Weighing of the dark matter at the center of the galaxy

A promising method for measuring the total mass of the dark matter near a supermassive black hole at the center of the Galaxy based on observations of nonrelativistic precession of the orbits of fast S0 stars together with constraints on the annihilation signal from the dark matter particles has been discussed. An analytical expression for the precession angle has been obtained under the assumption of a power-law profile of the dark matter density. In the near future, modern telescopes will be able to measure the precession of the orbits of S0 stars or to obtain a strong bound on it. The mass of the dark matter necessary for the explanation of the observed excess of gamma radiation owing to the annihilation of the dark matter particles has been calculated with allowance for the Sommerfeld effect.