Self-consistent models of quasi-relaxed rotating stellar systems
  Two new families of self-consistent axisymmetric truncated equilibrium models
for the description of quasi-relaxed rotating stellar systems are presented.
The first extends the spherical King models to the case of solid-body rotation.
The second is characterized by differential rotation, designed to be rigid in
the central regions and to vanish in the outer parts, where the energy
truncation becomes effective. The models are constructed by solving the
nonlinear Poisson equation for the self-consistent mean-field potential. For
rigidly rotating configurations, the solutions are obtained by an asymptotic
expansion on the rotation strength parameter. The differentially rotating
models are constructed by means of an iterative approach based on a Legendre
series expansion of the density and the potential. The two classes of models
exhibit complementary properties. The rigidly rotating configurations are
flattened toward the equatorial plane, with deviations from spherical symmetry
that increase with the distance from the center. For models of the second
family, the deviations from spherical symmetry are strongest in the central
region, whereas the outer parts tend to be quasi-spherical. The relevant
parameter spaces are explored and the intrinsic and projected structural
properties are described. Special attention is given to the effect of different
options for the truncation of the distribution function in phase space. Models
in the moderate rotation regime are best suited to applications to globular
clusters. For general interest in stellar dynamics, at high values of the
rotation strength the differentially rotating models exhibit a toroidal core
embedded in a quasi-spherical configuration. Physically simple analytical
models of the kind presented here provide insights into dynamical mechanisms
and may be a basis for more realistic investigations with the help of N-body
simulations.
