  The formation of nuclear star clusters (NSCs) remains an open question. In
this work, we use spatially resolved HST/STIS spectroscopic observations of
three nearby NSCs (hosted by NGC 5102, NGC 5206, and NGC 205) to constrain
their formation histories by exploring radial variations of the stellar
populations within each cluster. Utilizing full-spectrum fitting, we find
substantial age and metallicity gradients within the central 0."9 (16~pc) of
the NSC in NGC 5102 where populations near the center are young/metal-rich (age
~400~Myr and [M/H] ~-0.4) and become older/metal-poor at larger radii (mean age
~1~Gyr and mean [M/H] ~-1.6 in the radial range [0."3, 0."9]). This behavior
suggests that the young/metal-rich population at the center was formed from a
period of in situ formation, while the older/metal-poor populations were likely
formed by inspiraled globular clusters. The two broad populations observed in
the NGC 5102 NSC (young/metal-rich and old/metal-poor) appear to be linked to
the transition between the two morphological components of the NSC derived from
the surface-brightness profile in Nguyen et al. (2018)(arXiv:1711.04314). The
radial ranges explored in NGC 5206 and NGC 205 were much smaller due to poor
data quality; in NGC 5206 we find a similar metallicity gradient to NGC 5102
(but with much lower significance), while the data for NGC 205 is too poor to
reach any conclusions. Overall, this data highlights the links between the
morphological and stellar population complexity of NSCs and their formation
mechanisms.
