Osipkov-Merritt distribution function
= Osipkov-Merritt distribution function
{c}
{title2=$Q=E-L^2/(2r_a^2)$}
An Osipkov-Merritt spherical distribution has $F=f(Q)$ for $Q=E-L^2/(2r_a^2)>0$ and vanishes otherwise. Rescaling transverse velocities by $\sqrt{1+r^2/r_a^2}$ makes its velocity integral isotropic in the rescaled variables. Its <velocity-anisotropy parameter> is $\beta=r^2/(r^2+r_a^2)$.