paper

On the newtonian limit and cut--off scales of isothermal dark matter halos with cosmological constant

arXiv:astro-ph/0304385 · doi:10.1046/j.1365-8711.2003.07010.x

Abstract

We examine isothermal dark matter halos in hydrostatic equilibrium with a cosmological constant Lambda =Omega_Λrho_{crit}c^2, where Omega_Λ=0.7, and rho_{crit} is the present value of the critical density with h=0.65. The Newtonian limit of General Relativity yields equilibrium equations that are different from those arising by merely coupling an ``isothermal sphere'' to the Lambda-field within a Newtonian framework. The conditions for the existence and stability of circular geodesic orbits show the existence of (I) an ``isothermal region'' (0<r<r_2), circular orbits are stable and all variables behave almost identically to those of an isothermal sphere; (II) an ``asymptotic region'' (r>r_1) dominated by the Lambda-field, where the Newtonian potential oscillates and circular orbits exist in disconnected patches of the domain of r; (III) a ``transition region'' (r_2<r<r_1), circular orbits exist but are unstable. We also find that no stable configuration exists with central density, rho_c, smaller than 2 Lambda, hence any galactic haloes which virialized at in must have rho_c >0.008 M_\odot {pc}^3, in agreement with rotation curve studies of dwarf galaxies. Since r_2 marks the largest radius of a stable circular orbit, it provides a ``cut off'' radius. For current estimates of rho_c and velocity dispersion of galactic structures, this is around five times larger than the virialization radius. The effects of the Lambda$--field can hence be ignored in structure formation models, but could be significant in the dynamics of superclusters in the linear regime or of gravitational clustering at large scales.

arXiv comment13 pages, 19 figures, Accepted in MNRAS, includes minor corrections suggested by the referee

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