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) buildup of NSCs from consecutive infall of stellar clusters and (2) continuous in situ star formation. Though the cluster infall scenario has been extensively studied, the in situ formation scenario has been hardly explored. Here we use Fokker-Planck (FP) calculations to study the effects of star formation on the buildup of NSCs and its implications for their long-term evolution and their resulting structure. We use the FP equation to describe the evolution of 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 buildup of an NSC with properties similar to those of the Milky Way NSC. We find that the 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 populations do not yet achieve a steady state. In particular, formed/evolved NSCs with in situ star formation contain differential age-segregated stellar populations that are not yet fully mixed. Younger stellar populations formed in the outer regions of the NSC have a cuspy structure toward the NSC outskirts, while showing a core-like distribution inward, with younger populations having larger core sizes. In principal, such a structure can give rise to an apparent core-like radial distribution of younger stars, as observed in the Galactic center.