Higher order moment models of dense stellar systems: Applications to the
  modeling of the stellar velocity distribution function
  Dense stellar systems such as globular clusters, galactic nuclei and nuclear
star clusters are ideal loci to study stellar dynamics due to the very high
densities reached, usually a million times higher than in the solar
neighborhood; they are unique laboratories to study processes related to
relaxation. There are a number of different techniques to model the global
evolution of such a system. In statistical models we assume that relaxation is
the result of a large number of two-body gravitational encounters with a net
local effect. We present two moment models that are based on the collisional
Boltzmann equation. By taking moments of the Boltzmann equation one obtains an
infinite set of differential moment equations where the equation for the moment
of order $n$ contains moments of order $n+1$. In our models we assume spherical
symmetry but we do not require dynamical equilibrium. We truncate the infinite
set of moment equations at order $n=4$ for the first model and at order $n=5$
for the second model. The collisional terms on the right-hand side of the
moment equations account for two-body relaxation and are computed by means of
the Rosenbluth potentials. We complete the set of moment equations with closure
relations which constrain the degree of anisotropy of our model by expressing
moments of order $n+1$ by moments of order $n$. The accuracy of this approach
relies on the number of moments included from the infinite series. Since both
models include fourth order moments we can study mechanisms in more detail that
increase or decrease the number of high velocity stars. The resulting model
allows us to derive a velocity distribution function, with unprecedented
accuracy, compared to previous moment models.
