Self-similarity and scaling behavior of scale-free gravitational clustering
- NASA/Fermilab Astrophysics Centre, Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510 (United States)
- Institut d`Astrophysique de Paris, CNRS, 98 bis boulevard Arago, F-75014 Paris (France)
- Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030 (United States)
We determine the scaling properties of the probability distribution of the smoothed density field in {ital N}-body simulations of expanding universes with scale-free initial power-spectra, {l_angle}{vert_bar}{delta}{sub {ital k}}{vert_bar}{sup 2}{r_angle}{proportional_to}{ital k}{sup {ital n}}, with particular attention to the predictions of the stable clustering hypothesis. We concentrate our analysis on the ratios {ital S}{sub {ital Q}}({ital l}){equivalent_to}{bar {xi}}{sub {ital Q}}/{bar {xi}}{sup {ital Q}-1}{sub 2}, where {bar {xi}{sub Q}} is the average {ital Q}-body correlation function over a cell of radius l. According to the stable clustering hypothesis, {ital S{sub Q}} should not depend on scale. We performed measurements for {ital Q}{le}5. The behavior of the higher order correlations is studied through that of the void probability distribution, {ital P}{sub 0}(l), which is the probability of finding an empty cell of radius l. If the stable clustering hypothesis applies, the function {ital P}{sub 0} should also exhibit remarkable scaling properties. In our analysis, we take carefully into account various misleading effects, such as initial grid contamination, loss of dynamics due to the short-range softening of the forces, and finite volume size of our simulations. Only after correcting for the latter do we find agreement of the measured {ital S{sub Q}} with the expected self-similar behavior. Otherwise, {ital P}{sub 0} is only weakly sensitive to such effects and closely follows the expected self-similar behavior. The ratios {ital S{sub Q}} exhibit two plateaus separated by a smooth transition when {bar {xi}}{sub 2}(l){approximately}1. In the weakly nonlinear regime, {bar {xi}}{sub 2}{approx_lt}1, the results are in agreement with the predictions of perturbation theory. In the strongly nonlinear regime, {bar {xi}}{sub 2}{approx_gt}1, the {ital S{sub Q}} values are larger than in the weakly nonlinear regime, and increasingly so with -{ital n}.
- OSTI ID:
- 288896
- Journal Information:
- Astrophysical Journal, Vol. 465, Issue 1; Other Information: PBD: Jul 1996
- Country of Publication:
- United States
- Language:
- English
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