A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quantitative way to measure this morphological feature. This will allow comparison of spiral galaxy pitch angle to other galactic parameters and test spiral arm genesis theories. In this work, we detail our image processing and analysis of spiral galaxy images and discuss the robustness of our analysis techniques.

We present a relationship between spiral arm pitch angle (a measure of the tightness of spiral structure) and the mass of supermassive black holes (BHs) in the nuclei of disk galaxies. We argue that this relationship is expected through a combination of other relationships, whose existence has already been demonstrated. The recent discovery of AGN in bulgeless disk galaxies suggests that halo concentration or virial mass may be one of the determining factors in BH mass. Taken together with the result that mass concentration seems to determine spiral arm pitch angle, one would expect a relation to exist between spiral arm pitch angle and supermassive BH mass in disk galaxies, and we find that this is indeed the case. We conclude that this relationship may be important for estimating evolution in BH masses in disk galaxies out to intermediate redshifts, since regular spiral arm structure can be seen in galaxies out to z ≃ 1.

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We present new and stronger evidence for a previously reported relationship between galactic spiral arm pitch angle P (a measure of the tightness of spiral structure) and the mass M BH of a disk galaxy's nuclear supermassive black hole (SMBH). We use an improved method to accurately measure the spiral arm pitch angle in disk galaxies to generate quantitative data on this morphological feature for 34 galaxies with directly measured black hole masses. We find a relation of log(M/M ⊙ ) = (8.21 ± 0.16) − (0.062 ± 0.009)P. This method is compared with other means of estimating black hole mass to determine its effectiveness and usefulness relative to other existing relations. We argue that such a relationship is predicted by leading theories of spiral structure in disk galaxies, including the density wave theory. We propose this relationship as a tool for estimating SMBH masses in disk galaxies. This tool is potentially superior when compared to other methods for this class of galaxy and has the advantage of being unambiguously measurable from imaging data alone.

We present our determination of the nuclear supermassive black hole mass (SMBH) function for spiral galaxies in the local universe, established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the southern (δ < 0 • ) hemisphere. Our SMBH mass function agrees well at the high-mass end with previous values given in the literature. At the low-mass end, inconsistencies exist in previous works that still need to be resolved, but our work is more in line with expectations based on modeling of black hole evolution. This low-mass end of the spectrum is critical to our understanding of the mass function and evolution of black holes since the epoch of maximum quasar activity. A limiting luminosity (redshift-independent) distance, D L = 25.4 Mpc (z = 0.00572) and a limiting absolute B-band magnitude, M B = −19.12 define the sample. These limits define a sample of 140 spiral galaxies, with 128 measurable pitch angles to establish the pitch angle distribution for this sample. This pitch angle distribution function may be useful in the study of the morphology of late-type galaxies. We then use an established relationship between the logarithmic spiral arm pitch angle and the mass of the central SMBH in a host galaxy in order to estimate the mass of the 128 respective SMBHs in this volume-limited sample. This result effectively gives us the distribution of mass for SMBHs residing in spiral galaxies over a lookback time, t L ≤ 82.1 h . We estimate that the density of SMBHs residing in spiral galaxies in the local universe is ρ = 5.54 . Thus, our derived cosmological SMBH mass density for spiral galaxies is Ω BH = 4.35 of the universal baryonic inventory (Ω BH /ω b ) is confined within nuclear SMBHs at the center of spiral galaxies.