My notes are telling me that anisotropy of a stellar system is given by:
$$\beta \equiv 1-\frac{\sigma_{\theta}^{2}+\sigma_{\phi}^{2}}{2 \sigma_{r}^{2}}=1-\frac{\overline{v_{\theta}^{2}}+\overline{v_{\phi}^{2}}}{2 \overline{v_{r}^{2}}}$$
For a spherically symmetric stellar system, I believe that $\overline{v_{\phi}^{2}}=\overline{v_{\theta}^{2}}=\overline{v_{r}^{2}}$. Therefore, $$\beta=0 \text{ }\forall\text{ spherically symmetric stellar system}$$
Is this true, or am I misunderstanding something?
