TY - JOUR

T1 - Self-consistent models of quasi-relaxed rotating stellar systems

AU - Varri, A. L.

AU - Bertin, G.

PY - 2012/4/1

Y1 - 2012/4/1

N2 - Aims: 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 well-known 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 imposed energy truncation
becomes effective. Methods: The models are constructed by solving
the relevant nonlinear Poisson equation for the self-consistent
mean-field potential. For rigidly rotating configurations, the solutions
are obtained by an asymptotic expansion based on the rotation strength
parameter, following a procedure developed earlier by us for the case of
tidally generated triaxial models. The differentially rotating models
are constructed by means of a spectral iterative approach, with a
numerical scheme based on a Legendre series expansion of the density and
the potential. Results: 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 thoroughly explored
and the corresponding 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.
Conclusions: 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 tend to exhibit a toroidal core embedded in an otherwise
quasi-spherical configuration. Physically simple analytical models of
the kind presented here provide insights into dynamical mechanisms and
may be a useful basis for more realistic investigations carried out with
the help of N-body simulations.

AB - Aims: 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 well-known 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 imposed energy truncation
becomes effective. Methods: The models are constructed by solving
the relevant nonlinear Poisson equation for the self-consistent
mean-field potential. For rigidly rotating configurations, the solutions
are obtained by an asymptotic expansion based on the rotation strength
parameter, following a procedure developed earlier by us for the case of
tidally generated triaxial models. The differentially rotating models
are constructed by means of a spectral iterative approach, with a
numerical scheme based on a Legendre series expansion of the density and
the potential. Results: 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 thoroughly explored
and the corresponding 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.
Conclusions: 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 tend to exhibit a toroidal core embedded in an otherwise
quasi-spherical configuration. Physically simple analytical models of
the kind presented here provide insights into dynamical mechanisms and
may be a useful basis for more realistic investigations carried out with
the help of N-body simulations.

KW - globular clusters: general

KW - methods: analytical

UR - http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-84859308657&md5=c7b1b8e8f3ed0db5fbecdc442a3d518d

U2 - 10.1051/0004-6361/201118300

DO - 10.1051/0004-6361/201118300

M3 - Article

AN - SCOPUS:84859308657

SN - 0004-6361

VL - 540

JO - Astronomy & Astrophysics

JF - Astronomy & Astrophysics

ER -