On the Dynamical Evolution of the Arches Cluster
  We study the dynamical evolution of the young star cluster Arches and its
dependence on the assumed initial stellar mass function (IMF). We perform many
direct $N$-body simulations with various initial conditions and two different
choices of IMFs. One is a standard Kroupa IMF without any mass segregation. The
other is a radially dependent IMF, as presently observed in the Arches. We find
that it is unlikely for the Arches to have attained the observed degree of mass
segregation at its current age starting from a standard non-segregated Kroupa
IMF. We also study the possibility of a collisional runaway developing in the
first $\sim 2-3 \rm{Myr}$ of dynamical evolution. We find that the evolution of
this cluster is dramatically different depending on the choice of IMF: if a
primordially mass segregated IMF is chosen, a collisional runaway should always
occur between $2-3 \rm{Myr}$ for a broad range of initial concentrations. In
contrast, for a standard Kroupa IMF no collisional runaway is predicted. We
argue that if Arches was created with a mass segregated IMF similar to what is
observed today then at the current cluster age a very unusual, high-mass star
should be created. However, whether a collisional runaway leads to the
formation of an intermediate-mass black hole (IMBH) depends strongly on the
mass loss rate via winds from massive stars. Growth of stellar mass through
collisions can be quenched by strong wind mass loss. In that case, the
inter-cluster as well as intra-cluster medium are expected to have a
significant Helium enrichment which may be observed via Helium recombination
lines. The excess amount of gas lost in winds may also be observed via X-ray
observations as diffused X-ray sources.
