Nuclear Astrophysics

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CNO-Cycle Luminosity vs Core Temperature From page 17, we had: Dropping the “CNO” subscripts, and considering this formula at the centre of the star: Substitute in the previous result for : Last lecture, we derived, for Polytrope (n = 3) the result: Refer to Page 2 to understand that . 30
The power per unit mass produced in the stellar core is, after all, what is responsible for the luminosity at the stellar surface. We now try to come up with a generalized formula for the nuclear energy generation rate for any Main Sequence star. We do this by performing a mass-averaged energy generation rate. And this massaveraged rate times the stellar mass should, if the model is anywhere close to reality, give us a quantitative trend that is similar to the observational data. We now have all the ingredients we need to determine the relationship between surface temperature (effective temperature) and the stellar luminosity. Start substituting the results from previous slides. I will do the case for the pp-chain Multiply and divide by unity: so that numerator will have 31
Page 1 and 2: Nuclear Astrophysics Lecture 9 &10
Page 3 and 4: We have (again) Set the argument of
Page 5 and 6: Let’s pull out the physics of thi
Page 7 and 8: Finally, recall 7
Page 9 and 10: Examples: The core of our Sun has a
Page 11 and 12: Reaction Rate: Temperature Dependen
Page 13 and 14: Using the equations on previous sli
Page 15 and 16: Finally, then, we have that the mas
Page 17 and 18: The power series expansion of , for
Page 19 and 20: Structure of Polytrope Sun Let us d
Page 21 and 22: Derivative of Luminosity 21
Page 23 and 24: Arbitrary Units Standard Solar Mode
Page 25 and 26: Proton-Proton-Chain p + p d + e +
Page 27 and 28: The nuclear energy production in Ma
Page 29: PP-Chain Nuclear Energy Rate vs Cor
Page 33 and 34: From page 15, Lecture 6, the Main S
Page 35 and 36: Main Sequence: Core Temperature vs
Page 37 and 38: Luminosity vs Effective Temperature
Page 39 and 40: We have a first “hint” here of
Page 41 and 42: Main Sequence: Luminosity vs Effect
Page 43 and 44: Hertzprung-Russel Diagram CNO Cycle
Page 45 and 46: Integrated Luminosity Let us take 9
Page 47 and 48: Mass Interior to Radius Mass contai
Page 49: Nuclear Generation Rate Using the p

Nuclear Astrophysics

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