Question regarding maximum accretion of black holes

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SUMMARY

The discussion centers on calculating the maximum accretion rate of black holes using the formula L=εM(dot)c², where ε is set at 0.1. Participants explore the relationship between the Eddington luminosity, Ledd = 4πcGMmp/σT, and the accretion efficiency. The key insight is that the maximum accretion rate can be expressed as M(dot)=κM, where κ is defined as κ=mp/σT. The concept of the accretion disk being optically thin is also mentioned as a relevant factor in this context.

PREREQUISITES
  • Understanding of black hole physics and accretion processes
  • Familiarity with the Eddington luminosity concept
  • Knowledge of the variables involved in the equations, such as mass (M), gravitational constant (G), and proton mass (mp)
  • Basic grasp of optical thickness in astrophysical disks
NEXT STEPS
  • Study the derivation of the Eddington luminosity in detail
  • Research the implications of optical thickness in accretion disks
  • Examine the role of accretion efficiency in black hole growth
  • Explore numerical simulations of black hole accretion processes
USEFUL FOR

Astronomers, astrophysicists, and students studying black hole dynamics and accretion phenomena will benefit from this discussion.

can't.do.phys
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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?
 
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Try not assuming there is a maximum accretion rate.
 

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