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

Abstract

In this paper we want to compare the theoretical predictions of a law proposed by Feoli and Mancini, with the most recent experimental data about galaxies and Supermassive black holes. The physical principle behind this law is the transformation of the angular momentum of the interstellar material, which falls into the black hole, into the angular momentum of the radiation emitted in this process. Despite the simplicity of the model, this law shows an excellent agreement with the experimental data for early -type galaxies while a new approach is proposed for spirals.

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).…”

“…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).…”

A note on the interpretation of the statistical analysis of the $M_{\bullet}-M_{G}\sigma ^{2}$ scaling relation

“…• The 2nd Sample is made up of 174 galaxies, obtained starting from the van den Bosch's sample (van den Bosch 2016), but excluding those galaxies whose mass of the SMBH shows a relative error on log(M • ) greater than or equal to 1 (Beltramonte et al 2019), NGC404, since its mass is too low for an SMBH and NGC4486b which "deviates strongly from any correlation involving the mass of its black hole" Saglia et al (2016). Finally, we also preferred to exclude NGC221, NGC1277, NGC1316, NGC5845 and UGC1841.…”