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).
L = Flux = Diusion Energy Density = c d(aT 4) :
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
L / R T R (M=R) M 3 :
R M R
Notice that the R's cancel, so we never had to use the mass-radius 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:
here −1 log(L /L )
ta da 4 n tio ic
red p 2 −0.5 0.5
−2 Mass-Luminosity Relation for Stars 122 1 1.5 log(M/M ) ...
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