Formation and evolution of nuclear star clusters with in-situ
  star-formation: Nuclear cores and age segregation
  Nuclear stellar cluster (NSCs) are known to exist around massive black holes
(MBHs) in galactic nuclei. Two formation scenarios were suggested for their
origin: (1) Build-up of NSCs from consecutive infall of stellar cluster and (2)
Continuous in-situ star-formation. Though the cluster-infall scenario has been
extensively studied in recent years, the in-situ formation scenario have been
hardly explored. Here we use Fokker-Planck (FP) calculations to study the
effects of star formation on the build-up of NSCs and its implications for
their long term evolution and their resulting structure. We use the FP equation
to describe the evolution of several stellar populations, and add appropriate
source terms to account for the effects of newly formed stars. We show that
continuous star-formation even 1-2 pc away from the MBH can lead to the
build-up of an NSC with properties similar to those of the Milky-way NSC. We
also find that the general structure of the old stellar population in the NSC
with in-situ star-formation could be very similar to the steady-state
Bahcall-Wolf cuspy structure. However, its younger stellar population do not
yet achieve a steady state. In particular, formed/evolved NSCs with in-situ
star-formation contain differential age-segregated stellar populations which
are not yet fully mixed. Younger stellar populations formed in the outer
regions of the NSC have a cuspy structure towards the NSC outskirts, while
showing a core-like distribution inwards; with younger populations having
larger core sizes. In principal, such a structure can give rise to an apparent
core-like radial distribution of younger (up to 2-3 Gyrs) stars, as observed in
the Galactic center. Such an NSC still preserves an underlying stellar cusp of
older stars, that can be potentially be missed by current observations of
red-giants.
