= Isothermal collisionless tracer
{title2=$\rho=\rho_0e^{\psi/\sigma_0^2}$}
A steady <galactic distribution function> depending only on <relative energy> $E=\psi-v^2/2$ is isotropic and has zero mean <velocity>. If its one-dimensional <velocity dispersion> is constant, the <Spherical Jeans equation> reduces to $\sigma_0^2\rho'=\rho\psi'$, yielding the displayed density. This is a tracer relation in a specified <gravitational potential>, not a requirement that the tracer generate that potential. With no escape-energy cutoff its local <velocity> distribution is <Maxwell-Boltzmann velocity distribution>.
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