332 research outputs found
Perturbative Growth of Cosmological Clustering II: The Two Point Correlation
We use the BBGKY hierarchy equations to calculate, perturbatively, the lowest
order nonlinear correction to the two point correlation and the pair velocity
for Gaussian initial conditions in a critical density matter dominated
cosmological model. We compare our results with the results obtained using the
hydrodynamic equations which neglect pressure and we find that the two match,
indicating that thare are no effects of multistreaming at this order of
perturbation. We analytically study the effect of small scales on the large
scales by calculating the nonlinear correction for a Dirac delta function
initial two point correlation. We find that the induced two point correlation
has a behaviour at large separations. We have considered a class of
initial conditions where the initial power spectrum at small has the form
with and have numerically calculated the nonlinear
correction to the two point correlation, its average over a sphere and the pair
velocity over a large dynamical range. We find that at small separations the
effect of the nonlinear term is to enhance the clustering whereas at
intermediate scales it can act to either increase or decrease the clustering.
At large scales we find a simple formula which gives a very good fit for the
nonlinear correction in terms of the initial function. This formula explicitly
exhibits the influence of small scales on large scales and because of this
coupling the perturbative treatment breaks down at large scales much before one
would expect it to if the nonlinearity were local in real space. We physically
interpret this formula in terms of a simple diffusion process. We have also
investigated the case and we find that it differs from the other cases in
certain respects. We investigate a recently proposed scaling property ofComment: 41 pages,(including 13 figure) uuencoded, to appear in Ap
The Evolution of Correlation Functions in the Zel'dovich Approximation and its Implications for the Validity of Perturbation Theory
We investigate whether it is possible to study perturbatively the transition
in cosmological clustering between a single streamed flow to a multi streamed
flow. We do this by considereing a system whose dynamics is governed by the
Zel'dovich approximation (ZA) and calculating the evolution of the two point
correlation function using two methods: 1.Distribution functions 2.Hydrodynamic
equations without pressure and vorticity. The latter method breaks down once
multistreaming occurs whereas the former does not. We find that the two methods
give the same results to all orders in a perturbative expansion of the two
point correlation function. We thus conclude that we cannot study the
transition from a single stream flow to a multi-stream flow in a perturbative
expansion. We expect this conclusion to hold even if we use the full
gravitational dynamics (GD) instead of ZA. We use ZA to look at the evolution
of the two point correlation function at large spatial separations and we find
that until the onset of multi-streaming the evolution can be described by a
diffusion process where the linear evolution at large scales gets modified by
the rearrangement of matter on small scales. We compare these results with the
lowest order nonlinear results from GD. We find that the difference is only in
the numerical value of the diffusion coefficient and we interpret this
physically. We also use ZA to study the induced three point correlation
function. At the lowest order we find that, as in the case of GD, the three
point correlation does not necessarily have the hierarchical form. We also find
that at large separations the effect of the higher order terms for the three
point correlatin function is very similar to that for the the two point
correlation and in this case too the evolution can be be described in terms ofComment: 28 pages including 6 figures, Latex, Aastex macros, Accepted in
Astrophysical Journa
Modeling non-linear effects in the redshift space two-point correlation function and its implications for the pairwise velocity dispersion
The anisotropies in the galaxy two-point correlation function measured from
redshift surveys exhibits deviations from the predictions of the linear theory
of redshift space distortion on scales as large 20 Mpc/h where we expect linear
theory to hold in real space. Any attempt at analyzing the anisotropies in the
redshift correlation function and determining the linear distortion parameter
\beta requires these deviations to be correctly modeled and taken into account.
These deviations are usually attributed to galaxy random motions and these are
incorporated in the analysis through a phenomenological model where the linear
redshift correlation is convolved with the random pairwise velocity
distribution function along the line of sight. We show that a substantial part
of the deviations arise from non-linear effects in the mapping from real to
redshift space caused by the coherent flows. Models which incorporate this
effect provide a better fit to N-body results as compared to the
phenomenological model which has only the effect of random motions. We find
that the pairwise velocity dispersion predicted by all the models that we have
considered are in excess of the values determined directly from the N-body
simulations. This indicates a shortcoming in our understanding of the
statistical properties of peculiar velocities and their relation to redshift
distortion.Comment: Minor Revisions, Accepted to MNRA
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