Scale invariance and self-similar behavior of dark matter halos

Details Scale invariance and self-similar behavior of dark matter halos Scale invariance and self-similar behavior of dark matter halos

Mar 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995apj...441...10m&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 441, no. 1, p. 10-17

Computer Science

Numerical Analysis

14

Baryons, Cosmology, Dark Matter, Galactic Evolution, Galactic Halos, Invariance, Adiabatic Conditions, Fluctuation Theory, Gravitational Effects, Numerical Analysis, Random Processes

Scientific paper

We study the formation and evolution of dark matter halos in an Omega = 1 universe. Only smooth and isolated initial overdensities are considered, in the same spirit as the works of Fillmore and Goldreich and Bertschinger. In a previous paper we have shown analytically that, in the spherically symmetric case, a power-law density profile is expected shortly before shell-crossing. Here we derive a general formula giving this slope as a function of the initial overdensity characteristics. We then investigate numerically the evolution after shell-crossing. This is done for a variety of initial perturbations, in particular strongly nonspherically symmetric ones. We find that, soon after the collapse time, the evolution may be well described for some time as being self-similar. This (quasi) self-similar regime holds for several factors of expansion of the metrics; it arises thanks to the preparation of the system in the precollapse phase. We proceed to check the theoretical predictions that follow by assuming, from start, a self-similar regime, as was done by Fillmore and Goldreich. Those predictions are fulfilled. It brings support to the idea that self-similar solutions are adequate descriptions of the dynamically established, postcollapse, characteristics. In particular, we confirm the existence of an adiabatic invariant along the particles' trajectories. We introduce a generalized version of this invariant that holds in the nonspherically symmetric cases we investigated. In addition, we complement Fillmore and Goldreich's solutions by a new set, in the cylindrical collapse case. Finally, we find that the self-similar slope is identical to the slope at the time of collapse, if the latter is steep enough. Otherwise it takes on a minimum value which depends on the geometry of the infall. Since these properties of scale invariance and quasi self-similarity appear for quite different initial configurations, they ought to be rather generic for the collisionless gravitational collapse of smooth initial overdensities.

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