Predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere

Abstract

We develop a model of Bose-Einstein condensate dark matter halos with a solitonic core and an isothermal atmosphere based on a generalized Gross-Pitaevskii-Poisson equation [P.H. Chavanis, Eur. Phys. J. Plus 132, 248 (2017)]. This equation provides a heuristic coarse-grained parametrization of the ordinary Gross-Pitaevskii-Poisson equation accounting for violent relaxation and gravitational cooling. It involves a cubic nonlinearity taking into account the self-interaction of the bosons, a logarithmic nonlinearity associated with an effective temperature, and a source of dissipation. It leads to superfluid dark matter halos with a core-halo structure. The quantum potential or the self-interaction of the bosons generates a solitonic core that solves the cusp problem of the cold dark matter model. The logarithmic nonlinearity generates an isothermal atmosphere accounting for the flat rotation curves of the galaxies. The dissipation ensures that the system relaxes towards an equilibrium configuration. In the Thomas-Fermi approximation, the dark matter halo is equivalent to a barotropic gas with an equation of state $P=2\pi a_s\hbar^2\rho^2/m^3+\rho k_B T/m$, where $a_s$ is the scattering length of the bosons and $m$ is their individual mass. We numerically solve the equation of hydrostatic equilibrium and determine the corresponding density profiles and rotation curves. Our model has no free parameter so it is completely predictive. Extension of this model to noninteracting bosons and fermions will be presented in forthcoming papers.