  The volumetric rate of tidal disruption events (TDEs) encodes information on
the still-unknown demographics of central massive black holes (MBHs) in
low-mass galaxies ($\lesssim 10^9$~M$_\odot$). Theoretical TDE rates from model
galaxy samples can extract this information, but this requires accurately
defining the nuclear stellar density structures. This region is typically
dominated by nuclear star clusters (NSCs), which have been shown to increase
TDE rates by orders of magnitude. Thus, we assemble the largest available
sample of pc-scale 3-D density profiles that include NSC components. We
deproject the PSF-deconvolved surface brightness profiles of 91 nearby galaxies
of varying morphology and combine these with nuclear mass-to-light ratios
estimated from measured colors or spectral synthesis to create 3-D mass density
profiles. We fit the inner 3-D density profile to find the best-fit power-law
density profile in each galaxy. We compile this information as a function of
galaxy stellar mass to fit new empirical density scaling relations. These fits
reveal positive correlations between galaxy stellar mass and central stellar
density in both early- and late-type galaxies. We find that early-type galaxies
have somewhat higher densities and shallower profiles relative to late-type
galaxies at the same mass. We also use the density profiles to estimate the
influence radius of each galaxy's MBH and find that the sphere of influence was
likely resolved in most cases. These new relations will be used in future works
to build mock galaxy samples for dynamical TDE rate calculations, with the aim
of constraining MBH demographics in low-mass galaxies.
