Finite temperature effects in Bose-Einstein condensed dark matter halos

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 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.

Cosmological evolution of finite temperature Bose-Einstein condensate dark matter

“…In the case of dark matter halos with a large number of particles this represents a very good approximation, the contribution of the anomalous density and of the three-field correlation function to the total density being of the order of a few percents [23].…”

“…The equilibrium density of the thermal excitations is obtained by integrating the equilibrium Bose -Einstein distribution over the momentum. Thus we obtain [22][23][24][25] …”

“…The Heisenberg equation of motion for the quantum field operatorΦ describing the dynamics of a BoseEinstein condensate at arbitrary temperatures is given by [22][23][24][25] i ∂Φ ( r, t) ∂t…”

“…By introducing the non-condensate field operator ψ ( r, t) so thatΦ ( r, t) = Ψ ( r, t) +ψ ( r, t), where the average value ofψ ( r, t) is zero, ψ ( r, t) = 0, we can separate out the condensate component of the quantum field operator to obtain the equation of motion for Ψ as follows [22][23][24][25] i ∂Ψ ( r, t) ∂t…”

“…However, in the early Universe, immediately after the condensation, finite temperature effects could have played an important role in the dark matter dynamics, and significantly influence the cosmological evolution. The study of the finite temperature Bose-Einstein Condensate dark matter was initiated in [23], where the first order temperature corrections to the density profile of the galactic halos and the static properties of the condensates interacting with a thermal cloud have been obtained.…”