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.
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