Large-amplitude isothermal fluctuations and high-density dark-matter clumps

Abstract

Large-amplitude isothermal fluctuations in the dark-matter energy density, parametrized by \ensuremath{\Phi}\ensuremath{\equiv}\ensuremath{\delta}${\mathrm{\ensuremath{\rho}}}_{\mathrm{DM}}$/${\mathrm{\ensuremath{\rho}}}_{\mathrm{DM}}$, are studied within the framework of a spherical collapse model. For \ensuremath{\Phi}\ensuremath{\gtrsim}1, a fluctuation collapses in the radiation-dominated epoch and produces a dense dark-matter object. The final density of the virialized object is found to be ${\mathrm{\ensuremath{\rho}}}_{\mathit{F}}$\ensuremath{\approxeq}140${\mathrm{\ensuremath{\Phi}}}^{3}$(\ensuremath{\Phi}+1)${\mathrm{\ensuremath{\rho}}}_{\mathrm{eq}}$, where ${\mathrm{\ensuremath{\rho}}}_{\mathrm{eq}}$ is the matter density at equal matter and radiation energy density. This expression is valid for the entire range of possible values of \ensuremath{\Phi}, both for \ensuremath{\Phi}\ensuremath{\gg}1 and \ensuremath{\Phi}\ensuremath{\ll}1. Some astrophysical consequences of high-density dark-matter clumps are discussed.