Direct N-body simulations of globular clusters: (I) Palomar 14
  We present the first ever direct $N$-body computations of an old Milky Way
globular cluster over its entire life time on a star-by-star basis. Using
recent GPU hardware at Bonn University, we have performed a comprehensive set
of $N$-body calculations to model the distant outer halo globular cluster
Palomar 14 (Pal 14). By varying the initial conditions we aim at finding an
initial $N$-body model which reproduces the observational data best in terms of
its basic parameters, i.e. half-light radius, mass and velocity dispersion. We
furthermore focus on reproducing the stellar mass function slope of Pal 14
which was found to be significantly shallower than in most globular clusters.
While some of our models can reproduce Pal 14's basic parameters reasonably
well, we find that dynamical mass segregation alone cannot explain the mass
function slope of Pal 14 when starting from the canonical Kroupa initial mass
function (IMF). In order to seek for an explanation for this discrepancy, we
compute additional initial models with varying degrees of primordial mass
segregation as well as with a flattened IMF. The necessary degree of primordial
mass segregation turns out to be very high. This modelling has shown that the
initial conditions of Pal 14 after gas expulsion must have been a half-mass
radius of about 20 pc, a mass of about 50000 M$_{\odot}$, and possibly some
mass segregation or an already established non-canonical IMF depleted in
low-mass stars. Such conditions might be obtained by a violent early
gas-expulsion phase from an embedded cluster born with mass segregation. Only
at large Galactocentric radii are clusters likely to survive as bound entities
the destructive gas-expulsion process we seem to have uncovered for Pal 14. In
addition we compute a model with a 5% primordial binary fraction to test if
such a population has an effect on the cluster's evolution.
