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On the distribution and evolution of supermassive black holes and host galaxies

Presentation #309.01 in the session AGN, QSOs, and Galactic Evolution.

Published onJul 01, 2023
On the distribution and evolution of supermassive black holes and host galaxies

Strong correlations exist between supermassive black holes (SMBHs) and their host galaxies. These correlations suggest a missing component in our current understanding: the role of energy cascade in SMBH-bulge coevolution. In this picture, energy is continuously cascaded from bulge scale rb down to the BH scale (Schwarzschild radius rs). Energy cascade has a scale-independent, but decreasing rate εb(t)≈ σb3/rb due to the cooling of baryonic component, where σb is bulge velocity dispersion. The bulge mass-size (Mb-rb) relation can be expressed as Mb ≈εb2/3rb5/3G-1, or a bulge density-size relation ρb ≈ εb2/3rb-4/3G-1, with εb≈ a-5/210-4m2/s3, as confirmed by the galaxy survey, where a is the scale factor and G is the gravitational constant. For SMBH with a mass MB, bolometric luminosity LB, energy cascade leads to a “cascade” force that must be balanced by the BH radiation force in its early life, i.e. LB/c ~ MBεb, where c is light speed. Since εb is much larger in the early universe, BH accretion can be super-Eddington with LB exceeding the Eddington limit. In addition, the BH mass-dispersion relation (MBb5) is a natural result of the cascade theory. A three stage mathematical model is proposed for SMBH evolution involving co-evolution, transitional, and dormant stages, respectively. Models are finally compared against the BH accretion history from quasar luminosity function from 2dF Redshift Survey, local galaxy and SMBHs data, and high redshift quasars from SDSS DR7 and CFHQS surveys. Accompanying slides and datasets for this work can be found at

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