The Virial Equations I Department of Astronomy（我天文系的维里方程）.pdf

The Virial Equations I We can obtain an important tensor equation relating global properties of the system, by multiplying the CBE by both and and then integrating over the entire phase-space. The first step of this has already been performed in our derivation of the Jeans equations, and yielded the momentum equations Multiplying all terms with and integrating over real space yields Using integration by parts the first term on the r.h.s. becomes where we have defined the kinetic energy tensor The Virial Equations II It is customary to split the kinetic energy tensor into contributions from ordered and random motions: where In addition to the we also define the potential energy