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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.