New applications of the equations of stellar hydrodynamics

For a subsystem of stars in an axisymmetric galaxy in equilibrium, the equations of stellar hydrodynamics are extended to include equations involving the third and fourth moments of the velocity distribution; and the extended system of equations is combined with certain auxiliary relations derived from an approximate solution of Liouville's equation for the distribution of stars in the six-dimensional phase space. Formulae are derived which enable the determination of the curvature in the law of galactic rotation and a characteristic scale length of galactic structure parallel to the galactic plane from a knowledge of the velocity of galactic rotation, the slope in the law of rotation, and the moments of the velocity distribution. When supplemented with considerations bearing on the stability of the galactic disk, these formulae provide a practical basis for an approximate determination of the gradients of the density and velocity dispersion of the common stars in the solar neighborhood. Accordingly, the asymmetric drift of the common stars can be determined by inverting the conventional application of the standard hydrodynamic equations.