# Direct N-body simulations of globular clusters -- III. Palomar\,4 on an eccentric orbit

## TL;DR

This study uses direct N-body simulations to model Palomar 4's orbit and properties, suggesting it follows a highly eccentric orbit with significant primordial mass segregation, influenced by tidal shocks, to explain its current state.

## Contribution

It introduces a detailed N-body simulation approach to determine Palomar 4's initial conditions and orbital parameters, highlighting the importance of tidal effects and primordial mass segregation.

## Key findings

- Palomar 4 likely on an eccentric orbit with e≈0.9
- Initial cluster size similar to typical GCs (~4-5 pc)
- Predicted proper motion ranges for Palomar 4

## Abstract

Palomar 4 is a low-density globular cluster with a current mass $\approx30000 M_{\odot}$ 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 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 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 $R_p\approx5$ kpc. In this scenario, the required 3D half-mass radius at birth is similar to the average sizes of typical GCs ($R_h\approx4-5$ pc), while its birth mass is about $M_0\approx10^5 M_{\odot}$. 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$^{-1}$.