4,300 research outputs found
Constrained realizations and minimum variance reconstruction of non-Gaussian random fields
With appropriate modifications, the Hoffman--Ribak algorithm that constructs
constrained realizations of Gaussian random fields having the correct ensemble
properties can also be used to construct constrained realizations of those
non-Gaussian random fields that are obtained by transformations of an
underlying Gaussian field. For example, constrained realizations of lognormal,
generalized Rayleigh, and chi-squared fields having degrees of freedom
constructed this way will have the correct ensemble properties. The lognormal
field is considered in detail. For reconstructing Gaussian random fields,
constrained realization techniques are similar to reconstructions obtained
using minimum variance techniques. A comparison of this constrained realization
approach with minimum variance, Wiener filter reconstruction techniques, in the
context of lognormal random fields, is also included. The resulting
prescriptions for constructing constrained realizations as well as minimum
variance reconstructions of lognormal random fields are useful for
reconstructing masked regions in galaxy catalogues on smaller scales than
previously possible, for assessing the statistical significance of small-scale
features in the microwave background radiation, and for generating certain
non-Gaussian initial conditions for -body simulations.Comment: 12 pages, gzipped postscript, MNRAS, in pres
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
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
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
One step beyond: The excursion set approach with correlated steps
We provide a simple formula that accurately approximates the first crossing
distribution of barriers having a wide variety of shapes, by random walks with
a wide range of correlations between steps. Special cases of it are useful for
estimating halo abundances, evolution, and bias, as well as the nonlinear
counts in cells distribution. We discuss how it can be extended to allow for
the dependence of the barrier on quantities other than overdensity, to
construct an excursion set model for peaks, and to show why assembly and scale
dependent bias are generic even at the linear level.Comment: 5 pages, 1 figure. Uses mn2e class styl
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
Linear theory and velocity correlations of clusters
Linear theory provides a reasonable description of the velocity correlations
of biased tracers both perpendicular and parallel to the line of separation,
provided one accounts for the fact that the measurement is almost always made
using pair-weighted statistics. This introduces an additional term which, for
sufficiently biased tracers, may be large. Previous work suggesting that linear
theory was grossly in error for the components parallel to the line of
separation ignored this term.Comment: 5 pages, 2 figures, MNRAS accepte
The importance of stepping up in the excursion set approach
Recently, we provided a simple but accurate formula which closely
approximates the first crossing distribution associated with random walks
having correlated steps. The approximation is accurate for the wide range of
barrier shapes of current interest and is based on the requirement that, in
addition to having the right height, the walk must cross the barrier going
upwards. Therefore, it only requires knowledge of the bivariate distribution of
the walk height and slope, and is particularly useful for excursion set models
of the massive end of the halo mass function. However, it diverges at lower
masses. We show how to cure this divergence by using a formulation which
requires knowledge of just one other variable. While our analysis is general,
we use examples based on Gaussian initial conditions to illustrate our results.
Our formulation, which is simple and fast, yields excellent agreement with the
considerably more computationally expensive Monte-Carlo solution of the first
crossing distribution, for a wide variety of moving barriers, even at very low
masses.Comment: 10 pages, 5 figure
- …