TY - JOUR

T1 - The construction of nonspherical models of quasi-relaxed stellar systems

AU - Bertin, G.

AU - Varri, A. L.

PY - 2008/12/20

Y1 - 2008/12/20

N2 - Spherical models of collisionless but quasi-relaxed stellar systems have long been studied as a natural framework for the description of globular clusters. Here we consider the construction of self-consistent models under the same physical conditions, but including explicitly the ingredients that lead to departures from spherical symmetry. In particular, we focus on the effects of the tidal field associated with the hosting galaxy. We then take a stellar system on a circular orbit inside a galaxy represented as a "frozen" external field. The equilibrium distribution function is obtained from the one describing the spherical case by replacing the energy integral with the relevant Jacobi integral in the presence of the external tidal field. Then the construction of the model requires the investigation of a singular perturbation problem for an elliptic partial differential equation with a free boundary, for which we provide a method of solution to any desired order, with explicit solutions to 2 orders. We outline the relevant parameter space, thus opening the way to a systematic study of the properties of a two-parameter family of physically justified nonspherical models of quasi-relaxed stellar systems. The general method developed here can also be used to construct models for which the nonspherical shape is due to internal rotation. Eventually, the models will be a useful tool to investigate whether the shapes of globular clusters are primarily determined by internal rotation, by external tides, or by pressure anisotropy.

AB - Spherical models of collisionless but quasi-relaxed stellar systems have long been studied as a natural framework for the description of globular clusters. Here we consider the construction of self-consistent models under the same physical conditions, but including explicitly the ingredients that lead to departures from spherical symmetry. In particular, we focus on the effects of the tidal field associated with the hosting galaxy. We then take a stellar system on a circular orbit inside a galaxy represented as a "frozen" external field. The equilibrium distribution function is obtained from the one describing the spherical case by replacing the energy integral with the relevant Jacobi integral in the presence of the external tidal field. Then the construction of the model requires the investigation of a singular perturbation problem for an elliptic partial differential equation with a free boundary, for which we provide a method of solution to any desired order, with explicit solutions to 2 orders. We outline the relevant parameter space, thus opening the way to a systematic study of the properties of a two-parameter family of physically justified nonspherical models of quasi-relaxed stellar systems. The general method developed here can also be used to construct models for which the nonspherical shape is due to internal rotation. Eventually, the models will be a useful tool to investigate whether the shapes of globular clusters are primarily determined by internal rotation, by external tides, or by pressure anisotropy.

KW - globular clusters: general

KW - methods: analytical

KW - stellar dynamics

UR - http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-58149116770&md5=cf3143bfdd962397b7f885f7829bab99

U2 - 10.1086/592684

DO - 10.1086/592684

M3 - Article

AN - SCOPUS:58149116770

VL - 689

SP - 1005

EP - 1019

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

ER -