Slowly rotating Bose Einstein condensate galactic dark matter halos, and their rotation curves

Abstract

If dark matter is composed of massive bosons, a Bose-Einstein condensation process must have occurred during the cosmological evolution. Therefore galactic dark matter may be in a form of a condensate, characterized by a strong self-interaction. We consider the effects of rotation on the Bose-Einstein condensate dark matter halos, and we investigate how rotation might influence their astrophysical properties. In order to describe the condensate we use the Gross-Pitaevskii equation, and the Thomas-Fermi approximation, which predicts a polytropic equation of state with polytropic index n = 1. By assuming a rigid body rotation for the halo, with the use of the hydrodynamic representation of the Gross-Pitaevskii equation we obtain the basic equation describing the density distribution of the rotating condensate. We obtain the general solutions for the condensed dark matter density, and we derive the general representations for the mass distribution, boundary (radius), potential energy, velocity dispersion, tangential velocity and for the logarithmic density and velocity slopes, respectively. Explicit expressions for the radius, mass, and tangential velocity are obtained in the first order of approximation, under the assumption of slow rotation. In order to compare our results with the observations we fit the theoretical expressions of the tangential velocity of massive test particles moving in rotata

Partition function of the Bose–Einstein condensate dark matter and the modified Gross–Pitaevskii equation

“…Let us announce immediately that h 2 = 3 to give a 2 1 ≈ 4.4934. This is shown in [2,5] and is reproduced below.…”

“…Solving, we derive that h 2 = 3 as it must be [5]. Substituting h 2 = 3 and h 0 = 1 into V in , we reproduce (up to multiplier 4πG) the effective potential from [2]. It results also in c −1 = 0.…”

“…Since the boson cloud has the ellipsoidal shape revealed by equation ρ 0 (r, θ) = const, some macroscopic characteristics can be corrected due to this fact [2,5]. Here we omit these considerations.…”

“…Among the famous and developed models of dark matter (DM), we decided to focus on the Bose-Einstein condensate (BEC) DM, which is formulated on the basis of the non-relativistic Gross-Pitaevskii equation (GPE) and, as can be seen from the recent works [1][2][3], well describes the observed rotation curves of dwarf galaxies. Here we omit the history of this idea, the diverse argumentation of which has already been given by its authors [1,4], as well as its direct astronomical applications.…”

“…However, we do not ini- * Electronic address: nazarenko@bitp.kiev.ua tially impose the geometric constraints that are used in differential calculus. It is admitted that our generalization will affect the determination of the size of boson system described in the Thomas-Fermi approximation [2,4].…”