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 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.

Spiral structure is the most distinctive feature of disk galaxies and yet debate persists about which theory of spiral structure is correct. Many versions of the density wave theory demand that the pitch angle be uniquely determined by the distribution of mass in the bulge and disk of the galaxy. We present evidence that the tangent of the pitch angle of logarithmic spiral arms in disk galaxies correlates strongly with the density of neutral atomic hydrogen in the disk and with the central stellar bulge mass of the galaxy. These three quantities, when plotted against each other, form a planar relationship that we argue should be fundamental to our understanding of spiral structure in disk galaxies. We further argue that any successful theory of spiral structure must be able to explain this relationship.

The density-wave theory of galactic spiral-arm structure makes a striking prediction that the pitch angle of spiral arms should vary with the wavelength of the galaxy's image. The reason is that stars are born in the density wave but move out of it as they age. They move ahead of the density wave inside the co-rotation radius, and fall behind outside of it, resulting in a tighter pitch angle at wavelengths that image stars (optical and near infrared) than those that are associated with star formation (far infrared and ultraviolet). In this study we combined large sample size with wide range of wavelengths, from the ultraviolet to the infrared to investigate this issue. For each galaxy we used an optical wavelength image (B-band: 445 nm) and images from the Spitzer Space Telescope at two infrared wavelengths (infrared: 3.6 and 8.0 µm) and we measured the pitch angle with the 2DFFT and Spirality codes (Davis et al. 2012;Shields et al. 2015). We find that the B-band and 3.6 µm images have smaller pitch angles than the infrared 8.0 µm image in all cases, in agreement with the prediction of density-wave theory. We also used images in the ultraviolet from Galaxy Evolution Explorer, whose pitch angles agreed with the measurements made at 8 µm. Because stars imaged at those wavelengths have not had time during their short lives to move out of the star-forming region.