6 research outputs found
Local Lagrangian Approximations for the Evolution of the Density Distribution Function in Large-Scale Structure
We examine local Lagrangian approximations for the gravitational evolution of
the density distribution function. In these approximations, the final density
at a Lagrangian point q at a time t is taken to be a function only of t and of
the initial density at the same Lagrangian point. A general expression is given
for the evolved density distribution function for such approximations, and we
show that the vertex generating function for a local Lagrangian mapping applied
to an initially Gaussian density field bears a simple relation to the mapping
itself. Using this result, we design a local Lagrangian mapping which
reproduces nearly exactly the hierarchical amplitudes given by perturbation
theory for gravitational evolution. When extended to smoothed density fields
and applied to Gaussian initial conditions, this mapping produces a final
density distribution function in excellent agreement with full numerical
simulations of gravitational clustering. We also examine the application of
these local Lagrangian approximations to non-Gaussian initial conditions.Comment: LaTeX, 22 pages, and 11 postscript figure
Skewness of the Large-Scale Velocity Divergence from Non-Gaussian Initial Conditions
We compute the skewness and the corresponding hierarchical amplitude
of the divergence of the velocity field for arbitrary non-Gaussian
initial conditions. We find that qualitatively resembles the
corresponding hierarchical amplitude for the density field, , in that it
contains a term proportional to the initial skewness, which decays inversely as
the linear growth factor, plus a constant term which differs from the
corresponding Gaussian term by a complex function of the initial three- and
four- point functions. We extend the results for and with
non-Gaussian initial conditions to evolved fields smoothed with a spherical
tophat window function. We show that certain linear combinations, namely , , and , lead to expressions which are
much simpler, for non-Gaussian initial conditions, than and (or
and ) considered separately.Comment: 13 pages, latex, no figure
The Topology of Large Scale Structure in the 1.2 Jy IRAS Redshift Survey
We measure the topology (genus) of isodensity contour surfaces in volume
limited subsets of the 1.2 Jy IRAS redshift survey, for smoothing scales
\lambda=4\hmpc, 7\hmpc, and 12\hmpc. At 12\hmpc, the observed genus
curve has a symmetric form similar to that predicted for a Gaussian random
field. At the shorter smoothing lengths, the observed genus curve shows a
modest shift in the direction of an isolated cluster or ``meatball'' topology.
We use mock catalogs drawn from cosmological N-body simulations to investigate
the systematic biases that affect topology measurements in samples of this size
and to determine the full covariance matrix of the expected random errors. We
incorporate the error correlations into our evaluations of theoretical models,
obtaining both frequentist assessments of absolute goodness-of-fit and Bayesian
assessments of models' relative likelihoods. We compare the observed topology
of the 1.2 Jy survey to the predictions of dynamically evolved, unbiased,
gravitational instability models that have Gaussian initial conditions. The
model with an , power-law initial power spectrum achieves the best
overall agreement with the data, though models with a low-density cold dark
matter power spectrum and an power-law spectrum are also consistent. The
observed topology is inconsistent with an initially Gaussian model that has
, and it is strongly inconsistent with a Voronoi foam model, which has a
non-Gaussian, bubble topology.Comment: ApJ submitted, 39 pages, LaTeX(aasms4), 12 figures, 1 Tabl