How Does Eddington Luminosity Limit Black Hole Mass Accretion Rates?

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SUMMARY

The Eddington luminosity establishes a critical threshold for the mass accretion rate of black holes, defined by the formula L_edd = 13*10^38 M/M_sun [erg s-1]. This discussion reveals that calculating the maximum black hole mass results in M = 10^(-8)M_sun, which is deemed impossible. Participants seek clarification on the luminosity values used in these calculations to reconcile the discrepancies in black hole mass estimates.

PREREQUISITES
  • Understanding of Eddington luminosity
  • Familiarity with black hole physics
  • Basic knowledge of astrophysical formulas
  • Concept of mass accretion rates
NEXT STEPS
  • Research the implications of Eddington luminosity on black hole formation
  • Explore the relationship between luminosity and mass in astrophysics
  • Investigate methods for measuring black hole mass accretion rates
  • Learn about the limitations of current black hole mass estimation techniques
USEFUL FOR

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

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Homework Statement
I need help with the following problem (this is from the book Accretion Power in Astrophysics):

Consider a black hole accreting spherically symmetrically from a fixed medium (constant density and temperature). What is the maximum mass a seed black hole could
grow to before its luminosity would limit further growth? Assume that the efficiency
η for spherically symmetrical accretion is a free parameter. Calculate its value for
fiducial ISM parameters, T = 104 K, n = 1 cm−3. Does this maximum mass have
an astrophysical interpretation?
Relevant Equations
L_edd = 13*10^38 M/M_sun [erg s-1]
The Eddington luminosity gives a limit on the mass accretion rate of the black hole and therefore of the mass of the black hole.
L_edd = 13*10^38 M/M_sun [erg s-1]. When I calculate from this I get that the maximum mass is M = 10^(-8)M_sun... which is impossible. Any ideas?
 
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How did you get that mass?
Or, asked differently, what did you use as luminosity?
 

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