The Effect of Spatial Correlations on Merger Trees of Dark Matter Haloes

The effects of spatial correlations of density fluctuations on merger histories of dark matter haloes (so-called `{\it merger trees}') are analysed. We compare the mass functions of dark haloes derived by a new method for calculating merger trees, that proposed by Rodrigues \& Thomas (RT), with those given by other methods such as the Block model, the Press-Schechter formula and our own formula in which the mass functions are analytically expressed in a way that takes into consideration the spatial correlations. It is found that the mass functions given by the new method are well fit by those given by our formula. We believe that new method (RT) {\it naturally} and correctly takes into account the spatial correlations of the density fluctuations due to a calculated, grid-based realisation of the density fluctuations and so is very useful for estimating the merger tree accurately in a way that takes into consideration spatial correlations. Moreover, by applying our formula, we present an analytic expression which reproduces the mass function derived by the Block model. We therefore show clearly why and how the mass functions given by the new method and the Block model are different from each other. Furthermore, we note that the construction of merger trees is sensitive to the criterion of collapse and merging of overlapped haloes in cases in which two or more haloes happen to overlap. In fact, it is shown that the mass function is very much affected when the criterion of overlapping is changed.Comment: Submitted to MNRAS; 10 pages MN latex file, including 5 figures (epsf

Astrometric mock observations for determining the local dark matter density

To determine the local dark matter density (LDMD) of the solar system is a classical problem in astronomy. Recently, a novel method of determining the LDMD from stellar distribution and vertical velocity dispersion profiles perpendicular to the Galactic plane was devised. This method has the advantage of abolishing conventional approximations and using only a few assumptions. Our aims are to carefully scrutinize this method and to examine influences by uncertainties of astrometric observations. We discuss how the determinations of the LDMD vary with observational precisions on parallax, proper motion, and line-of-sight velocity measurements. To examine the influences by the observational imprecision, we created mock observation data for stars that are dynamical tracers based on an analytical galaxy model and applied parametrized observational errors to the mock data. We evaluated the accuracy of determining the LDMD by applying the method to the mock data. In addition, we estimated a sample size and observational precision required to determine the LDMD with accuracy. We find that the method is capable of determining the LDMD with accuracy if the sample size and observational precisions are satisfactory. The random errors of parallaxes and proper motions can cause systematic overestimation of the LDMD. We estimate the required precisions of the parallax measurements to be approximately 0.1-0.3 milliarcseconds at 1 kpc away from the Sun; the proper motion precisions do not seem to be as important as the parallaxes. From these results, we expect that using the Hipparcos catalog would overestimate the LDMD because of the imprecise parallax measurements if this method is applied; however, we emphasize the capability of the method. We expect that Gaia will provide data precise enough to determine the LDMD.Comment: 16 pages, 14 figures, A&A accepte

The Detection Rate of Molecular Gas in Elliptical Galaxies: Constraints on Galaxy Formation Theories

In order to constrain parameters in galaxy formation theories, especially those for a star formation process, we investigate cold gas in elliptical galaxies. We calculate the detection rate of cold gas in them using a semi-analytic model of galaxy formation and compare it with observations. We show that the model with a long star formation time-scale (~20 Gyr) is inconsistent with observations. Thus, some mechanisms of reducing the mass of interstellar medium, such as the consumption of molecular gas by star formation and/or reheating from supernovae, are certainly effective in galaxies. Our model predicts that star formation induced when galaxies in a halo collide each other reduces the cold gas left until the present. However, we find that the reduction through random collisions of satellite (non-central) galaxies in mean free time-scale in a halo is not required to explain the observations. This may imply that the collisions and mergers between satellite galaxies do not occur so often in clusters or that they do not stimulate the star formation activity as much as the simple collision model we adopted. For cD galaxies, the predicted detection rate of cold gas is consistent with observations as long as the transformation of hot gas into cold gas is prevented in halos whose circular velocities are larger than 500 km s^-1. Moreover, we find that the cold gas brought into cDs through captures of gas-rich galaxies is little. We also show that the fraction of galaxies with observable cold gas should be small for cluster ellipticals in comparison with that for field ellipticals.Comment: 6 pages, accepted by PAS

Algebraic properties of some varieties of central loops

Isotopes of C-loops with unique non-identity squares are shown to be both C-loops and A-loops. The relationship between C-loops and Steiner loops is further studied. Central loops with the weak and cross inverse properties are also investigated. C-loops are found to be Osborn loops if every element in them are squares.Comment: 20 page

HI-selected Galaxies as a probe of Quasar Absorption Systems

We investigate the properties of HI-rich galaxies detected in blind radio surveys within the hierarchical structure formation scenario using a semi-analytic model of galaxy formation. By drawing a detailed comparison between the properties of HI-selected galaxies and HI absorption systems, we argue a link between the local galaxy population and quasar absorption systems, particularly for Damped Ly-alpha absorption (DLA) systems and sub-DLA systems. First, we evaluate how many HI-selected galaxies exhibit HI column densities as high as those of DLA systems. We find that HI-selected galaxies with HI masses M(HI) > 10^8 solar masses have gaseous disks that produce HI column densities comparable to those of DLA systems. We conclude that DLA galaxies where the HI column densities are as high as those of DLA systems, contribute significantly to the population of HI-selected galaxies at M(HI) > 10^8 solar masses. Second, we find that star formation rates (SFRs) correlate tightly with HI masses rather than B- (and J-) band luminosities. In the low-mass range M(HI) < 10^8 solar masses, sub-DLA galaxies replace DLA galaxies as the dominant population. The number fraction of sub-DLA galaxies relative to galaxies reaches 40%-60% at HI masses 10^8 solar masses and 30%-80% at 10^7 solar masses. The HI-selected galaxies at 10^7 solar masses are a strong probe of sub-DLA systems that place stringent constraints on galaxy formation and evolution.Comment: 25 pages, 13 figures, Accepted for publication in the Astrophysical Journa