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Unformatted text preview: photons. I will write down the calculation, even though it is beyond the scope
of this course. You can study it for extra credit (or intellectual curiosity).
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L = Flux = Diusion Energy Density = c d(aT 4) :
Coecient
Gradient
4r2
3 dr
Here is the opacity, which comes from atomic physics. Let us assume that
this is a constant (as it very nearly is for highly ionized matter). Then,
neglecting constants, we have M=R3
T M=R (virial theorem) : So 24
5
4
L / R T R (M=R) M 3 :
R M R
Notice that the R's cancel, so we never had to use the massradius relation,
or the empirical formula for central temperature, but only the virial theorem.
How good is this? Since we do not at this stage know a numerical value for
, we cannot check the constant, but only the scaling from the solar value:
6
prediction
normalized
here −1 log(L /L )
ta da 4 n tio ic
red p 2 −0.5 0.5
−2 MassLuminosity Relation for Stars 122 1 1.5 log(M/M ) ...
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 Fall '09
 dion

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