Finite temperature effects in Bose-Einstein Condensed dark matter halos

TL;DR

This paper investigates how finite temperature influences the structure and properties of Bose-Einstein Condensed dark matter halos, extending zero-temperature models to include thermal effects relevant in early universe conditions.

Contribution

It introduces a generalized Gross-Pitaevskii equation accounting for thermal clouds and provides explicit density and mass profiles at finite temperatures.

Findings

Finite temperature effects are negligible at temperatures much lower than the critical temperature.

Zero temperature profiles accurately describe dark matter halos at low temperatures.

Finite temperature effects may be significant during early cosmological evolution.

Abstract

Once the critical temperature of a cosmological boson gas is less than the critical temperature, a Bose-Einstein Condensation process can always take place during the cosmic history of the universe. Zero temperature condensed dark matter can be described as a non-relativistic, Newtonian gravitational condensate, whose density and pressure are related by a barotropic equation of state, with barotropic index equal to one. In the present paper we analyze the effects of the finite dark matter temperature on the properties of the Bose-Einstein Condensed dark matter halos. We formulate the basic equations describing the finite temperature condensate, representing a generalized Gross-Pitaevskii equation that takes into account the presence of the thermal cloud. The static condensate and thermal cloud in thermodynamic equilibrium is analyzed in detail, by using the Hartree-Fock-Bogoliubov and Thomas-Fermi approximations. The condensed dark matter and thermal cloud density and mass profiles at finite temperatures are explicitly obtained. Our results show that when the temperature of the condensate and of the thermal cloud are much smaller than the critical Bose-Einstein transition temperature, the zero temperature density and mass profiles give an excellent description of the dark matter halos. However, finite temperature effects may play an important role in the early stages of the cosmological evolution of the dark matter condensates.