Fundamental Planes and the BarlessMBH‐σ Relation for Supermassive Black Holes

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Abstract
The residuals about the standard Mbh-σ relation correlate with the effective radius, absolute magnitude, and Sérsic index of the host bulge, giving rise to an apparent black hole "fundamental plane." However, we show that the elliptical galaxies do not define such a plane. Instead, it is a handful of barred galaxies, which are shown to systematically deviate from the Mbh-σ relation by δ log Mbh ≈ − 0.5 to –1.0 dex (their σ-values are too large) and generate much of the aforementioned three-parameter correlations. Removal of the seven barred galaxies from the Tremaine et al. set of 31 galaxies gives a "barless" Mbh-σ relation with an intrinsic scatter of 0.17 dex (vs. 0.27 dex for the 31 galaxies) and a total scatter of 0.25 dex (vs. 0.34 dex for the 31 galaxies). Furthermore, removal of the barred galaxies, or all the disk galaxies, from an expanded and updated set of 40 galaxies with direct black hole mass measurements gives a consistent result, such that log (Mbh/M☉) = (8.25 ± 0.05) + (3.68 ± 0.25) log (σ/200 km s−1) . In addition, the barless σ-L relation for galaxies with direct black hole mass measurements is found to be consistent with that from the SDSS sample of early-type galaxies, and the barless Mbh-σ relation, the Mbh-n relation, and the K-band Mbh-L relation are all shown to yield SMBH masses less than 2–4 × 109 M☉.