The discovery of a relationship between supermassive black hole (SMBH) mass and spiral arm pitch angle (P) is evidence that SMBHs are tied to the overall secular evolution of a galaxy. The discovery of SMBHs in late-type galaxies with little or no bulge suggests that an underlying correlation between the dark matter halo concentration and SMBH mass (MBH) exists, rather than between the bulge mass and MBH. In this paper we measure P using a two-dimensional fast fourier transform and estimate the bar pattern speeds of 40 barred spiral galaxies from the Carnegie-Irvine Galaxy Survey. The pattern speeds were derived by estimating the gravitational potentials of our galaxies from Ks-band images and using them to produce dynamical simulation models. The pattern speeds allow us to identify those galaxies with low central dark halo densities, or fast rotating bars, while P provides an estimate of MBH. We find that a wide range of MBH exists in galaxies with low central dark matter halo densities, which appears to support other theoretical results. We also find that galaxies with low central dark halo densities appear to follow more predictable trends in P versus de Vaucouleurs morphological type (T) and bar strength versus T than barred galaxies in general. The empirical relationship between MBH and total gravitational mass of a galaxy (Mtot) allows us to predict the minimum Mtot that will be observationally measured of our fast bar galaxies. These predictions will be investigated in a subsequent paper.
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