  Direct N-body simulations of star clusters in a realistic Milky Way-like
potential are carried out using the code NBODY6. Based on these simulations a
new relationship between scale size and galactocentric distance is derived: the
scale size of star clusters is proportional to the hyperbolic tangent of the
galactocentric distance. The half-mass radius of star clusters increases
systematically with galactocentric distance but levels off when star clusters
orbit the galaxy beyond ~40 kpc. These simulations show that the half-mass
radius of individual star clusters varies significantly as they evolve over a
Hubble time, more so for clusters with shorter relaxation times, and remains
constant through several relaxation times only in certain situations when
expansion driven by the internal dynamics of the star cluster and the influence
of the host galaxy tidal field balance each other. Indeed, the radius of a star
cluster evolving within the inner 20 kpc of a realistic galactic gravitational
potential is severely truncated by tidal interactions and does not remain
constant over a Hubble time. Furthermore, the half-mass radius of star clusters
measured with present day observations bears no memory of the original cluster
size. Stellar evolution and tidal stripping are the two competing physical
mechanisms that determine the present day size of globular clusters. These
simulations also show that extended star clusters can form at large
galactocentric distances while remaining fully bound to the host galaxy. There
is thus no need to invoke accretion from an external galaxy to explain the
presence of extended clusters at large galactocentric distances in a Milky
Way-type galaxy.
