1,733 research outputs found
Introduction to Focus Issue: Lagrangian Coherent Structures
The topic of Lagrangian coherent structures (LCS) has been a rapidly growing area of research in nonlinear dynamics for almost a decade. It provides a means to rigorously define and detect transport barriers in dynamical systems with arbitrary time dependence and has a wealth of applications, particularly to fluid flow problems. Here, we give a short introduction to the topic of LCS and review the new work presented in this Focus Issue
Eulerian bias and the galaxy density field
We investigate the effects on cosmological clustering statistics of empirical
biasing, where the galaxy distribution is a local transformation of the
present-day Eulerian density field. The effects of the suppression of galaxy
numbers in voids, and their enhancement in regions of high density, are
considered, independently and in combination. We compare results from numerical
simulations with the predictions of simple analytic models. We find that the
bias is generally scale-dependent, so that the shape of the galaxy power
spectrum differs from that of the underlying mass distribution. The degree of
bias is always a monotonic function of scale, tending to an asymptotic value on
scales where the density fluctuations are linear. The scale dependence is often
rather weak, with many reasonable prescriptions giving a bias which is nearly
independent of scale. We have investigated whether such an Eulerian bias can
reconcile a range of theoretical power spectra with the twin requirements of
fitting the galaxy power spectrum and reproducing the observed mass-to-light
ratios in clusters. It is not possible to satisfy these constraints for any
member of the family of CDM-like power spectra in an Einstein - de Sitter
universe when normalised to match COBE on large scales and galaxy cluster
abundances on intermediate scales. We discuss what modifications of the mass
power spectrum might produce agreement with the observational data.Comment: 14 pages, LaTeX (using mn.sty, epsfig), 17 Postscript figures
included. Accepted for publication in MNRA
Halo abundances within the cosmic web
We investigate the dependence of the mass function of dark-matter haloes on
their environment within the cosmic web of large-scale structure. A dependence
of the halo mass function on large-scale mean density is a standard element of
cosmological theory, allowing mass-dependent biasing to be understood via the
peak-background split. On the assumption of a Gaussian density field, this
analysis can be extended to ask how the mass function depends on the
geometrical environment: clusters, filaments, sheets and voids, as classified
via the tidal tensor (the Hessian matrix of the gravitational potential). In
linear theory, the problem can be solved exactly, and the result is
attractively simple: the conditional mass function has no explicit dependence
on the local tidal field, and is a function only of the local density on the
filtering scale used to define the tidal tensor. There is nevertheless a strong
implicit predicted dependence on geometrical environment, because the local
density couples statistically to the derivatives of the potential. We compute
the predictions of this model and study the limits of their validity by
comparing them to results deduced empirically from -body simulations. We
have verified that, to a good approximation, the abundance of haloes in
different environments depends only on their densities, and not on their tidal
structure. In this sense we find relative differences between halo abundances
in different environments with the same density which are smaller than 13%.
Furthermore, for sufficiently large filtering scales, the agreement with the
theoretical prediction is good, although there are important deviations from
the Gaussian prediction at small, non-linear scales. We discuss how to obtain
improved predictions in this regime, using the 'effective-universe' approach.Comment: 14 pages, 6 figures. Revision matching journal versio
Fourier analysis of luminosity-dependent galaxy clustering
We extend the Fourier transform based method for the analysis of galaxy
redshift surveys of Feldman, Kaiser & Peacock (1994: FKP) to model
luminosity-dependent clustering. In a magnitude limited survey, galaxies at
high redshift are more luminous on average than galaxies at low redshift.
Galaxy clustering is observed to increase with luminosity, so the inferred
density field is effectively multiplied by an increasing function of radius.
This has the potential to distort the shape of the recovered power spectrum. In
this paper we present an extension of the FKP analysis method to incorporate
this effect, and present revised optimal weights to maximize the precision of
such an analysis. The method is tested and its accuracy assessed using mock
catalogues of the 2-degree field galaxy redshift survey (2dFGRS). We also show
that the systematic effect caused by ignoring luminosity-dependent bias was
negligible for the initial analysis of the 2dFGRS of Percival et al. (2001).
However, future surveys, sensitive to larger scales, or covering a wider range
of galaxy luminosities will benefit from this refined method.Comment: 9 pages, 4 figures, accepted for publication in MNRA
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