The equilibrium of cool stellar disks.

A system of finite infinitesimally thin self-gravitating disks is constructed. The sequence begins with the uniformly rotating disk and approaches the isothermal disk, and the latter members of the sequence resemble real disk galaxies. A mathematical description of cool stellar disks is presented for application to model galaxies in which the ratio of random to mean velocity is small, except near the center. Phase-space moments of the modified Schwarzschild stellar distribution function are shown to have an expansion in powers of the ratio of the star's random kinetic energy to gravitational potential energy