The scaling relation between the mass of supermassive black holes and the kinetic energy of random motions of the host galaxies

¹ Max-Planck-Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
e-mail: mancini@mpia.de
² Department of Physics, University of Salerno, via Ponte Don Melillo, 84084 Fisciano (SA), Italy
³ Department of Engineering, University of Sannio, Piazza Roma 21, 82100 Benevento, Italy
e-mail: feoli@unisannio.it

Received: 2 May 2011
Accepted: 13 October 2011

Abstract

Context. Thanks to the improved angular resolution of modern telescopes and kinematic models, the existence of supermassive black holes (SMBHs) in the inner part of galaxies, regardless their morphology and nuclear activity, has been established on quite solid grounds. A possible correlation between the mass of SMBHs (M_•) and the evolutionary state of their host galaxies is expected and is currently under a heated debate.

Aims. Based on the recent 2D decomposition of 3.6 μm Spitzer/IRAC images of local late- and early-type galaxies with M_• measurements, we investigated various scaling laws, studying what is the best predictor of the mass of the central black holes, that is the one with the lowest value of intrinsic scatter. In particular, we focused on the M_• − M_Gσ² law, that is the relation between the mass of SMBHs and the kinetic energy of random motions of the corresponding host galaxies, M_G is the mass and σ the velocity dispersion of the host galaxy (bulge).

Methods. In order to find the best fit for each of the scaling laws examined, we performed a least-squares regression of M_• on x for the considered sample of galaxies, x being a whatever known parameter of the galaxy bulge. For this purpose, we made use of both the linear regression LINMIX_ERR and FITEXY methods.

Results. Our analysis shows that M_• − M_Gσ² law fits the examined experimental data successfully as much as the other known scaling laws (all correlations have similar intrinsic scatters within the errors) and shows a value of χ² (estimated by FITEXY) better than the others, a result which is consistent with previous determinations at shorter wavelengths. This means that a combination of σ and M_G (or R_e) could be necessary to drive the correlations between M_• and other bulge properties. This issue has been investigated by a careful, although not fully conclusive, analysis of the residuals of the various relations.

Conclusions. In order to avoid rushed conclusions on galaxy activity and evolution, the indirect inferring of the masses of the supermassive black holes from the kinetic energy of random motions via the M_• − M_Gσ² relation should be considered, especially when applied to higher redshift galaxies (z > 0.01). This statement is suggested by a reanalysis of Sloan Digital Sky Survey (SDSS) data used to study the black hole growth in the nearby Universe. By adopting the M_• − M_Gσ² relation instead of the M_• − σ relation, a radio-quiet/radio-loud dichotomy appears in the SMBH mass distribution of the corresponding SDSS early-type AGN galaxies.