ASTR 330 Problem Set 03

Problems

1. Schematic core temperature 20 points

Using the schematic mass-scaling relation T_core ≈ T_core,⊙(M/M⊙)^0.7 (Lecture 06), estimate Alpha Centauri A's core temperature (M = 1.0788 M⊙), and express your answer as T6.

2. Gamow peak energy 15 points

Using your Problem 1 core temperature, compute the proton-proton Gamow peak energy (Z1=Z2=1, μ=0.5 amu), and compare it to the Sun's own pp Gamow peak energy from Lecture 05/Lab 03.

3. pp/CNO classification 15 points

Using the crossover temperature T6 ≈ 24.2 derived in Lecture 06/Lab 03, classify Alpha Centauri A as pp-dominated or CNO-dominated, and explain whether this is consistent with its near-solar mass and G2V spectral type.

4. Comparative reasoning 20 points

Sirius A (T6 ≈ 26.1, Lecture 06) is CNO-dominated while Alpha Centauri A (your Problem 1 answer) is not. Using the two stars' mass ratio (1.91), explain quantitatively why such a modest mass difference produces such a sharp qualitative difference in dominant burning mechanism.

Due and Scope

Submit a complete derivation with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without a visible derivation receives partial credit at most, and quoting a lecture number without adapting it to this problem's specific inputs receives no credit for that step.

OpenStax Companion Reading

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 16.3.

References and Data Sources

Corresponding lecture slides and notes for this unit.
OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt).
Course datasets under materials/ASTR330/data/ where referenced above.