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

Nuclear star clusters (NSCs) are dense stellar clusters that are found at the centers of a majority of 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 x 10(8)-8 x 10(10)Mand 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/Lrelationships and examine their correlation. We use the multi-Gaussian expansion to derive the NSC densities and their 3D mass-density profiles. The 3D density profiles characterize the NSC densities on scales as small as similar to 1 pc, approaching the likely spheres of influence for BHs in these objects. We find that these densities correlate with galaxy mass, with NSC density profiles becoming both denser and flatter at higher galaxy masses. Most galaxy NSCs are denser than typical globular clusters. We parameterize the 3D NSC density profiles and their scatter and slope as a function of galaxy stellar mass to enable the construction of realistic nuclear mass profiles. Our fitted profiles and the derived relations 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.