Abstract
The paper estimates the average components of the velocities \(V_{R}\) , \(V_{\theta}\) , \(V_{z}\) , specific kinetic energies \(T_{k}\) , and dispersions \(\sigma_{V}^{2}\) of the velocities of open star clusters (OSCs) in the solar neighborhood based on the Gaia DR3 data. The dependences of the dispersions of the \(T_{k}\) values and the velocities of the open-clusters on the distance \(R\) of the clusters to the Galactic rotation axis are constructed. A number of local maxima and minima in these dependences are noted. Numerical modeling of the trajectories of the OSC motions in the force field of the axisymmetric part of the Galaxy (the three-component model of Miyamoto, Nagai) and a four-armed spiral pattern was performed. Comparison of the values \(T_{k}\) , the amplitudes of \(T_{k}\) oscillations and the cylindrical galactocentric coordinates ( \(R,\theta,z\) ) of the OSCs with time and kinematic data on the motion of clusters results in estimating the ratio of the potentials of the spiral arms and the axisymmetric part of the Galaxy \(Q=0.0010{-}0.0012\) . Within the framework of the considered model of the Galaxy, the following was obtained: (1) the ratio of the disk mass to the total mass of the three components of the Galaxy (in the range of distances from its center from 0 to \(r\) ) equal to \(0.4\) is achieved with \(r=r_{b}\simeq 14.69\) kpc; (2) the contribution of the halo potential to the total potential of the Galaxy is equal to 0.778, 0.708, and 0.667 with \(r=r_{b}\) , 9, and 7 kpc, respectively. In this range of \(r\) values, the influence of the halo on the motion of OSCs in the Galaxy is approximately three times greater than the influence of the disk. Therefore, radial oscillations of the halo can make a significant contribution to the motion of OSCs in the Galaxy; (3) a formula for the frequency of small oscillations of the halo was obtained, the period of such oscillations is \(7.135\times 10^{9}\) yrs; (4) a formula for the free-fall time \(\tau_{\textrm{ ff}}\) of a star from a distance \(r_{0}\) to the halo center was obtained; (5) using \(\tau_{\textrm{ff}}\) and the data obtained in 2022 by Bird et al. on the velocities \(\sigma_{V}\) of Galactic halo stars, an estimate of the Jeans radius was obtained for the halo: \(r_{J}=26.7^{+4.1}_{-2.9}\) kpc. For the central part of the Galaxy, enclosed within a sphere of the radius \(r_{0}=35\) kpc, using \(\tau_{\textrm{ ff}}\) from our 2024 work for a homogeneous gravitating sphere, we obtained the estimate \(r_{J}=33.83\pm 1.41\) kpc indicating the gravitational instability of regions of the Galaxy with the distances \(r\) from \(r=0\) to \(r>r_{J}\) .
