Luminosity Models and Density Profiles for Nuclear Star Clusters for a Nearby Volume-Limited Sample of 29 Galaxies

Nuclear Star Clusters (NSCs) are dense clusters of stars that reside in the centers of a majority of the galaxies. In this paper, we study the density profiles for 29 galaxies in a volume-limited survey within 10 Mpc to characterize their NSCs. These galaxies span a 3$\times$10$^8$ - 8$\times$10$^{10}$ M$_\odot$ and a wide range of Hubble types. We use high-resolution Hubble space telescope archival data to create luminosity models for the galaxies using Sersic profiles to parameterize the NSCs. We also provide estimates for photometric masses of NSCs and their host galaxies using color-M/L relationships and examine their correlation. We use the Multi-Gaussian Expansion (MGE) to derive the NSC densities and their 3-D mass density profiles. The 3-D density profiles characterize the NSC densities on the scales as small as $\sim$1 pc, approaching the likely spheres of influence for black holes in these objects. We find that these densities correlate with galaxy mass, with galaxies most NSCs being denser than typical globular clusters. We parametrize the 3-D NSC density profiles, and their scatter and slope as a function of galaxy stellar mass to enable the construction of realistic nuclear mass profiles. These are useful in predicting the rate of tidal disruption events in galaxies. We will verify the results of this paper in a follow-up paper that presents the dynamical modeling of the same sample of NSCs.