ISSN 1063-7788, Physics of Atomic Nuclei, 2015, Vol. 77, No. 13, pp. 1–3. © Pleiades Publishing, Ltd., 2015. Original Russian Text © V.I. Dokuchaev , 2015, published in Yadernaya fizika i inzhiniring, 2015, No. 9–10, pp. 000–000. 1 INTRODUCTION Located in the Galactic Center is the supermassive black hole Sgr A* nearest to Earth with the mass measured by the observed orbital parameters of the so-called S0 stars that travel in the black hole’s gravitational field at velocities of ~10 3 km/s [1, 2]. The major difficulty in observing the SgrA* supermassive black hole is that it is a “drowsing” quasar, i.e., it does not display any signs of activity and only flashes very rarely for a short period of time. Nev- ertheless, it has become possible to record quasi-peri- odic oscillations of the Sgr A* radiation in the X-rays [3] and the near IR region [4]. The basis of a new method for interpretation of the quasi-periodic oscillations is the hypothesis about the existence in the accretion flow of numerous hot spots or plasma clumps that cause modulations of the accre- tion source radiation [5–9]. The frequencies of these modulations do not depend on the accretion model and are completely determined by the properties of the black hole’s gravitational field. The method under consideration is applicable for black holes with a low accretion rate when the accretion disk plasma is trans- parent up to the event horizon. The hot spots are assumed to be generated owing to the instability and the turbulence of the accretion flow. Numerical MHD simulations confirm the existence of hot plasma spots in the accretion disks [10]. 6 (4 1 0 4) 10 , M M = . ± . ⋅ ⊙ The system of units G = c = 1is used and the dimen- sionless Kerr parameter where M and J are the mass and the angular momentum of the black hole, respectively, is used as the spin. The equa- tions of motion of test particles—for example, of planets, compact gas clouds, or plasma clumps—in the Kerr metric in the Boyer–Lindquist coordinates, have the form [11] (1) (2) (3) where is the intrinsic lifetime of particle τ nor- malized to its mass μ and (4) (5) (6) The motion of the particles is completely deter- mined by three integrals of motion: the total energy of particle E, its azimuthal angular momentum L, and Carter’s constant Q related to the total angular momentum of particle and the nonequatorial motion. It is convenient to use dimensionless quantities and 2 0 1, a J M ≤ = ≤ (, , , ) tr θφ 2 2 , r dr d V V d d θ θ ρ =± ρ =± , λ λ 2 2 1 sin ( ) d L a P E d - - φ ρ = θ+ Δ − , λ 2 2 2 2 1 ( sin ) ( ) dt aL aE r a P d - ρ = − θ+ + Δ , λ λ=τμ 2 2 2 2 [ ( ) ] r V P r L aE Q = −Δμ + − + , 2 2 2 2 2 2 cos [ ( ) sin ] V Q a E L - θ = − θ μ − + θ, 2 2 2 2 2 2 2 2 ( ) cos 2 P Er a aL r a r r a = + − , ρ = + θ, Δ= − + . Spin and Mass of the Supermassive Black Hole in the Galactic Center V. I. Dokuchaev Institute for Nuclear Research, Russian Academy of Sciences, pr. 60-letiya Oktybrya 7a, Moscow, 117312 Russia National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409 Russia e-mail: dokuchaev@inr.ac.ru @ Abstract—A new method for exact determination of the masses and spins of black holes from the observa- tions of quasi-periodic oscillations is discussed. The detected signal from the hot clumps in the accretion plasma must contain modulations with two characteristic frequencies: the frequency of rotation of the black hole event horizon and the frequency of the latitudinal precession of the clump’s orbit. Application of the method of two characteristic frequencies for interpretation of the observed quasi-periodic oscillations from the supermassive black hole in the Galactic center in the X-rays and in the near IR region yields the most exact, for the present, values of the mass and the spin (Kerr parameter) of the SgrA* black hole: and The observed quasi-periodic oscillations with a period of about 11.5 min are identified as the black hole event horizon rotation period and those with a period of about 19 min are identified as the latitudinal oscillation period of the hot spot orbits in the accretion disk. Keywords: Galactic Center, black holes. DOI: 10.1134/S1063778815130074 6 (4 2 0 2) 10 M M = . ± . ⋅ ⊙ 0 65 0 05. a = . ± .