Quantifying Feedback from Narrow Line Region Outflows in Nearby Active
  Galaxies. IV. The Effects of Different Density Estimates on the Ionized Gas
  Masses and Outflow Rates
  Active galactic nuclei (AGN) can launch outflows of ionized gas that may
influence galaxy evolution, and quantifying their full impact requires
spatially resolved measurements of the gas masses, velocities, and radial
extents. We previously reported these quantities for the ionized narrow-line
region (NLR) outflows in six low-redshift AGN, where the gas velocities and
extents were determined from Hubble Space Telescope long-slit spectroscopy.
However, calculating the gas masses required multi-component photoionization
models to account for radial variations in the gas densities, which span
$\sim$6 orders of magnitude. In order to simplify this method for larger
samples with less spectral coverage, we compare these gas masses with those
calculated from techniques in the literature. First, we use a recombination
equation with three different estimates for the radial density profiles. These
include constant densities, those derived from [S II], and power-law profiles
based on constant values of the ionization parameter ($U$). Second, we use
single-component photoionization models with power-law density profiles based
on constant $U$, and allow $U$ to vary with radius based on the [O
III]/H$\beta$ ratios. We find that assuming a constant density of $n_\mathrm{H}
=$ 10$^2$ cm$^{-3}$ overestimates the gas masses for all six outflows,
particularly at small radii where the outflow rates peak. The use of [S II]
marginally matches the total gas masses, but also overestimates at small radii.
Overall, single-component photoionization models where $U$ varies with radius
are able to best match the gas mass and outflow rate profiles when there are
insufficient emission lines to construct detailed physical models.
