The effect of light refraction in a galaxy’s halo of dark matter, described by profiles of Navarro-Frenk-White and Burkert, was considered. Powers of the Cherenkov radiation for the refractive indexes of gravitational fields with these profiles were calculated. It was shown that correspondent radiation temperature in the X-rays diapason have the magnitude about T~10^-6K . It was also marked that its detection may be the criteria on choosing the preferable dark matter density distribution in a galaxy.