model takes account of the metallicity evolution, metallicity-dependent cooling of gas, supernova energy feedback, and heating due to jets of radio galaxies in a consistent manner. The observed properties of galaxy clusters can be explained in models with higher non-gravitational heating efficiency than that in the conventional model. Possibilities include jet heating by the Fanaroff-Riley Type II radio galaxies, and the enhanced star formation efficiency and/or supernova energy feedback, especially at high redshifts.Comment: 29 pages, 12 figures. To appear in PASJ, February 25, 200

Reliability of merger tree realizations of dark halos in the Monte-Carlo modeling of galaxy formation

We examine the reliability of the merger trees generated for the Monte-Carlo modeling of galaxy formation. In particular we focus on the cold gas fraction predicted from the merger trees with different assumptions on the progenitor distribution function, the timestep, and the mass resolution. We show that the cold gas fraction is sensitive to the accuracy of the merger trees at small-mass scales of progenitors at high redshifts. One can reproduce the Press-Schechter prediction to a reasonable degree by adopting a fairly large number of redshift bins, N_{step} ~ 1000 in generating merger trees, which is a factor of ten larger than the canonical value used in previous literature.Comment: 9 pages, 10 figures. To appear in PASJ, October 25, 200

Black Hole Perturbation

We present analytic calculations of gravitational waves from a particle orbiting a black hole. We first review the Teukolsky formalism for dealing with the gravitational perturbation of a black hole. Then we develop a systematic method to calculate higher order post-Newtonian corrections to the gravitational waves emitted by an orbiting particle. As applications of this method, we consider orbits that are nearly circular, including exactly circular ones, slightly eccentric ones and slightly inclined orbits off the equatorial plane of a Kerr black hole and give the energy flux and angular momentum flux formulas at infinity with higher order post-Newtonian corrections. Using a different method that makes use of an analytic series representation of the solution of the Teukolsky equation, we also give a post-Newtonian expanded formula for the energy flux absorbed by a Kerr black hole for a circular orbit.Comment: 120 pages ptptex file. To appear in Progress of Theoretical Physics Supplement No.128 (1997) `Perturbative and Numerical Approaches to Gravitational Radiation