Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails

We consider the Boltzmann equations for mixtures ofMaxwell gases. It is shown that in certain limiting case the equations admit self-similar solutions that can be constructed in explicit form. More precisely, the solutions have simple explicit integral representations. The most interesting solutions have finite energy and power like tails. This shows that power like tails can appear not just for granular particles (Maxwell models are far from reality in this case), but also in the system of particles interacting in accordance with laws of classical mechanics. In addition, non-existence of positive self-similar solutions with finite moments of any order is proven for a wide class of Maxwell models.Comment: 20 page

Rotation Curve and Mass Distribution in the Galaxy from the Velocities of Objects at Distances up to 200 kpc

Three three-component (bulge, disk, halo) model Galactic gravitational potentials differing by the expression for the dark matter halo are considered. The central (bulge) and disk components are described by the Miyamoto-Nagai expressions. The Allen-Santill'an (I), Wilkinson-Evans (II), and Navarro-Frenk-White (III) models are used to describe the halo. A set of present-day observational data in the range of Galactocentric distances R from 0 to 200 kpc is used to refine the parameters of these models. The model rotation curves have been fitted to the observed velocities by taking into account the constraints on the local matter density \rho_\odotand the force K_{z=1.1} acting perpendicularly to the Galactic plane. The Galactic mass within a sphere of radius 50 kpc, M_G (R<=50 kpc)=(0.41+/-0.12)x10^12 M_\odot, is shown to satisfy all three models. The differences between the models become increasingly significant with increasing radius R. In model I, the Galactic mass within a sphere of radius 200 kpc turns out to be greatest among the models considered, M_G (R<=200 kpc)=(1.45+/-0.30)x10^12 M_\odot, and the smallest value has been found in model II, M_G (R<=200 kpc)=(0.61+/-0.12)x10^{12} M_\odot. In our view, model III is the best one among those considered, because it ensures the smallest residual between the data and the constructed model rotation curve provided that the constraints on the local parameters hold with a high accuracy. Here, the Galactic mass is M_G (R<=200 kpc)=(0.75+/-0.19)x10^12 M_\odot. A comparative analysis with the models by Irrgang et al. (2013), including those using the integration of orbits for the two globular clusters NGC 104 and NGC 1851 as an example, has been performed. The third model is shown to have subjected to a significant improvement.Comment: 22 pages, 7 figures, 2 table

OB Stars and Cepheids From the Gaia TGAS Catalogue: Test of their Distances and Proper Motions

We consider young distant stars from the Gaia TGAS catalog. These are 250 classical Cepheids and 244 OB stars located at distances up to 4 kpc from the Sun. These stars are used to determine the Galactic rotation parameters using both trigonometric parallaxes and proper motions of the TGAS stars. In this case the considered stars have relative parallax errors less than 200%. Following the well-known statistical approach, we assume that the kinematic parameters found from the line-of-sight velocities $V_r$ are less dependent on errors of distances than the found from the velocity components $V_l$. From values of the first derivative of the Galactic rotation angular velocity $\Omega{'}_0$, found from the analysis of velocities $V_r$ and $V_l$ separately, the scale factor of distances is determined. We found that from the sample of Cepheids the scale of distances of the TGAS should be reduced by 3%, and from the sample of OB stars, on the contrary, the scale should be increased by 9%.Comment: 5 pages, 1 figure, 2 table

Determination of the Solar Galactocentric distance from masers kinemics

We have determined the Galactic rotation parameters and the solar Galactocentric distance $R_0$ by simultaneously solving Bottlinger's kinematic equations using data on masers with known line-of-sight velocities and highly accurate trigonometric parallaxes and proper motions measured by VLBI. Our sample includes 93 masers spanning the range of Galactocentric distances R from 3 to 15 kpc. The solutions found are \Omega_0 = 29.7+/-0.5 km s^{-1} kpc^{-1}, \Omega'_0 = -4.20+/-0.11 km s^{-1} kpc^{-2}, \Omega"_0 =0.730+/-0.029 km s^{-1} kpc^{-3}, and R_0=8.03+/-0.12 kpc. In this case, the linear rotation velocity at the solar distance R_0 is V_0=238+/-6 km s^{-1}.Comment: 8 pages, 2 figures, 1 table. Paper was presented at the Conference "Modern Stellar Astronomy-2014" held in Rostov-on-Don State University on May 28-30, 2014, accepted for pubication in Baltic Astronom