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An expanded Mbh–σ diagram, and a new calibration of active galactic nuclei masses




We present an updated and improved Mbh–σ diagram containing 64 galaxies for which Mbh measurements (not just upper limits) are available. Because of new and increased black hole masses at the high-mass end, and a better representation of barred galaxies at the low-mass end, the ‘classical’ (all morphological type) Mbh–σ relation for predicting black hole masses is log (Mbh/M) = (8.13 ± 0.05) + (5.13 ± 0.34)log [σ/200 km s−1], with an rms scatter of 0.43 dex. Modifying the regression analysis to correct for a hitherto overlooked sample bias in which black holes with masses <106 M are not (yet) detectable, the relation steepens further to give log (Mbh/M) = (8.15 ± 0.06) + (5.95 ± 0.44)log [σ/200 km s−1]. We have also updated the ‘barless’ and ‘elliptical-only’Mbh–σ relations introduced by Graham and Hu in 2008 due to the offset nature of barred galaxies. These relations have a total scatter as low as 0.34 dex and currently define the upper envelope of points in the Mbh–σ diagram. They also have a slope consistent with a value 5, in agreement with the prediction by Silk & Rees based on feedback from massive black holes in bulges built by monolithic collapse.

Using updated virial products and velocity dispersions from 28 active galactic nuclei, we determine that the optimal scaling factor f– which brings their virial products in line with the 64 directly measured black hole masses – is 2.8+0.7−0.5. This is roughly half the value reported by Onken et al. and Woo et al., and consequently halves the mass estimates of most high-redshift quasars. Given that barred galaxies are, on average, located 0.5 dex below the ‘barless’ and ‘elliptical-only’Mbh–σ relations, we have explored the results after separating the samples into barred and non-barred galaxies, and we have also developed a preliminary corrective term to the velocity dispersion based on bar dynamics. In addition, given the recently recognized coexistence of massive black holes and nuclear star clusters, we present the first ever (Mbh+Mnc)–σ diagram and begin to explore how galaxies shift from their former location in the Mbh–σ diagram.