Numerical simulations of the motions of stars in the gravitational fields of binary black holes with various component mass ratios have been carried out. Two models are considered: (1) the two-body problem with two fixed centers; (2) the general three-body problem. The first model is applicable only over short times Δt ≫ T, where T is the period of the binary system. The second model is applicable at all times except for during close encounters of stars with one of the binary components, r ≤ 0.00002 pc, where r is the distance from the star to the nearer black hole. In very close passages, relativistic corrections must be taken into account. Estimates of the probability of formation of high-velocity stars as a result of such interactions are obtained. It is shown that this mechanism is not suitable for the nucleus of our Galaxy due to the probable absence of a second massive black hole in the central region of the Galaxy.

We compiled published data on Galactic masers with VLBI-measured trigonometric parallaxes and determined the residual tangential, ∆Vcirc, and radial, ∆VR, velocities for 120 masers. We used these data to redetermine the parameters of the Galactic spiral density wave using the method of spectral analysis. The most interesting result of this study is the detection of wavelike oscillations of vertical spatial velocities (W) versus distance R from the Galactic rotation axis. Spectral analysis allowed us to determine the perturbation wavelength and the amplitude of this wave, which we found to be equal to λW = 3.4 ± 0.7 kpc and fW = 4.9 ± 1.2 km s−1, respectively.

Open star clusters from the MWSC (Milky Way Star Clusters) catalogue have been used to determine the Galactic rotation parameters. The circular rotation velocity of the solar neighborhood around the Galactic center has been found from data on more than 2000 clusters of various ages to be V_0=236+/-6 km s^{-1} for the adopted Galactocentric distance of the Sun R_0=8.3+/-0.2 kpc. The derived angular velocity parameters are \Omega_0=28.48+/-0.36 km s^{-1} kpc^{-1}, \Omega'_0=-3.50+/-0.08 km s^{-1} kpc^{-2}, and \Omega_0= 0.331+/-0.037 km s^{-1} kpc^{-3}. The influence of the spiral density wave has been detected only in the sample of clusters younger than 50 Myr. For these clusters the amplitudes of the tangential and radial velocity perturbations are f_\theta=5.6+/-1.6 km s^{-1} and f_R=7.7+/-1.4 km s^{-1}, respectively; the perturbation wavelengths are \lambda_\theta=2.6+/-0.5 kpc (i_\theta=-11+/-2 degrees) and \lambda_R=2.1+/-0.5 kpc (i_R=-9+/-2 degrees) for the adopted four-armed model (m=4). The Sun's phase in the spiral density wave is (\chi_\odot)_\theta=-62+/-9 degrees and (\chi_\odot)_R =-85+/-10 degrees from the residual tangential and radial velocities, respectively.

Open star clusters from the MWSC (Milky Way Star Clusters) catalogue have been used to determine the Galactic rotation parameters. The circular rotation velocity of the solar neighborhood around the Galactic center has been found from data on more than 2000 clusters of various ages to be V 0 = 236 ± 6 km s−1 for the adopted Galactocentric distance of the Sun R 0 = 8.3 ± 0.2 kpc. The derived angular velocity parameters are Ω 0 = 28.48 ± 0.36 km s−1 kpc−1, Ω’0 = −3.50 ± 0.08 km s−1 kpc−2, and Ω″0 = 0.331 ± 0.037 km s−1 kpc−3. The influence of the spiral density wave has been detected only in the sample of clusters younger than 50 Myr. For these clusters the amplitudes of the tangential and radial velocity perturbations are f θ = 5.6 ± 1.6 km s−1 and f R = 7.7 ± 1.4 km s−1, respectively; the perturbation wavelengths are λ θ = 2.6 ± 0.5 kpc (i θ = −11◦ ± 2◦) and λ R = 2.1 ± 0.5 kpc (i R = −9◦ ± 2◦) for the adopted four-armed model (m = 4). The Sun’s phase in the spiral density wave is (χ⊙)θ = −62◦ ± 9◦ and (χ⊙)R = −85◦ ± 10◦ from the residual tangential and radial velocities, respectively.

The probability of forming a Galactic hypervelocity star is estimated for the scenario of Hills, which describes the dynamical capture of one component of a binary star by the gravitational field of the supermassive black hole in the Galactic center, leading to the ejection of the other component. Ten thousand initial orientations of the binary orbits were considered, and the semi-major axes of the binary orbits were varied in a wide range from 11.3 R ⊙ to 425 R ⊙ . Two series of computations were carried out, in which the mass of the supermassive black hole was taken to be 10 6 M ⊙ and 3.4 × 10 6 M ⊙ . Numerical simulations of encounters of the binary and black hole in the framework of the three-body and N-body problems are used to localize regions favorable for the formation of hypervelocity stars. The motion of the ejected star in the regular field of the Galaxy is calculated, and the conditions under which the star escapes the Galaxy defined. The probability of escaping the Galaxy is caluclated as a function of various parameters the initial separation of the binary components and the distance of the binary from the black hole. On average, the probability of forming a hypervelocity star is higher for closer encounters and more tightly bound binary pairs.

Motions of stars escaping from the Galactic center are simulated. It is shown that the Galactic bar reduces the initial velocity needed to escape from the Galaxy.