Nearly radial orbits have small transverse motion: $\boxed{\sigma_t^2\ll\sigma_r^2,\quad\beta\to1}$. A bounded steady population contains both inward and outward phases, so large radial dispersion is compatible with zero mean radial velocity. Positivity of the distribution function and stability can impose further restrictions on particular radial models.


Solution

Past exam of the astrophysics course of the University of Oxford / 2015 / 7 / a / ii / Solution

 Solution (source code)