Finite Temperature Density Profile in SFDM

Recent high-quality observations of low surface brightness (LSB) galaxies have shown that their dark matter (DM) halos prefer flat central density profiles. On the other hand the standard cold dark matter model simulations predict a more cuspy behavior. Feedback from star formation has been widely used to reconcile simulations with observations, this might be successful in field dwarf galaxies but its success in high mass LSB galaxies remains unclear. Additionally, including too much feedback in the simulations is a double-edged sword, in order to obtain a cored DM distribution from an initially cuspy one, feedback recipes require to remove a large quantity of baryons from the center of galaxies, however, other feedback recipes produce twice more satellite galaxies of a given luminosity and with much smaller mass to light ratios from those that are observed. Therefore, one DM profile that produces cores naturally and that does not require large amounts of feedback would be preferable. We find both requirements to be satisfied in the scalar field dark matter model. Here, we consider that the dark matter is an auto-interacting real scalar field in a thermal bath of temperature T with an initial Z 2 symmetric potential, as the universe expands the temperature drops so that the Z 2 symmetry is spontaneously broken and the field rolls down to a new minimum. We give an exact analytic solution to the Newtonian limit of this system and show both, that it satisfies the two desired requirements and that the rotation curve profile is not longer universal.