How Does Eddington Luminosity Limit Black Hole Mass Accretion Rates?

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fishlens
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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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