Abstract
Palomar 4 (Pal 4) is a low-density globular cluster (GC) with a current mass approximate to 30 000M(circle dot) in the outer halo of the Milky Way with a two-body relaxation time of the order of a Hubble time. Yet, it is strongly mass segregated and contains a stellar mass function depleted of low-mass stars.
Pal 4 was either born this way or it is a result of extraordinary dynamical evolution. Since two-body relaxation cannot explain these signatures alone, enhanced mass-loss through tidal shocking may have had a strong influence on Pal 4.
Here, we compute a grid of direct N-body simulations to model Pal 4 on various eccentric orbits within the Milky Way potential to find likely initial conditions that reproduce its observed mass, half-light radius, stellar slope of the mass function and line-of-sight velocity dispersion. We find that Pal 4 is most likely orbiting on an eccentric orbit with an eccentricity of e approximate to 0.9 and pericentric distance of R-p approximate to 5 kpc.
In this scenario, the required 3D half-mass radius at birth is similar to the average sizes of typical GCs (Rh approximate to 4-5 pc), while its birth mass is about M-0 approximate to 10(5) M-circle dot We also find a high degree of primordial mass segregation among the cluster stars, which seems to be necessary in every scenario we considered. Thus, using the tidal effect to constrain the perigalactic distance of the orbit of Pal 4, we predict that the proper motion of Pal 4 should be in the range -0.52 (<=) mu(delta) <= -0.38 mas yr(-1) and -0.30 <= mu(alpha cos delta) <= -0.15 mas yr(-1).