Eddington Luminosity

Consider a proton and electron (i.e. an ionized hydrogen atom) located at some distance d
from star that has mass M, radius R, luminosity L and temperature T. For purposes of this
problem, assume d >> R.
1. Consider two forces acting on the ion: radiation pressure and gravity. Write down an
expression for the net force, F, on the ion as a function of the variables described above.
You may have to “invent” an expression for the force due to radiation on the electron,
but remember that force is the change in momentum per unit time. Recall that the
cross section for photons scattering via Thomson scattering on electrons is σT .
2. Solve the equation determined in the previous part for L in the F = 0 case. Describe
what the solution means physically.
3. The luminosity that you have just determined is called the Eddington Luminosity.
Evaluate the Eddington Luminosity, LEdd, for the Sun.
4. Finally, for stars on the main sequence, the observed mass-luminosity relationship gives
L ∝ M4
. What mass of stars are at the Eddington luminosity? What would happen
to stars more massive than this?

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