Frequency ratio of the spherical isochrone model (source code)

= Frequency ratio of the spherical isochrone model

The radial and azimuthal frequencies obey
$$
\frac{\Omega_\phi}{\Omega_r}
=\frac12\left(1+\frac{L}{\sqrt{L^2+4GMb}}\right).
$$
The ratio tends to one half in the harmonic core and to one in the Keplerian exterior.