The Fluid-Dynamical Method

Abstract

The use of a fluid-dynamical technique for computing the evolution of stars clusters has been described briefly earlier in this volume, and in more detail by Larson (1970a, b). For convenience we repeat here the fundamental definitions and equations used in this method. We consider a spherical stellar system described by a distribution function of the form f(r, u, v, w, t), where u is the velocity component in the r-direction and v and w are the two transverse velocity components. As the basic fluid-dynamical variables to be solved for, we define the following six moments of the velocity distribution at each point in space and time: the density of stars ϱ, the mean outward velocity <u>, and the higher-order moments $$ \left. {\begin{array}{*{20}{c}} {\alpha \equiv \left\langle {{{\left( {u - \left\langle u \right\rangle } \right)}^2}} \right\rangle } \\ {\beta \equiv \left\langle {{v^2}} \right\rangle = \left\langle {{w^2}} \right\rangle } \\ {\varepsilon \equiv \left\langle {{{\left( {u - \left\langle u \right\rangle } \right)}^3}} \right\rangle } \\ {\xi \equiv \left\langle {{{\left( {u - \left\langle u \right\rangle } \right)}^4}} \right\rangle - 3{\alpha ^2}.} \end{array}} \right\} $$ Here α and β are the squares of the radial and transverse velocity dispersions, ε represents an outward energy flux or ‘heat flow’, and ζ represents an excess or deficiency of high velocity stars relative to a Maxwellian distribution. KeywordsDifference EquationGlobular ClusterTransverse VelocityStar ClusterMonthly NoticeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.