The environmental dependence of clustering in hierarchical models

In hierarchical models, density fluctuations on different scales are correlated. This induces correlations between dark halo masses, their formation histories, and their larger-scale environments. In turn, this produces a correlation between galaxy properties and environment. This correlation is entirely statistical in nature. We show how the observed clustering of galaxies can be used to quantify the importance of this statistical correlation relative to other physical effects which may also give rise to correlations between the properties of galaxies and their surroundings. We also develop a halo model description of this environmental dependence of clustering.Comment: 11 pages, 6 figures, MNRAS in pres

Halo abundances and counts-in-cells: The excursion set approach with correlated steps

The Excursion Set approach has been used to make predictions for a number of interesting quantities in studies of nonlinear hierarchical clustering. These include the halo mass function, halo merger rates, halo formation times and masses, halo clustering, analogous quantities for voids, and the distribution of dark matter counts in randomly placed cells. The approach assumes that all these quantities can be mapped to problems involving the first crossing distribution of a suitably chosen barrier by random walks. Most analytic expressions for these distributions ignore the fact that, although different k-modes in the initial Gaussian field are uncorrelated, this is not true in real space: the values of the density field at a given spatial position, when smoothed on different real-space scales, are correlated in a nontrivial way. As a result, the problem is to estimate first crossing distribution by random walks having correlated rather than uncorrelated steps. In 1990, Peacock & Heavens presented a simple approximation for the first crossing distribution of a single barrier of constant height by walks with correlated steps. We show that their approximation can be thought of as a correction to the distribution associated with what we call smooth completely correlated walks. We then use this insight to extend their approach to treat moving barriers, as well as walks that are constrained to pass through a certain point before crossing the barrier. For the latter, we show that a simple rescaling, inspired by bivariate Gaussian statistics, of the unconditional first crossing distribution, accurately describes the conditional distribution, independently of the choice of analytical prescription for the former. In all cases, comparison with Monte-Carlo solutions of the problem shows reasonably good agreement. (Abridged)Comment: 14 pages, 9 figures; v2 -- revised version with explicit demonstration that the original conclusions hold for LCDM, expanded discussion on stochasticity of barrier. Accepted in MNRA

On estimating redshift and luminosity distributions in photometric redshift surveys

The luminosity functions of galaxies and quasars provide invaluable information about galaxy and quasar formation. Estimating the luminosity function from magnitude limited samples is relatively straightforward, provided that the distances to the objects in the sample are known accurately; techniques for doing this have been available for about thirty years. However, distances are usually known accurately for only a small subset of the sample. This is true of the objects in the Sloan Digital Sky Survey, and will be increasingly true of the next generation of deep multi-color photometric surveys. Estimating the luminosity function when distances are only known approximately (e.g., photometric redshifts are available, but spectroscopic redshifts are not) is more difficult. I describe two algorithms which can handle this complication: one is a generalization of the V_max algorithm, and the other is a maximum likelihood approach. Because these methods account for uncertainties in the distance estimate, they impact a broader range of studies. For example, they are useful for studying the abundances of galaxies which are sufficiently nearby that the contribution of peculiar velocity to the spectroscopic redshift is not negligible, so only a noisy estimate of the true distance is available. In this respect, peculiar velocities and photometric redshift errors have similar effects. The methods developed here are also useful for estimating the stellar luminosity function in samples where accurate parallax distances are not available.Comment: 9 pages, 6 figures, submitted to MNRA

Substructure in dark matter halos: Towards a model of the abundance and spatial distribution of subclumps

I develop a model for the abundance and spatial distribution of dark matter subclumps. The model shows that subclumps of massive parent halos formed at earlier times than subclumps of the same mass in lower mass parents; equivalently, halos in dense regions at a given time formed earlier than halos of the same mass in less dense regions. This may provide the basis for interpreting recent observations which indicate that the stellar populations of the most massive elliptical galaxies are also the oldest.Comment: 5 pages, 2 figures, submitted to MNRA

An excursion set model for the distribution of dark matter and dark matter haloes

A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes. In addition to describing the evolution of the dark matter itself, the model allows one to describe the evolution of the Eulerian space distribution of the haloes. It can also be used to describe density profiles, on scales larger than the virial radius, of these haloes, and to quantify the way in which matter flows in and out of Eulerian cells. When the initial Lagrangian space distribution is white noise Gaussian, the model suggests that the Inverse Gaussian distribution should provide a reasonably good approximation to the evolved Eulerian density field, in agreement with numerical simulations. Application of this model to clustering from more general Gaussian initial conditions is discussed at the end.Comment: 15 pages, 5 figures, submitted to MNRAS Sept. 199

Refrigerant and Oil Migration and Retention in Air Conditioning and Refrigeration Systems

Air Conditioning and Refrigeration Project 16

Optimal linear reconstruction of dark matter from halo catalogs

We derive the weight function w(M) to apply to dark-matter halos that minimizes the stochasticity between the weighted halo distribution and its underlying mass density field. The optimal w(M) depends on the range of masses being used in the estimator. In N-body simulations, the Poisson estimator is up to 15 times noisier than the optimal. Implementation of the optimal weight yields significantly lower stochasticity than weighting halos by their mass, bias or equal. Optimal weighting could make cosmological tests based on the matter power spectrum or cross-correlations much more powerful and/or cost-effective. A volume-limited measurement of the mass power spectrum at k=0.2h/Mpc over the entire z<1 universe could ideally be done using only 6 million redshifts of halos with mass M>6\times10^{13}h^{-1}M_\odot (1\times10^{13}) at z=0 (z=1); this is 5 times fewer than the Poisson model predicts. Using halo occupancy distributions (HOD) we find that uniformly-weighted catalogs of luminous red galaxies require >3 times more redshifts than an optimally-weighted halo catalog to reconstruct the mass to the same accuracy. While the mean HODs of galaxies above a threshold luminosity are similar to the optimal w(M), the stochasticity of the halo occupation degrades the mass estimator. Blue or emission-line galaxies are about 100 times less efficient at reconstructing mass than an optimal weighting scheme. This suggests an efficient observational approach of identifying and weighting halos with a deep photo-z survey before conducting a spectroscopic survey. The optimal w(M) and mass-estimator stochasticity predicted by the standard halo model for M>10^{12}h^{-1}M_\odot are in reasonable agreement with our measurements, with the important exceptions that the halos must be assumed to be linearly biased samples of a "halo field" that is distinct from the mass field. (Abridged)Comment: Added Figure 3 to show the scatter between the weighted halo field vs the mass field, Accepted for publication in MNRA