A simple way to classify supermassive black holes

Abstract

We propose a classification of supermassive black holes (SMBHs) based on their efficiency in the conversion of infalling mass in emitted radiation. We use a theoretical model that assumes a conservation of angular momentum between the gas falling inside the hole and the photons emitted outwards, and suggests the existence of the scaling relation M•-Reσ 3 , where M• is the mass of the central SMBH, whereas Re and σ are the effective radius and velocity dispersion of the host galaxies (bulges), respectively. We apply our model on a data set of 57 galaxies of different morphological types and with M• measurements, obtained through the analysis of Spitzer/IRAC 3.6-μm images. In order to find the best fit of the corresponding scaling law, we use the FITEXY routine to perform a least-squares regression of M• on Reσ 3 for the considered sample of galaxies. Our analysis shows that the relation is tight and our theoretical model allows to easily estimate the efficiency of mass conversion into radiation of the central SMBHs. Finally we propose a new appealing way to classify the SMBHs in terms of this parameter.

Some Predictions of Scaling Relations: The Case of the Black Hole in M87

“…The core of the model is the transformation of the angular momentum of the matter falling into the black hole, into the angular momentum of the radiation emitted during the process. Further details can be found in Feoli andMancini (2011), Feoli (2014a) and Beltramonte et al (2019). This model works better for the early-type galaxies, as can be observed in Feoli and Iannella (2019) and in Beltramonte et al (2019).…”

“…if we know the efficiency of the black hole we can calculate the angular momentum of the matter orbiting around the hole, but not the spin of the black hole itself. The argument of angular momentum has been faced in a series of papers cited in Feoli (2014a), Feoli andMancini (2011), andBeltramonte et al (2019). An interesting and more recent discussion of the angular momentum problem in an accretion disc can be found in Blandford and Globus (2022).…”

“…Feoli and Mele (2005) proposed a correlation between the mass of a supermassive black hole and the kinetic energy of the host galaxy. This correlation was tested with many different samples and fitting methods (Feoli and Mele, 2007;Feoli and Mancini, 2009;Mancini and Feoli, 2012;Benedetto et al 2013;Iannella and Feoli, 2020) and a theoretical background was proposed in Feoli (2014b). Furthermore, in Iannella et al (2021), the predictive power of the relation has been analysed and the statistical elaboration done previously has been enhanced.…”

“…where m H is the mass of the hydrogen atom, k the Boltzmann constant, m e is the electron mass and δ a parameter. Considering that the adiabatic index 102 IANNELLA & FEOLI for an ideal relativistic gas is γ = 4/3, we obtain (for more details see Feoli, 2014b):…”

A study of the scaling relation $M_{\bullet }\propto R_{e}\sigma ^{3}$ for supermassive black holes and an update of the corresponding theoretical model

“…It is clear that our report foresees the experimental data in the range of errors, unlike Thomas et al (2016), so the relation can be a useful tool to predict black hole masses in difficult cases. Furthermore, in Feoli (2014), a classification of black holes based on the value of the parameter ǫ has been proposed. This coefficient describes the efficiency of the black hole in the conversion of the matter captured into emitted radiation.…”