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It is generally accepted that supermassive black holes (SMBHs) grew fromprogenitor seeds; but it remains unclear when the seeds formed, how large theywere, and what were their growth rates. This study finds answers to such openquestions in an analysis and interpretation of available mass (MBH) and age (t)data of SMBHs at z>5.7. Their distribution reveals that a significant number(36) spread over 300 million years (Myr) of cosmic time have markedly similarmasses (within a factor of 2) even though MBH depends on age. Besides age, MBHdepends upon seed mass Ms, origin time ts, and a variable dubbed accretionratio AR. The analysis leads to the conclusion that the 36 SMBHs hadsimilar-size seeds that formed essentially concurrently and that AR isinversely proportional to t. Consequently, we get 36 equations with 1 variable(t) and 3 parameters. Solving these equations using the SANN method, theoptimum values of the parameters define AR as a function of age t, and MBH as afunction of Ms and t. These relationships are tested and applied to thousandsof SMBHs. The results indicate that ts ~100Myr (z=30); that SMBHS > 1E+09M*(solar masses) require seeds > 1E+03M* but < 5E+04M*; that seeds grew at anexponentially increasing rate that reached a maximum near z=7 and decreasedthereafter; that seeds may have initially experienced a short period (150 Myr)of super-Eddington accretion or accretion efficiency much <0.1; that about halfof the growth occurs from z=30-3.5 and the rest thereafter, and that accretionis the predominant mode of growth with an upper limit of 2.2E+06Ms orMBH=(6.7+/-2)E+10M*. This study provides quantitative estimates of accretionrates, constraints for models of seed formation, and insights into the originsand growth of Sagittarius A*.

Insights into the origins and growth of seeds of supermassive black holes