Does the Number Density of Elliptical Galaxies Change at z<1?

We have performed a detailed V/Vmax test for a sample of the Canada-France Redshift Survey (CFRS) for the purpose of examining whether the comoving number density of field galaxies changes significantly at redshifts of z<1. Taking into account the luminosity evolution of galaxies which depends on their morphological type through different history of star formation, we obtain \sim 0.5 in the range of 0.3<z<0.8, where reliable redshifts were secured by spectroscopy of either absorption or emission lines for the CFRS sample. This indicates that a picture of mild evolution of field galaxies without significant mergers is consistent with the CFRS data. Early-type galaxies, selected by their (V-I)_{AB} color, become unnaturally deficient in number at z>0.8 due to the selection bias, thereby causing a fictitious decrease of . We therefore conclude that a reasonable choice of upper bound of redshift z \sim 0.8 in the V/Vmax test saves the picture of passive evolution for field ellipticals in the CFRS sample, which was rejected by Kauffman, Charlot, & White (1996) without confining the redshift range. However, about 10% of the CFRS sample consists of galaxies having colors much bluer than predicted for irregular galaxies, and their \avmax is significantly larger than 0.5. We discuss this population of extremely blue galaxies in terms of starburst that has just turned on at their observed redshifts.Comment: 11 pages including 3 figures, to appear in ApJ Letter

Perturbative Analysis of Adaptive Smoothing Methods in Quantifying Large-Scale Structure

Smoothing operation to make continuous density field from observed point-like distribution of galaxies is crucially important for topological or morphological analysis of the large-scale structure, such as, the genus statistics or the area statistics (equivalently the level crossing statistics). It has been pointed out that the adaptive smoothing filters are more efficient tools to resolve cosmic structures than the traditional spatially fixed filters. We study weakly nonlinear effects caused by two representative adaptive methods often used in smoothed hydrodynamical particle (SPH) simulations. Using framework of second-order perturbation theory, we calculate the generalized skewness parameters for the adaptive methods in the case of initially power-law fluctuations. Then we apply the multidimensional Edgeworth expansion method and investigate weakly nonlinear evolution of the genus statistics and the area statistics. Isodensity contour surfaces are often parameterized by the volume fraction of the regions above a given density threshold. We also discuss this parameterization method in perturbative manner.Comment: 42 pages including 9 figure, ApJ 537 in pres

Quasar Candidates in the Hubble Deep Field

We focus on the search for unresolved faint quasars and AGN in the crude combine images using a multicolor imaging analysis that has proven very successful in recent years. Quasar selection was carried out both in multicolor space and in "profile space," defined as the multi-parameter space formed by the radial profiles of the objects in the different images. By combining the dither frames available for each filter, we were able to obtain well-sampled radial profiles of the objects and measure their deviation from that of a stellar source. We also generated synthetic quasar spectra in the range 1.0 < z < 5.5 and computed expected quasar colors. We determined that the data are 90% complete for point sources at 26.2, 28.0, 27.8, 26.8 in the F300W, F450W, F606W and F814W filters, respectively. We find 41 compact objects in the HDF: 8 pointlike objects with colors consistent with quasars or stars, 18 stars, and 15 slightly resolved objects, 12 of which have colors consistent with quasars or stars. We estimate the upper limit of unresolved and slightly resolved quasars/AGNs with V < 27.0 and z < 3.5 to be 20 objects (16,200 per deg^2). We find good agreement among authors on the number of stars and the lack of quasar candidates with z > 3.5. We find more quasar candidates than previous work because of our more extensive modeling and use of all of the available color information. (abridged)Comment: We have clarified our discussion and conclusions, added some references and removed the appendix, which is now available from the first author. 37 pages including 10 embedded postscript figures and 6 tables. To appear in the Feb. 99 issue of A

Renormalized Cosmological Perturbation Theory

We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing non-linearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbation theory, where different loop corrections can become of the same magnitude in the nonlinear regime. In companion papers we compare the resummation of the propagator with numerical simulations, and apply these results to the calculation of the nonlinear power spectrum. Remarkably, the expressions in renormalized perturbation theory can be written in a way that closely resembles the halo model.Comment: 22 pages, 13 figures. Final (published) versio

Tests of Statistical Methods for Estimating Galaxy Luminosity Function and Applications to the Hubble Deep Field

We studied the statistical methods for the estimation of the luminosity function (LF) of galaxies. We focused on four nonparametric estimators: $1/V_{\rm max}$ estimator, maximum-likelihood estimator of Efstathiou et al. (1988), Cho{\l}oniewski's estimator, and improved Lynden-Bell's estimator. The performance of the $1/V_{\rm max}$ estimator has been recently questioned, especially for the faint-end estimation of the LF. We improved these estimators for the studies of the distant Universe, and examined their performances for various classes of functional forms by Monte Carlo simulations. We also applied these estimation methods to the mock 2dF redshift survey catalog prepared by Cole et al. (1998). We found that $1/V_{\rm max}$ estimator yields a completely unbiased result if there is no inhomogeneity, but is not robust against clusters or voids. This is consistent with the well-known results, and we did not confirm the bias trend of $1/V_{\rm max}$ estimator claimed by Willmer (1997) in the case of homogeneous sample. We also found that the other three maximum-likelihood type estimators are quite robust and give consistent results with each other. In practice we recommend Cho{\l}oniewski's estimator for two reasons: 1. it simultaneously provides the shape and normalization of the LF; 2. it is the fastest among these four estimators, because of the algorithmic simplicity. Then, we analyzed the photometric redshift data of the Hubble Deep Field prepared by Fern\'{a}ndez-Soto et al. (1999) using the above four methods. We also derived luminosity density $\rho_{\rm L}$ at $B$- and $I$-band. Our $B$-band estimation is roughly consistent with that of Sawicki, Lin, & Yee (1997), but a few times lower at $2.0 < z < 3.0$. The evolution of $\rho_{\rm L}(I)$ is found to be less prominent.Comment: To appear in ApJS July 2000 issue. 36 page

The Halo Occupation Distribution: Towards an Empirical Determination of the Relation Between Galaxies and Mass

We investigate galaxy bias in the framework of the ``Halo Occupation Distribution'' (HOD), which defines the bias of a population of galaxies by the conditional probability P(N|M) that a dark matter halo of virial mass M contains N galaxies, together with prescriptions that specify the relative spatial and velocity distributions of galaxies and dark matter within halos. By populating the halos of a cosmological N-body simulation using a variety of HOD models, we examine the sensitivity of different galaxy clustering statistics to properties of the HOD. The galaxy correlation function responds to different aspects of P(N|M) on different scales. Obtaining the observed power-law form of xi(r) requires rather specific combinations of HOD parameters, implying a strong constraint on the physics of galaxy formation; the success of numerical and semi-analytic models in reproducing this form is entirely non-trivial. Other clustering statistics such as the galaxy-mass correlation function, the bispectrum, the void probability function, the pairwise velocity dispersion, and the group multiplicity function are sensitive to different combinations of HOD parameters and thus provide complementary information about galaxy bias. We outline a strategy for determining the HOD empirically from redshift survey data. This method starts from an assumed cosmological model, but we argue that cosmological and HOD parameters will have non-degenerate effects on galaxy clustering, so that a substantially incorrect cosmological model will not reproduce the observations for any choice of HOD. Empirical determinations of the HOD as a function of galaxy type from the 2dF and SDSS redshift surveys will provide a detailed target for theories of galaxy formation, insight into the origin of galaxy properties, and sharper tests of cosmological models.Comment: 60 pages + 21 eps figures. Replaced with accepted ApJ version. Minor changes + added reference

A Look At Three Different Scenarios for Bulge Formation

In this paper, we present three qualitatively different scenarios for bulge formation: a secular evolution model in which bulges form after disks and undergo several central starbursts, a primordial collapse model in which bulges and disks form simultaneously, and an early bulge formation model in which bulges form prior to disks. We normalize our models to the local z=0 observations of de Jong & van der Kruit (1994) and Peletier & Balcells (1996) and make comparisons with high redshift observations. We consider model predictions relating directly to bulge-to-disk properties. As expected, smaller bulge-to-disk ratios and bluer bulge colors are predicted by the secular evolution model at all redshifts, although uncertainties in the data are currently too large to differentiate strongly between the models.Comment: 19 pages, 6 figures, accepted for publication in the Astrophysical Journa