A prescription and fast code for the long-term evolution of star
  clusters - II. Unbalanced and core evolution
  We introduce version two of the fast star cluster evolution code Evolve Me A
Cluster of StarS (EMACSS). The first version (Alexander & Gieles) assumed that
cluster evolution is balanced for the majority of the life-cycle, meaning that
the rate of energy generation in the core of the cluster equals the diffusion
rate of energy by two-body relaxation, which makes the code suitable for
modelling clusters in weak tidal fields. In this new version we extend the
model to include an unbalanced phase of evolution to describe the pre-collapse
evolution and the accompanying escape rate such that clusters in strong tidal
fields can also be modelled. We also add a prescription for the evolution of
the core radius and density and a related cluster concentration parameter. The
model simultaneously solves a series of first-order ordinary differential
equations for the rate of change of the core radius, half-mass radius and the
number of member stars N. About two thousand integration steps in time are
required to solve for the entire evolution of a star cluster and this number is
approximately independent of N. We compare the model to the variation of these
parameters following from a series of direct N-body calculations of single-mass
clusters and find good agreement in the evolution of all parameters. Relevant
time-scales, such as the total lifetimes and core collapse times, are
reproduced with an accuracy of about 10% for clusters with various initial
half-mass radii (relative to their Jacobi radii) and a range of different
initial N up to N = 65536. We intend to extend this framework to include more
realistic initial conditions, such as a stellar mass spectrum and mass loss
from stars. The EMACSS code can be used in star cluster population studies and
in models that consider the co-evolution of (globular) star clusters and large
scale structures.
