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.

In this paper, we apply a method identified by Puerari & Dottori to find the corotation radii (CR) in spiral galaxies. We apply our method to 57 galaxies, 17 of which have already have their CR locations determined using other methods. The method we adopted entails taking Fourier transforms along radial cuts in the u, g, r, i, and z wavebands and comparing the phase angles as a function of radius between them. The radius at which the phase angles cross indicates the location of the corotation radius. We then calculated the relative bar pattern speed, R, and classified the bar as "fast", where R < 1.4, slow, where R 1.4, or intermediate, where the errors on R are consistent with the bar being "slow" or "fast". For the 17 galaxies that had their CR locations previously measured, we found that our results were consistent with the values of R obtained by the computer simulations of Rautiainen, Salo & Laurikainen. For the larger sample, our results indicate that 34 out of 57 galaxies (≃60%) have fast bars. We discuss these results in the context of its implications for dark matter concentrations in disk galaxies. We also discuss these results in the context of different models for spiral structure in disk galaxies.

Work done to date on the SMBH mass function has brought to light some interesting puzzles, the best known of which is cosmic downsizing. The solution to this problem is based upon the methodology by which we determine SMBH masses, which comes mainly from studies of active galaxies. The most massive SMBHs cease to be active at earlier epochs than their less massive counterparts, thus leading to an apparent decrease in the SMBH mass function with time. The larger SMBHs should still be present in the local Universe, but they lie in quiescent galaxies. This lack of certainty reflects the biggest gap in the observational record -the mass of SMBHs in quiescent galaxies. We are addressing this issue, using three methods described here: Spiral arm pitch angle: We are exploiting a relationship between the tightness of the spiral arms of local galaxies (measured using the pitch angle) and the mass of their central SMBH as determined by Seigar et al. (2008; see Figure 1) to determine the masses of SMBHs out to z ≈ 1 using archival HST imaging data. Binary SMBHs: A very tantalizing source for LISA will be binary SMBH mergers. We are searching for SMBH binaries using archival Chandra images of ULIRGs.Quasar Gas Dynamics: We are estimating SMBH masses for a sample of SDSS quasars at z = 1.88, 2.80, and 4.06. To compute the SMBH mass, we are using single-epoch spectra to measure the speed of gas in the broad-line region (BLR) by measuring the linewidths. To probe possible evolution in the relation in Figure 1, we are using a sample of nearby spirals from the GOODS fields that elso exhibit AGN activity, and we can then use both spiral arm pitch angle and BLR dynamics to estimate the SMBH masses.

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