= Planar isotropic stellar distribution function
{title2=$F(E),\quad E=v^2/2+\Phi$}
= Planar isotropic distribution
{synonym}
For a stationary <collisionless stellar system> confined to a plane, <velocity> isotropy makes the <galactic distribution function> depend on <speed> through $u=v^2/2$. The <Collisionless Boltzmann equation> implies $\nabla_x f=f_u\nabla_x\Phi$, hence $f=F(E)$ with <specific orbital energy> $E=u+\Phi$. This conclusion requires stationarity as well as isotropy.
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