How a Klein-Nishina Modified Eddington limited accretion explains rapid black hole growth in the early universe

The discovery of quasars and their supermassive black holes (SMBHs) over $10^{9} M_{\odot}$ merely hundreds of millions of years after the Big Bang generates tension with the idea of Eddington-limited accretion and pressures the community into exploring the concept of massive black hole seeds and/or super-Eddington accretion. The observation that many black holes have reached supermassive status while obeying the Eddington limit is puzzling as accretion models are not spherically symmetric. We address this issue by illustrating the physics behind a picture of inner disk accretion involving a geometrically thick, hot quasi-spherical flow and argue that such an inner region provides the radiation that instantiates the Eddington limit. Given the energetics of the inner disk edge, we show how the characteristic electron cross-section drops below its Thomson value, allowing black holes to grow rapidly despite being Eddington-limited. Indeed, after implementing a modified cross-section calculated via the Klein-Nishina Formula, we find that SMBH formation time drops by up to $47\%$. In this context, we show how a $10^{9} M_{\odot}$ black hole can form from a seed $10 M_{\odot}$ black hole within $500$ Myr by way of accretion and mergers. While our picture is over-simplified and contrived in a number of ways that we discuss, we suggest that our scenario is interesting in that it offers a solution to two issues at the intersection of astrophysics and cosmology, namely the reason the Eddington limit is obeyed and how some black holes have grown rapidly despite that limit.