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ay45c5-page10 - photons I will write down the calculation...

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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). " #" # ! L = Flux = Di usion  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 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: 6 prediction normalized 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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