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

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- Solution iii

Solution

An isotropic velocity distribution has equal variance in every direction and zero mixed moments:

σ_{r}^{2} = σ_{θθ}^{2} = σ_{ϕϕ}^{2}, β = 0 .

This is a statement about random velocity directions at each radius, not a requirement that every star follows a circular orbit.

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