Direct N-body simulations of globular clusters – II. Palomar 4

Abstract

We use direct $N$-body calculations to study the evolution of the unusually\nextended outer halo globular cluster Palomar 4 (Pal~4) over its entire lifetime\nin order to reproduce its observed mass, half-light radius, velocity dispersion\nand mass function slope at different radii.\n We find that models evolving on circular orbits, and starting from a non-mass\nsegregated, canonical initial mass function (IMF) can reproduce neither Pal 4's\noverall mass function slope nor the observed amount of mass segregation.\nIncluding either primordial mass segregation or initially flattened IMFs does\nnot reproduce the observed amount of mass segregation and mass function\nflattening simultaneously. Unresolved binaries cannot reconcile this\ndiscrepancy either. We find that only models with both a flattened IMF and\nprimordial segregation are able to fit the observations. The initial (i.e.\nafter gas expulsion) mass and half-mass radius of Pal~4 in this case are about\n57000 M${\\odot}$ and 10 pc, respectively. This configuration is more extended\nthan most globular clusters we observe, showing that the conditions under which\nPal~4 formed must have been significantly different from that of the majority\nof globular clusters. We discuss possible scenarios for such an unusual\nconfiguration of Pal~4 in its early years.\n