So I've got a question that I can't seem to figure out. If the accretion efficiency of a black hole is L=εM(dot)c2 with ε=0.1 I have to set this to the Eddington luminosity which is Ledd = 4πcGMmp/σT to find the maximum rate at which a black hole can accrete by. I found that κ=mp/σT so I substituted that but then I got stuck. Has it got something to do with the accretion disk being optically thin? the answer should be M(dot)=κM but i can't figure out how to get it. help?