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 S\'ersic 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.
