  We present observations of the HCN and HCO+ J=1-0 transitions in the center
of the nearby spiral galaxy NGC 6946 made with the BIMA and CARMA
interferometers. Using the BIMA SONG CO map, we investigate the change in the
I_HCN/I_CO and I_ HCO/I_CO integrated intensity ratios as a function of radius
in the central kiloparsec of the galaxy, and find that they are strongly
concentrated at the center. We use the 2MASS K_S band image to find the stellar
surface density, and then construct a map of the hydrostatic midplane pressure.
We apply a PDR model to the observed I_HCN/I_HCO+ integrated intensity ratio to
calculate the number density of molecular hydrogen in the dense gas tracer
emitting region, and find that it is roughly constant at 10^5 cm^-3 across our
map. We explore two hypotheses for the distribution of the dense gas. If the
HCN and HCO+ emission comes from self-gravitating density peaks inside of a
less dense gas distribution, there is a linear proportionality between the
internal velocity dispersion of the dense gas and the size of the density peak.
Alternatively, the HCN and HCO+ emission could come from dense gas
homogeneously distributed throughout the center and bound by ambient pressure,
similar to what is observed toward the center of the Milky Way. We find both of
these hypotheses to be plausible. We fit the relationships between I_HCN,
I_HCO+, and I_CO. Correlations between the hydrostatic midplane pressure and
I_HCN and I_HCO+ are demonstrated, and power law fits are provided. We confirm
the validity of a relation found by Blitz & Rosolowsky (2006) between pressure
and the molecular to atomic gas ratio in the high hydrostatic midplane pressure
regime (10^6-10^8 cm^-3 K).
