THE<i>M</i>-σ AND<i>M</i>-<i>L</i>RELATIONS IN GALACTIC BULGES, AND DETERMINATIONS OF THEIR INTRINSIC SCATTER

TLDR

We aim to derive improved M‑σ and M‑L relations for supermassive black holes using 49 mass measurements and 19 upper limits. We focus on accurately recovering the intrinsic scatter (ε₀) in both relations. The best‑fit relations are log(M_BH/M⊙)=8.12+4.24 log(σ/200 km s⁻¹) with ε₀=0.44 for all galaxies and 8.23+3.96 log(σ/200 km s⁻¹) with ε₀=0.31 for ellipticals; the M‑L relation is log(M_BH/M⊙)=8.95+1.11 log(L_V/10¹¹ L⊙,V) with ε₀=0.38 for early‑type galaxies, and the larger scatter in spirals implies selection bias and the need to account for scatter when estimating the local black hole mass function.

Abstract

We derive improved versions of the relations between supermassive black hole mass (M_BH) and host-galaxy bulge velocity dispersion (sigma) and luminosity (L) (the M-sigma and M-L relations), based on 49 M_BH measurements and 19 upper limits. Particular attention is paid to recovery of the intrinsic scatter (epsilon_0) in both relations. We find log(M_BH / M_sun) = alpha + beta * log(sigma / 200 km/s) with (alpha, beta, epsilon_0) = (8.12 +/- 0.08, 4.24 +/- 0.41, 0.44 +/- 0.06) for all galaxies and (alpha, beta, epsilon_0) = (8.23 +/- 0.08, 3.96 +/- 0.42, 0.31 +/- 0.06) for ellipticals. The results for ellipticals are consistent with previous studies, but the intrinsic scatter recovered for spirals is significantly larger. The scatter inferred reinforces the need for its consideration when calculating local black hole mass function based on the M-sigma relation, and further implies that there may be substantial selection bias in studies of the evolution of the M-sigma relation. We estimate the M-L relationship as log(M_BH / M_sun) = alpha + beta * log(L_V / 10^11 L_sun,V) of (alpha, beta, epsilon_0) = (8.95 +/- 0.11, 1.11 +/- 0.18, 0.38 +/- 0.09); using only early-type galaxies. These results appear to be insensitive to a wide range of assumptions about the measurement errors and the distribution of intrinsic scatter. We show that culling the sample according to the resolution of the black hole's sphere of influence biases the relations to larger mean masses, larger slopes, and incorrect intrinsic residuals.