Steady-state solutions for the motion of a globular cluster in an inhomogeneous, rotating elliptical galaxy

Abstract

Steady-state solutions for the motion of a passively gravitating globular cluster (GC) inside an inhomogeneous, rotating, ellipsoidal elliptical galaxy (EG) are considered. It is assumed that an EG with a halo is comprised of a triaxial ellipsoid consisting of two layers. The first is formed by an inner, uniform ellipsoid representing the luminous part of the galaxy, while the second corresponds to the space between an inner and outer ellipsoid, which is uniformly filled with dark matter. The triaxial ellipsoids are taken to be homothetic and to have a common center; the space between them is called a homeoid. The outer boundary of the homeoid is the boundary of the galaxy halo. The densities of the luminous part of the EG and the homeoid are different. This picture of an EG is in agreement with our current understanding of galactic structure. The motion of the GC occurs outside the luminous part of the EG, but inside the homeoid, which is treated like a perturbing body. Steady-state solutions (libration points) are found for the GC, and its Lyapunov stability determined. The elliptical galaxies NGC 4472 (M49), NGC 4636, and NGC 4374, which contain a large number of GCs, are used as examples. Analysis of these galaxies shows that the exact expression for the potential of the luminous part of the EG must be used to find the libration points and study their stability, rather than an approximate expression for this potential.

Motion of Stars in Layered Inhomogeneous Elliptical Galaxies

“…In addition, the direction of gravity is not involved. Obviously, the system of equations ( 1) allows an analogue of the Jacobi integral in the form [1,2,10] dx dt…”

“…The problem of the spatial motion of a passively gravitating body (PGB) in the gravitational field of an elliptical galaxy (EG) according to models 1 and 2 is considered in [1,2]. A similar problem of the PGB motion inside (near) a globular cluster (GC) belonging to an EG is studied in [3].…”

“…A similar problem of the PGB motion inside (near) a globular cluster (GC) belonging to an EG is studied in [3]. The results obtained in [1][2][3] are applied to model elliptical galaxies with parameters that exactly coincide with the parameters of the elliptical galaxies NGC 4472 (M 49), NGC 4697, and NGC 4374 (M 84); these results are presented in the form of figures and atable. Three new EG models (Models 3, 4, and 5) are considered in [4].…”

Three New Models of Layered Inhomogeneous Elliptical Galaxies

“…In [1,2], the problem of the spatial motion of a passively gravitating body (a star or the center of mass of a globular cluster, GC) inside a rotating elliptical galaxy (EG) was considered. An EG was regarded as a two -layer ellipsoidal body: its luminous part is a triaxial ellipsoid, and the space between the boundaries of its luminous part and the halo is a homeoid filled with homogeneous dark matter.…”

“…In [1], the luminous part of an EG (LP EG) is considered a homogeneous triaxial ellipsoid, and, in [2], uses the so-called astrophysical law of density distribution. The EG model considered in [1] will be called model 1, and the model in [2], model 2.…”