An Indicator of Nonlinear Gravitational Clustering

Alignment of velocity and acceleration before shell crossing, and later misalignment are used to define velocity contrast, an indicator of dynamical state of matter undergoing gravitational collapse. We use this to study bias in clustering properties of dynamically nonlinear mass.Comment: 4 pages, uuencoded postscript file. To appear in 'Clusters, Lensing, and the Future of the Universe' ed. V.Trimble and A.Reisenegge

A New Statistical Indicator to Study Nonlinear Gravitational Clustering and Structure Formation

In an expanding universe, velocity field and gravitational force field are proportional to each other in the linear regime. Neither of these quantities evolve in time and these can be scaled suitably so that the constant of proportionality is unity and velocity and force field are equal. The Zeldovich approximation extends this feature beyond the linear regime, until formation of pancakes. Nonlinear clustering which takes place {\it after} the breakdown of Zeldovich approximation, breaks this relation and the mismatch between these two vectors increases as the evolution proceeds. We suggest that the difference of these two vectors could form the basis for a powerful, new, statistical indicator of nonlinear clustering. We define an indicator called velocity contrast, study its behaviour using N-Body simulations and show that it can be used effectively to delineate the regions where nonlinear clustering has taken place. We discuss several features of this statistical indicator and provide simple analytic models to understand its behaviour. Particles with velocity contrast higher than a threshold have a correlation function which is biased with respect to the original sample. This bias factor is scale dependent and tends to unity at large scales.Comment: 12 pages, 8 figures, LaTeX with uuencoded figures, uses MN.sty and epsf.sty; Discussion has been enlarged to clarify a few points. Introduction has been added. Some figures have change

Critical Index and Fixed Point in the Transfer of Power in Nonlinear Gravitational Clustering

We investigate the transfer of power between different scales and coupling of modes during non-linear evolution of gravitational clustering in an expanding universe. We start with a power spectrum of density fluctuations that is exponentially damped outside a narrow range of scales and use numerical simulations to study evolution of this power spectrum. Non-Linear effects generate power at other scales with most power flowing from larger to smaller scales. The ``cascade'' of power leads to equipartition of energy at smaller scales, implying a power spectrum with index $n\approx -1$. We find that such a spectrum is produced in the range $1 < \delta < 200$ for density contrast $\delta$. This result continues to hold even when small scale power is added to the initial power spectrum. Semi-analytic models for gravitational clustering suggest a tendency for the effective index to move towards a critical index $n_c\approx -1$ in this range. For n<n_c, power in this range grows faster than linear rate, while if n>n_c, it grows at a slower rate - thereby changing the index closer to n_c. At scales larger than the narrow range of scales with initial power, a k^4 tail is produced. We demonstrate that non-linear small scales do not effect the growth of perturbations at larger scales.Comment: Title changed. Added two figures and some discussion. Postscript file containing all the figures is available at http://www.ast.cam.ac.uk/~jasjeet/papers/powspec.ps.gz Accepted for publication in the MNRA

Comments on the size of the simulation box in cosmological N-Body simulations

N-Body simulations are a very important tool in the study of formation of large scale structures. Much of the progress in understanding the physics of high redshift universe and comparison with observations would not have been possible without N-Body simulations. Given the importance of this tool, it is essential to understand its limitations as ignoring the limitations can easily lead to interesting but unreliable results. In this paper we study the limitations arising out of the finite size of simulation volume. This finite size implies that modes larger than the size of the simulation volume are ignored and a truncated power spectrum is simulated. If the simulation volume is large enough then the mass in collapsed haloes expected from the full power spectrum and from the truncated power spectrum should match. We propose a quantitative measure based on this approach that allows us to compute the minimum box size for an N-Body simulation. We find that the required box size for simulations of LCDM model at high redshifts is much larger than is typically used. We can also use this approach to quantify the effect of perturbations at large scales for power law models and we find that if we fix the scale of non-linearity, the required box size becomes very large as the index becomes small. The appropriate box size computed using this approach is also an appropriate choice for the transition scale when tools like MAP (Tormen and Bertschinger, 1996) that add the contribution of the missing power are used.Comment: 7 pages, 8 figures, Accepted for publication in the MNRA