Palomar 4 is a low-density globular cluster with a current mass \approx 30000 { M } _ { \odot } 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 can not 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 MF-slope and line-of-sight velocity dispersion .
We find that Pal 4 is most likely orbiting on an eccentric orbit with an eccentricity of e \approx 0.9 and pericentric distance of R _ { p } \approx 5 kpc .
In this scenario , the required 3D half-mass radius at birth is similar to the average sizes of typical GCs ( R _ { h } \approx 4 - 5 pc ) , while its birth mass is about M _ { 0 } \approx 10 ^ { 5 } { M } _ { \odot } .
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 \leq \mu _ { \delta } \leq - 0.38 mas yr ^ { -1 } and -0.30 \leq \mu _ { \alpha \cos \delta } \leq - 0.15 mas yr ^ { -1 } .