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

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 G σ 2 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 G σ 2 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 χ 2 (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 G σ 2 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 G σ 2 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.

New calibration and some predictions of the scaling relations between the mass of supermassive black holes and the properties of the host galaxies

“…It is also evident that we obtain very similar results using the LYNMIX_ERR routine and using the least squares (LS − TEST) without considering errors in both variables. Different is the behavior obtained by FITEXY that gives always higher slopes, as it has already been shown in our previous works (Feoli & Mancini 2009;Mancini & Feoli 2012). It means that the routine FITEXY is more sensible to the estimation of errors with respect to LYNMIX_ERR.…”

“…However, the aim of this paper is not to discover what the best among all the correlations is, but only to emphasize that a not widely − used relation such as the M • − M b σ 2 e , is at least as tight as the most famous ones and that in many cases, as for example in Mancini & Feoli (2012), it can offer better predictions than the others. To this aim we have used our relation to infer the masses of the SMBHs in the center of the two giant galaxies NGC 3842 and NGC 4889 that, following McConnell et al (2011), show "experimental values significantly higher than the ones predicted by the standard M • −σ e and M • − L laws".…”

“…This could generate a bias in the final best fit lines, but the consistency of the results obtained in our previous papers with different samples and fitting methods induces us to believe that this effect must be very small. For example, in Mancini & Feoli (2012), we examined a reduced, but homogeneous sample in which we consider separately stellar masses and dynamical masses and in that case we obtain a very small difference in the slope of our relation from 0.65 to 0.63 respectively, using LYNMIX_ERR and from 0.77 to 0.69 using FITEXY. At the end we will perform a similar check also in this paper, comparing the fit obtained with our sample with the one derived from the use of a new set of bulge masses recently published by Cappellari et al (2013).…”

“…On the other hand, the kinetic energy of the stellar bulges directly determines the temperature of the galactic system. The validity of the M • −M b σ 2 relation, as a predictor of the SMBH mass in the center of galaxies, has been already tested, with clear positive results, using several independent galaxy samples (Feoli & Mele 2005, 2007Feoli & Mancini 2009, 2011Mancini & Feoli 2012) and in the framework of the ΛCDM cosmology ), using two galaxy formation models based on the Millennium Simulation, one (the Durham model) by Bower et al (2006) and the other (the MPA model) by De Lucia & Blaizot (2007) .…”

A simple way to classify supermassive black holes

“…The continuous stream of multiwavelength experimental data and the use of modern methods to analyze them, is now giving more and more convincing evidence that these SMBHs are strongly correlated to the characteristics of their parent galaxy (Magorrian, Tremaine & Richstone 1998;Tremaine et al 2002;Marconi & Hunt 2003;Gebhardt et al 2003;Häring & Rix 2004;Feoli & Mele 2005;Aller & Richstone 2007;Graham 2008aGraham , 2008bHu 2008;Kisaka, Kojima & Otani 2008;Feoli & Mancini 2009;Gültekin 2009a;Beifiori 2009Beifiori , 2011Mancini & Feoli 2012) and, on the other hand, affect the processes of galaxy formation and evolution (Silk & Rees 1998;Burkert & Silk 2001;Cavaliere & Vittorini 2002;King 2003;Wyithe & Loeb 2003;Haiman, Ciotti, & Ostriker 2004;Granato et al 2004;Sazonov et al 2005;Murray, Quataert & Thompson 2005;Begelman & Nath 2005;Hopkins et al 2006a;Croton et al 2006;Sijacki et al 2007;Pipino 2009aPipino , 2009b. In a more cosmological context, numerical simulations and semi-analytical models revealed that the environment, in which these galaxies reside, may heavily influence the growth and the activity of the SMBHs (Di Matteo, Springel & Hernquist 2005;Hopkins et al 2006b;Hopkins et al 2008;Ciotti, Ostriker ...…”