Deciphering the origins and growth of supermassive black holes

Abstract: We present a well-tested, theoretically supported empirical relation that helps decipher the origins, growth, and properties of SMBHs (supermassive black holes). Based on theoretical considerations and analysis of mass (MBH) versus age (t) distribution of 93 high-redshift (z>5.6) SMBHs, we get MBH = Ms exp [14.6(t-100)/t (Myr)], which gives the SMBH's seed mass Ms and its derivative gives the instantaneous mass-accretion rate. It yields seeds of ~ 20-420 Msun (solar masses) for the recently discovered SMBHs GNz11, CEERS-19, and UHZ1 and (~ 3E+04 Msun) for the largest (1.24E+10 Msun) high-z SMBH. It is applied to 132446 SMBHs at z <2.4, cataloged by Kozlowski. The resultant seeds are classified based on size and likely formation mechanism: ~54 percent are classified as light (<350 Msun) deemed to be Pop III remnants; ~40 percent as intermediate (350-2 x 3E+03 Msun) and ~6 percent as heavier seeds (2 x 103-3E+04 Msun), both of which may have formed by mergers of Pop III remnants. The direct collapse black hole (DCBH) mechanism is not required but is not excluded. Furthermore, the results show the following. The mass-accretion rate increases exponentially from the seed's inception at z ~30, reaches a broad plateau at z ~ 8.5 to 6 coincident with the epoch of reionization, and decreases monotonically towards z=0. Sub-Eddington accretion is the norm, except during the first ~150 Myr, SMBHs experienced super-Eddington accretion, or the radiative efficiency was <0.1. The largest seed can potentially grow via luminous accretion up to (6.6+/-2.2)E+10 Msun, consistent with a theoretical limit of ~ 5+10 Msun proposed by King. The Eddington ratio decreases, and the radiative efficiency increases as z decreases, consistent with recent findings.