Mutual Dependence between a Bosonic Black Hole and Dark Matter and the Explanation of Asymptotically Flat Galaxy Rotation Curves

Abstract

The possibility of an equilibrium static state of a collapsed black hole, surrounded by dark matter, makes it possible to understand the existence of flat rotation curves of stars on the periphery of a galaxy. Under the dominant gravity, a Bose–Einstein condensate is the energetically most favourable state of an extremely compressed black hole. It turned out that the longitudinal vector field, as a wave function, adequately describes the observed manifestations of dark matter. Considering as an example a condensate of Z, W, and H bosons of the Standard Model of Elementary Particles (with rest energy of the order of 100 GeV), the dependence of rotation curves of stars on the mass of a black hole at the galaxy center was investigated. With this composition of the black hole of a mass on the order of the solar mass (2 ×10³³ g), the dark matter gives the dominant contribution to the gravitational field. In this case, the plateau on the galaxy rotation curve is explicitly expressed. As the black hole mass increases, a contribution to the gravity from the dark matter decreases, while a contribution from the black hole increases. The mass of the black hole at the center of the Milky Way galaxy is seven orders of magnitude greater than the solar mass. The contribution to the gravity from the black hole dominates. Therefore, in our galaxy, the rotation velocity of stars \(V\left( r \right)\) as a function of radius decreases in proportion to \({1 \mathord{\left/ {\vphantom {1 {\sqrt r }}} \right. \kern-0em} {\sqrt r }}\) in accordance with Newton’s law.