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 supermassive black holes (SMBHs). Based on theoretical considerations and analysis of mass (MBH) versus age (t) distribution of high-redshift (>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 M☉ (solar masses) for the recently discovered SMBHs GNz11, CEERS_1019, and UHZ1, and ∼3 × 104 M☉ for the largest (1.24 × 1010 M☉) high-z SMBH. It is applied to 132446 SMBHs at z < 2.4. The resultant seeds are classified based on size and likely formation mechanism: ∼54 per cent are classified as light (<350 M☉) deemed to be Pop III remnants; ∼40 per cent as intermediate (350–2 × 103 M☉) and ∼6 per cent as heavier seeds (2 × 103–3 × 104 M☉), both of which formed possibly by mergers of Pop III remnants. The direct collapse black hole (DCBH) mechanism is not required but not excluded. Furthermore, the results show the following. The mass-accretion rate increases exponentially from the seed's inception (z ∼ 30), reaches a broad plateau at z ∼ 8.5–6 coincident with the epoch of reionization, and decreases monotonically thereafter. Sub-Eddington accretion is the norm, except during the first ∼150 Myr SMBHs either experienced super-Eddington accretion or the radiative efficiency was much < 0.1. The largest seed can potentially grow via luminous accretion to (6.6 ± 2.2) × 1010 M☉, consistent with a theoretical limit of ∼5 × 1010 M☉. The Eddington ratio decreases and radiative efficiency increases as z decreases, consistent with recent findings.