Axionic Dark Matter Halos as Ground State Mean-Field Spherical Solutions*

We consider a dark matter halo (DMH) of a spherical galaxy as a Bose-Einstein condensate (BEC) of the ultra-light axions (ULA) with and without the interaction with the baryonic matter [1,2], and the two-component BEC [3].  In the mean-field (MF) limit, we derived the integro-differential equation of the Hartree-Fock type for the spherically symmetrical wave function of the DMH component. Typically, this equation includes two independent dimensionless parameters: (i) the ratio of baryon and axion total mases and (ii) the ratio of characteristic baryon and axion spatial parameters. For the two-component DMH, the number of parameters increases. We developed the “dissipation algorithm" for studying numerically the ground state of the axion halo. We estimated the characteristic mass of the axion in our model.