A&A 435, 875-881 (2005)

DOI: 10.1051/0004-6361:20042595

## An exact equilibrium model of an unbound stellar system in a tidal field

**M. Fellhauer**

^{1}and D. C. Heggie^{2}^{1}Sternwarte Universität Bonn, Germany

e-mail: mike@astro.uni-bonn.de

^{2}School of Mathematics, University of Edinburgh, Scotland, UK

e-mail: d.c.heggie@ed.ac.uk

(Received 22 December 2004 / Accepted 9 February 2005 )

** Abstract **

Star clusters and dwarf galaxies gradually dissolve as they move in
the potential of their host galaxy. Once their density falls below
a certain critical density (which is comparable with the background
density of the galaxy) it is often assumed that their evolution is
completed. In fact the remnant of such a system forms a
distribution of stars which are unbound to each other and which move
on similar orbits in their host potential.
With this motivation we study the evolution of an idealised unbound
system and follow its expansion and dissolution in the tidal field
of a model galaxy. Initially the stars are uniformly distributed
(with a density below the critical density) within an ellipsoidal
volume. The system itself travels on a circular orbit within a
galaxy modelled as an isothermal sphere. The initial velocities of
the stars are chosen by assuming that they move on
(three-dimensional) epicycles with guiding centre at the centre of
the ellipsoid, though the usual epicyclic theory is altered to
account for the self-gravity of the system. This is believed to be
the first exact equilibrium model of a stellar system in a tidal
field.
Our main task is to study the stability of such configurations and
the time-scale of their dissolution, as a function of the initial
density and size of the ellipsoid. If the time of dissolution is
measured by an increase of the half-mass radius of 50%, we find
that systems of low density (1% of the background density)
and small radius (50 pc on an orbit of radius 10 kpc) can
survive for about 20 galactic orbits. For small systems we show
that the lifetime is approximately proportional to the inverse
square root of the density.

**Key words:**galaxies: star clusters

**--**methods:

*N*-body simulations

**--**Galaxy: kinematics and dynamics

**©**

*ESO 2005*