Analytical Approximations to Galaxy Clustering

We discuss some recent progress in constructing analytic approximations to the galaxy clustering. We show that successful models can be constructed for the clustering of both dark matter and dark matter haloes. Our understanding of galaxy clustering and galaxy biasing can be greatly enhanced by these models.Comment: 10 pages, Latex, crckapb.sty, figure included, to appear in the proceedings of Ringberg Workshop on Large-Scale Structure (ed. D. Hamilton; Kluwer Academic Publishers

Broadband boundary effects on Brownian motion

Brownian motion of particles in confined fluids is important for many applications, yet the effects of the boundary over a wide range of time scales are still not well understood. We report high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately flat wall. At short distances we observe anisotropic Brownian motion with respect to the wall. We find that surface confinement not only occurs in the long time scale diffusive regime but also in the short time scale ballistic regime, and the velocity autocorrelation function of the Brownian particle decays faster than that of a particle in bulk fluid. Furthermore, at low frequencies the thermal force loses its color due to the reflected flow from the no-slip boundary. The power spectrum of the thermal force on the particle near a no-slip boundary becomes flat at low frequencies. This detailed understanding of boundary effects on Brownian motion opens a door to developing a 3D microscope using particles as remote sensors.Sid W. Richardson FoundationR. A. Welch Foundation F-1258Physic

Low thrust viscous nozzle flow fields prediction

A Navier-Stokes code was developed for low thrust viscous nozzle flow field prediction. An implicit finite volume in an arbitrary curvilinear coordinate system lower-upper (LU) scheme is used to solve the governing Navier-Stokes equations and species transportation equations. Sample calculations of carbon dioxide nozzle flow are presented to verify the validity and efficiency of this code. The computer results are in reasonable agreement with the experimental data

An Analytical Approach to Inhomogeneous Structure Formation

We develop an analytical formalism that is suitable for studying inhomogeneous structure formation, by studying the joint statistics of dark matter halos forming at two points. Extending the Bond et al. (1991) derivation of the mass function of virialized halos, based on excursion sets, we derive an approximate analytical expression for the ``bivariate'' mass function of halos forming at two redshifts and separated by a fixed comoving Lagrangian distance. Our approach also leads to a self-consistent expression for the nonlinear biasing and correlation function of halos, generalizing a number of previous results including those by Kaiser (1984) and Mo & White (1996). We compare our approximate solutions to exact numerical results within the excursion-set framework and find them to be consistent to within 2% over a wide range of parameters. Our formalism can be used to study various feedback effects during galaxy formation analytically, as well as to simply construct observable quantities dependent on the spatial distribution of objects. A code that implements our method is publicly available at http://www.arcetri.astro.it/~evan/GeminiComment: 41 Pages, 11 figures, published in ApJ, 571, 585. Reference added, Figure 2 axis relabele

Accurate determination of the Lagrangian bias for the dark matter halos

We use a new method, the cross power spectrum between the linear density field and the halo number density field, to measure the Lagrangian bias for dark matter halos. The method has several important advantages over the conventional correlation function analysis. By applying this method to a set of high-resolution simulations of 256^3 particles, we have accurately determined the Lagrangian bias, over 4 magnitudes in halo mass, for four scale-free models with the index n=-0.5, -1.0, -1.5 and -2.0 and three typical CDM models. Our result for massive halos with $M \ge M_*$ ($M_*$ is a characteristic non-linear mass) is in very good agreement with the analytical formula of Mo & White for the Lagrangian bias, but the analytical formula significantly underestimates the Lagrangian clustering for the less massive halos $M < M_*. Our simulation result however can be satisfactorily described, with an accuracy better than 15%, by the fitting formula of Jing for Eulerian bias under the assumption that the Lagrangian clustering and the Eulerian clustering are related with a linear mapping. It implies that it is the failure of the Press-Schechter theories for describing the formation of small halos that leads to the inaccuracy of the Mo & White formula for the Eulerian bias. The non-linear mapping between the Lagrangian clustering and the Eulerian clustering, which was speculated as another possible cause for the inaccuracy of the Mo & White formula, must at most have a second-order effect. Our result indicates that the halo formation model adopted by the Press-Schechter theories must be improved.Comment: Minor changes; accepted for publication in ApJ (Letters) ; 11 pages with 2 figures include

Formation time distribution of dark matter haloes: theories versus N-body simulations

This paper uses numerical simulations to test the formation time distribution of dark matter haloes predicted by the analytic excursion set approaches. The formation time distribution is closely linked to the conditional mass function and this test is therefore an indirect probe of this distribution. The excursion set models tested are the extended Press-Schechter (EPS) model, the ellipsoidal collapse (EC) model, and the non-spherical collapse boundary (NCB) model. Three sets of simulations (6 realizations) have been used to investigate the halo formation time distribution for halo masses ranging from dwarf-galaxy like haloes ($M=10^{-3} M_*$, where $M_*$ is the characteristic non-linear mass scale) to massive haloes of $M=8.7 M_*$. None of the models can match the simulation results at both high and low redshift. In particular, dark matter haloes formed generally earlier in our simulations than predicted by the EPS model. This discrepancy might help explain why semi-analytic models of galaxy formation, based on EPS merger trees, under-predict the number of high redshift galaxies compared with recent observations.Comment: 7 pages, 5 figures, accepted for publication in MNRA

Evolution of Lyman Break Galaxies Beyond Redshift Four

The formation rate of luminous galaxies seems to be roughly constant from z~2 to z~4 from the recent observations of Lyman break galaxies (LBGs) (Steidel et al 1999). The abundance of luminous quasars, on the other hand, appears to drop off by a factor of more than twenty from z~2 to z~5 (Warren, Hewett, & Osmer 1994; Schmidt, Schneider, & Gunn 1995). The difference in evolution between these two classes of objects in the overlapping, observed redshift range, z=2-4, can be explained naturally, if we assume that quasar activity is triggered by mergers of luminous LBGs and one quasar lifetime is ~10^{7-8} yrs. If this merger scenario holds at higher redshift, for the evolutions of these two classes of objects to be consistent at z>4, the formation rate of luminous LBGs is expected to drop off at least as rapidly as exp(-(z-4)^{6/5}) at z>4.Comment: in press, ApJ Letters, 15 latex pages plus 1 fi

Toward an Improved Analytical Description of Lagrangian Bias

We carry out a detailed numerical investigation of the spatial correlation function of the initial positions of cosmological dark matter halos. In this Lagrangian coordinate system, which is especially useful for analytic studies of cosmological feedback, we are able to construct cross-correlation functions of objects with varying masses and formation redshifts and compare them with a variety of analytical approaches. For the case in which both formation redshifts are equal, we find good agreement between our numerical results and the bivariate model of Scannapieco & Barkana (2002; SB02) at all masses, redshifts, and separations, while the model of Porciani et al. (1998) does well for all parameters except for objects with different masses at small separations. We find that the standard mapping between Lagrangian and Eulerian bias performs well for rare objects at all separations, but fails if the objects are highly-nonlinear (low-sigma) peaks. In the Lagrangian case in which the formation redshifts differ, the SB02 model does well for all separations and combinations of masses, apart from a discrepancy at small separations in situations in which the smaller object is formed earlier and the difference between redshifts or masses is large. As this same limitation arises in the standard approach to the single-point progenitor distribution developed by Lacey & Cole (1993), we conclude that a more complete understanding of the progenitor distribution is the most important outstanding issue in the analytic modeling of Lagrangian bias.Comment: 22 pages, 8 figures, ApJ, in pres

Low Redshift QSO Lyman alpha Absorption Line Systems Associated with Galaxies

In this paper we present Monte-Carlo simulations of Lyman alpha absorption systems which originate in galactic haloes, galaxy discs and dark matter (DM) satellites around big central haloes. It is found that for strong Lyman alpha absorption lines galactic haloes and satellites can explain ~20% and 40% of the line number density of QSO absorption line key project respectively. If big galaxies indeed possess such large numbers of DM satellites and they possess gas, these satellites may play an important role for strong Lyman alpha lines. However the predicted number density of Lyman-limit systems by satellites is \~0.1 (per unit redshift), which is four times smaller than that by halo clouds. Including galactic haloes, satellites and HI discs of spirals, the predicted number density of strong lines can be as much as 60% of the HST result. The models can also predict all of the observed Lyman-limit systems. The average covering factor within 250 kpc/h is estimated to be ~0.36. And the effective absorption radius of a galaxy is estimated to be ~150 kpc/h. The models predict W_r propto rho^{-0.5} L_B^{0.15} (1+z)^{-0.5}. We study the selection effects of selection criteria similar to the imaging and spectroscopic surveys. We simulate mock observations through known QSO lines-of-sight and find that selection effects can statistically tighten the dependence of line width on projected distance. (abridged)Comment: 23 pages, 9 postscript figures; references updated, minor change in section