Astronomy and Astrophysics – Astrophysics
Scientific paper
1995-01-14
Mon.Not.Roy.Astron.Soc.276:L25-L29,1995
Astronomy and Astrophysics
Astrophysics
6 pages, uuencoded compressed postscript file, including 2 figures. Significantly revised, matches published version
Scientific paper
Hamilton et al. (1991) proposed a simple formula relating the nonlinear autocorrelation function of the mass distribution to the primordial spectrum of density fluctuations for gravitational clustering in an $\Omega=1$ universe. High resolution N-body simulations show this formula to work well for scale-free spectra $P(k) \propto k^n$ when the spectral index $n\sim 0$, but not when $n \lsim -1$. We show that a modified version of the formula can work well provided its form depends on $n$. This dependence can be derived from a simple physical model for collapse from Gaussian initial conditions. Our modified formula is easy to apply and is an excellent fit to N-body simulations with $0 \leq n \leq -2$. It can also be applied to non-power law initial spectra such as that of the standard Cold Dark Matter model by using the local spectral index at the current nonlinear scale as the effective value of $n$ at any given redshift. We give analytic expressions both for the nonlinear correlation function and for the nonlinear power spectrum.
Jain Bhuvnesh
Mo Hou-Jun
White Simon D. M.
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