The Black Hole Mass Function Derived from Local Spiral Galaxies

We present our determination of the nuclear supermassive black hole mass 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. The sample is defined by a limiting luminosity (redshift-independent) distance, D_L = 25.400 Mpc (z = 0.0057168) and a limiting absolute B-band magnitude, ℳ_B = -19.1223. 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 supermassive black hole in a host galaxy in order to estimate the mass of the 128 respective supermassive black holes in this volume-limited sample. This result effectively gives us the distribution of mass for supermassive black holes residing in spiral galaxies over a lookback time, t_L ≤ 82.140 h_67.77^-1 Myr and contained within a comoving volume, V_C = 3.3739 × 10⁴ h_67.77^-3 Mpc³. We estimate the density of supermassive black holes residing in spiral galaxies in the Local Universe is ρ = 5.54_-2.73^+6.55 × 10⁴ h_67.77³ M_⊙ Mpc^-3. Thus, our derived cosmological supermassive black hole mass density for spiral galaxies is Ω_BH = 4.35_-2.15^+5.14 × 10^-7 h_67.77. Assuming black holes grow via baryonic accretion, we predict that 0.0020_-0.0010^+0.0023 h_67.77³ % of the universal baryonic inventory (ΩBH/ω_b) is confined within nuclear supermassive black holes at the center of spiral galaxies.