Star-formation in nuclear clusters and the origin of the Galactic center apparent core distribution

Nuclear stellar clusters (NSCs) are known to exist around massive black holes (MBHs) in galactic nuclei. Two formation scenarios were suggested for their origin: build-up of NSCs and Continuous in-situ star-formation. Here we 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 show that continuous star-formation 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 does 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.