The differential energy distribution and the total integrated binding
  energy of dynamical models
  We revisit the differential energy distribution of steady-state dynamical
models. It has been shown that the differential energy distribution of
steady-state spherical models does not vary strongly with the anisotropy
profile, and that it is hence mainly determined by the density distribution of
the model. We explore this similarity in more detail. Through a worked example
and a simple proof, we show that the mean binding energy per unit mass
$\langle{\cal{E}}\rangle$, or equivalently the total integrated binding energy
$B_{\text{tot}} = M\langle{\cal{E}}\rangle$, is independent of the orbital
structure, not only for spherical models but for any steady-state dynamical
model. Only the higher-order moments of the differential energy distribution
depend on the details of the orbital structure. We show that the standard
deviation of the differential energy distribution of spherical dynamical models
varies systematically with the anisotropy profile: radially anisotropic models
tend to prefer more average binding energies, whereas models with a more
tangential orbital distribution slightly favour more extreme binding energies.
Finally, we find that the total integrated binding energy supplements the
well-known trio consisting of total kinetic energy, total potential energy, and
total energy on an equal footing. Knowledge of any one out of these four
energies suffices to calculate the other three.
