Extended perturbation theory for the local density distribution function
Oct, 1996
13 pages
Published in:
- Mon.Not.Roy.Astron.Soc. 287 (1997) 241
e-Print:
- astro-ph/9610253 [astro-ph]
Report number:
- SACLAY-SPH-T-96-081,
- CITA-96-11
View in:
Citations per year
Abstract: (arXiv)
Perturbation theory makes it possible to calculate the probability distribution function (PDF) of the large scale density field in the small variance limit. For top hat smoothing and scale-free Gaussian initial fluctuations, the result depends only on the linear variance, sigma_linear, and its logarithmic derivative with respect to the filtering scale -(n_linear+3)=dlog sigma_linear~2/dlog L (Bernardeau 1994). In this paper, we measure the PDF and its low-order moments in scale-free simulations evolved well into the nonlinear regime and compare the results with the above predictions, assuming that the spectral index and the variance are adjustable parameters, n_eff and sigma_eff=sigma, where sigma is the true, nonlinear variance. With these additional degrees of freedom, results from perturbation theory provide a good fit of the PDFs, even in the highly nonlinear regime. The value of n_eff is of course equal to n_linear when sigma << 1, and it decreases with increasing sigma. A nearly flat plateau is reached when sigma >> 1. In this regime, the difference between n_eff and n_linear increases when n_linear decreases. For initial power-spectra with n_linear=-2,-1,0,+1, we find n_eff -9,-3,-1,-0.5 when sigma~2 100.References(43)
Figures(0)