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Nuclear Star Clusters (NSCs) are dense clusters of stars that reside in thecenters of a majority of the galaxies. In this paper, we study the densityprofiles for 29 galaxies in a volume-limited survey within 10 Mpc tocharacterize their NSCs. These galaxies span a 3$\times$10$^8$ -8$\times$10$^{10}$ M$_\odot$ and a wide range of Hubble types. We usehigh-resolution Hubble space telescope archival data to create luminositymodels for the galaxies using S\'ersic profiles to parameterize the NSCs. Wealso provide estimates for photometric masses of NSCs and their host galaxiesusing color-M/L relationships and examine their correlation. We use theMulti-Gaussian Expansion (MGE) to derive the NSC densities and their 3-D massdensity profiles. The 3-D density profiles characterize the NSC densities onthe scales as small as $\sim$1 pc, approaching the likely spheres of influencefor black holes in these objects. We find that these densities correlate withgalaxy mass, with galaxies most NSCs being denser than typical globularclusters. We parametrize the 3-D NSC density profiles, and their scatter andslope as a function of galaxy stellar mass to enable the construction ofrealistic nuclear mass profiles. These are useful in predicting the rate oftidal disruption events in galaxies. We will verify the results of this paperin a follow-up paper that presents the dynamical modeling of the same sample ofNSCs.

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