Kinematic Control of the Inertiality of the System of Tycho-2 and UCAC2 Stellar Proper Motions

Based on the Ogorodnikov-Milne model, we analyze the proper motions of Tycho-2 and UCAC2 stars. We have established that the model component that describes the rotation of all stars under consideration around the Galactic y axis differs significantly from zero at various magnitudes. We interpret this rotation found using the most distant stars as a residual rotation of the ICRS/Tycho-2 system relative to the inertial reference frame. For the most distant ($d\approx900$ pc) Tycho-2 and UCAC2 stars, the mean rotation around the Galactic y axis has been found to be $M_{13}=-0.37\pm0.04$ mas yr$^{-1}$. The proper motions of UCAC2 stars with magnitudes in the range $12-15^m$ are shown to be distorted appreciably by the magnitude equation in $\mu_\alpha\cos\delta$, which has the strongest effect for northern-sky stars with a coefficient of $-0.60\pm0.05$ mas yr$^{-1}$ mag$^{-1}$. We have detected no significant effect of the magnitude equation in the proper motions of UCAC2 stars brighter than $\approx11^m$.Comment: 15 pages, 6 figure

Kinematics of Tycho-2 Red Giant Clump Stars

Based on the Ogorodnikov-Milne model, we analyze the proper motions of 95 633 red giant clump (RGC) stars from the Tycho-2 Catalogue. The following Oort constants have been found: A = 15.9+-0.2 km/s/kpc and B = -12.0+-0.2 km/s/kpc. Using 3632 RGC stars with known proper motions, radial velocities, and photometric distances, we show that, apart from the star centroid velocity components relative to the Sun, only the model parameters that describe the stellar motions in the XY plane differ significantly from zero. We have studied the contraction (a negative K-effect) of the system of RGC stars as a function of their heliocentric distance and elevation above the Galactic plane. For a sample of distant (500--1000 pc) RGC stars located near the Galactic plane (|Z|<200 pc) with an average distance of d=0.7 kpc, the contraction velocity is shown to be Kd= -3.5+-0.9 km/s; a noticeable vertex deviation, lxy = 9.1+-0.5 degrees, is also observed for them. For stars located well above the Galactic plane (|Z|>=200 pc), these effects are less pronounced, Kd = -1.7+-0.5 km/s and lxy = 4.9+-0.6 degrees. Using RGC stars, we have found a rotation around the Galactic X axis directed toward the Galactic center with an angular velocity of -2.5+-0.3 km/s/kpc, which we associate with the warp of the Galactic stellar-gaseous disk.Comment: 23 pages, 7 figures, 4 table

Cooling process for inelastic Boltzmann equations for hard spheres, Part II: Self-similar solutions and tail behavior

We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients. We prove the existence of self-similar solutions, and we give pointwise estimates on their tail. We also give general estimates on the tail and the regularity of generic solutions. In particular we prove Haff 's law on the rate of decay of temperature, as well as the algebraic decay of singularities. The proofs are based on the regularity study of a rescaled problem, with the help of the regularity properties of the gain part of the Boltzmann collision integral, well-known in the elastic case, and which are extended here in the context of granular gases.Comment: 41 page

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Analysis of Peculiarities of the Stellar Velocity Field in the Solar Neighborhood

Based on a new version of the Hipparcos catalogue and an updated Geneva-Copenhagen survey of F and G dwarfs, we analyze the space velocity field of about 17000 single stars in the solar neighborhood. The main known clumps, streams, and branches (Pleiades, Hyades, Sirius, Coma Berenices, Hercules, Wolf 630-alpha Ceti, and Arcturus) have been identified using various approaches. The evolution of the space velocity field for F and G dwarfs has been traced as a function of the stellar age. We have managed to confirm the existence of the recently discovered KFR08 stream. We have found 19 Hipparcos stars, candidates for membership in the KFR08 stream, and obtained an isochrone age estimate for the stream, 13 Gyr. The mean stellar ages of the Wolf 630-alpha Ceti and Hercules streams are shown to be comparable, 4--6 Gyr. No significant differences in the metallicities of stars belonging to these streams have been found. This is an argument for the hypothesis that these streams owe their origin to a common mechanism.Comment: 23 pages, 9 figure

Open Clusters IC 4665 and Cr 359 and a Probable Birthplace of the Pulsar PSR B1929+10

Based on the epicyclic approximation, we have simulated the motion of the young open star clusters IC 4665 and Collinder 359. The separation between the cluster centers is shown to have been minimal 7 Myr ago, 36 pc. We have established a close evolutionary connection between IC 4665 and the Scorpius-Centaurus association -- the separation between the centers of these structures was $\approx200$ pc 15 Myr ago. In addition, the center of IC 4665 at this time was near two well-known regions of coronal gas: the Local Bubble and the North Polar Spur. The star HIP 86768 is shown to be one of the candidates for a binary (in the past) with the pulsar PSR B1929+10. At the model radial velocity of the pulsar $V_r= 2\pm50$ km s$^{-1}$, a close encounter of this pair occurs in the vicinity of IC 4665 at a time of -1.1 Myr. At the same time, using currently available data for the pulsar B1929+10 at its model radial velocity $V_r=200\pm50$ km s$^{-1}$, we show that the hypothesis of Hoogerwerf et al. (2001) about the breakup of the $\zeta$Oph--B1929+10 binary in the vicinity of Upper Scorpius (US) about 0.9 Myr ago is more plausible.Comment: 19 pages, 8 figure

Derivation of transient relativistic fluid dynamics from the Boltzmann equation

In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inverse Reynolds number. We conclude that the equations of motion can be closed in terms of only 14 dynamical variables, as long as we only keep terms of second order in Knudsen and/or inverse Reynolds number. We show that, even though the equations of motion are closed in terms of these 14 fields, the transport coefficients carry information about all the moments of the distribution function. In this way, we can show that the particle-diffusion and shear-viscosity coefficients agree with the values given by the Chapman-Enskog expansion.Comment: 27 page

Power-law velocity distributions in granular gases

We report a general class of steady and transient states of granular gases. We find that the kinetic theory of inelastic gases admits stationary solutions with a power-law velocity distribution, f(v) ~ v^(-sigma). The exponent sigma is found analytically and depends on the spatial dimension, the degree of inelasticity, and the homogeneity degree of the collision rate. Driven steady-states, with the same power-law tail and a cut-off can be maintained by injecting energy at a large velocity scale, which then cascades to smaller velocities where it is dissipated. Associated with these steady-states are freely cooling time-dependent states for which the cut-off decreases and the velocity distribution is self-similar.Comment: 11 pages, 9 figure