Temperature and luminosity functions of X-ray clusters are computed semi-analytically, combining a simple model for the cluster gas properties with the distribution functions of halo formation epochs proposed by Lacey & Cole (1993) and . In contrast to several previous approaches which apply the Press-Schechter mass function in a straightforward manner, our method can explicitly take into account the temperature and luminosity evolution of clusters. In order to make quantitative predictions in a specific cosmological context, we adopt cold dark matter (CDM) universes.Assuming the baryon density parameter Ω B = 0.0125h −2 (h is the Hubble constant in units of 100km•sec −1 •Mpc −1 ) and the COBE normalization of matter fluctuations, temperature and luminosity functions of X-ray clusters depend sensitively on the density parameter Ω 0 . Allowing for several uncertainties in observational data as well as in our simplified assumptions, we conclude that Ω 0 ∼ 0.2 − 0.5 and h ∼ 0.7 CDM models with/without the cosmological constant reproduce simultaneously the observed temperature and luminosity functions of X-ray clusters at redshift z ∼ 0.

We study the formation and evolution of H ii regions around the first stars formed at redshifts z ¼ 10 30. We use a one-dimensional Lagrangian hydrodynamics code that self-consistently incorporates radiative transfer and nonequilibrium primordial gas chemistry. The star-forming region is defined as a spherical dense molecular gas cloud with a Population III star embedded at the center. We explore a large parameter space by considering, as plausible early star-forming sites, dark matter halos of mass M halo ¼ 10 5 10 8 M , gas density profiles with a power-law index w ¼ 1:5 2:25, and metal-free stars of mass M star ¼ 25 500 M . The formation of the H ii region is characterized by initial slow expansion of a weak D-type ionization front near the center, followed by rapid propagation of an R-type front throughout the outer gas envelope. We find that the transition between the two front types is indeed a critical condition for the complete ionization of halos of cosmological interest. In small-mass (P10 6 M ) halos, the transition takes place within a few 10 5 yr, yielding high escape fractions (>80%) of both ionizing and photodissociating photons. The gas is effectively evacuated by a supersonic shock, with the mean density within the halo decreasing to P1 cm À3 in a few million years. In larger mass (k10 7 M ) halos, the ionization front remains to be of D-type over the lifetime of the massive star, the H ii region is confined well inside the virial radius, and the escape fractions are essentially zero. We derive an analytic formula that reproduces well the results of our simulations for the critical halo mass below which the gas is completely ionized. We discuss immediate implications of the present results for the star formation history and early reionization of the universe.

Abstract. We present a newly measured X-ray temperature function of galaxy clusters using a complete flux-limited sample of 61 clusters. The sample is constructed with the total survey area of 8.14 steradians and the flux limit of 1.99 × 10 −11 ergs s −1 cm −2 in the 0.1-2.4 keV band. X-ray temperatures and fluxes of the sample clusters were accurately measured with ASCA and ROSAT data. The derived temperature function covers an unprecedentedly wide temperature range of 1.4-11 keV. By fitting these data with theoretically predicted temperature functions given by the Press-Schechter formalism together with a recent formation approximation and the CDM power spectrum, we obtained tight and individual constraints on Ωm,0 and σ8. We also employed the Formation-Epoch model in which the distribution in the formation epoch of clusters as well as the temperature evolution are taken into account, showing significantly different results. Systematics caused by the uncertainty in the mass-temperature relation are studied and found to be as large as the statistical errors.

We present angular power spectra of the cosmic microwave background radiation anisotropy due to fluctuations of the Sunyaev-Zeldovich (SZ) effect through clusters of galaxies. A contribution from the correlation among clusters, which has been neglected in previous analyses, is especially focused on. Employing the evolving linear bias factor based on the Press-Schechter formalism, we find that the clustering contribution amounts to 20%-30% of the Poissonian contribution at degree angular scales. If we exclude clusters in the local universe, it even exceeds the Poissonian noise and makes the dominant contribution to the angular power spectrum. As a concrete example, we demonstrate the subtraction of the ROSAT X-ray and Planck SZ flux-limited cluster samples. It indicates that we should include the clustering effect in the analysis of the SZ fluctuations. We further find that the degree scale spectra essentially depend upon the normalization of the density fluctuations, i.e., sigma8, and the gas mass fraction of the cluster, rather than the density parameter of the universe and details of cluster evolution models. Our results show that the SZ fluctuations at the degree scale will provide a possible measure of sigma8, while the arcminute spectra will provide a probe of the cluster evolution. In addition, the clustering spectrum will give us valuable information on the bias at high redshift, if we can detect it by removing X-ray or SZ luminous clusters.

We present the results of three-dimensional radiation hydrodynamics simulations of the formation and evolution of early H ii/He iii regions around the first stars. Cooling and recollapse of the gas in the relic H ii region is also followed in a full cosmological context, until second-generation stars are formed. We first carry out ray-tracing simulations of ionizing radiation transfer from the first star. Hydrodynamics is directly coupled with photoionization heating as well as radiative and chemical cooling. The photoionized hot gas is evacuated out of the host halo at a velocity of $30 km s À1. This radiative feedback effect quenches further star formation within the halo for over tens to a hundred million years. We show that the thermal and chemical evolution of the photoionized gas in the relic H ii region is remarkably different from that of a neutral primordial gas. Efficient molecular hydrogen production in the recombining gas enables it to cool to $100 K, where fractionation of HD/H 2 occurs. The gas further cools by HD line cooling down to a few tens of kelvins. Interestingly, at high redshifts (z > 10), the minimum gas temperature is limited by that of the cosmic microwave background with T CMB ¼ 2:728(1þ z). The gas cloud experiences runaway collapse when its mass is $40 M , which is significantly smaller than a typical clump mass of $200Y300 M for early primordial gas clouds. We argue that massive, rather than very massive, primordial stars may form in the relic H ii region. Such stars might be responsible for early metal enrichment of the interstellar medium from which recently discovered hyperYmetal-poor stars were born.