Apparatus and Setup
This lab computes the Gamow peak energy (Lecture 05) for proton-proton and CNO-cycle reactions and reproduces the pp-chain/CNO-cycle crossover-temperature calculation (Lecture 06) for the Sun and for Sirius A, using the same schematic power-law energy-generation scalings developed in the lecture.
Materials and Data
| Star | Core temperature (K) | T6 |
|---|---|---|
| Sun (standard published core temperature) | 1.570e+07 | 15.70 |
| Sirius A (2.063 M⊙, schematic mass-scaling estimate) | 2.606e+07 | 26.06 |
Procedure
- Compute the Gamow peak energy E0 for proton-proton reactions (Z1=Z2=1, μ=0.5 amu) at the Sun's core temperature, and compare it to kT at that same temperature.
- Compute the Gamow peak energy for a proton-nitrogen-14 reaction (Z1=1, Z2=7, μ=12/13 amu, the CNO cycle's rate-limiting step) at the same temperature, and compare it to the pp-chain Gamow peak from step 1.
- Using ε_pp ∝ T6⁴ and ε_CNO ∝ T6²⁰ (both normalized so the Sun is 1000:1 pp-dominated, per Lecture 06), find the crossover T6 at which the two curves are equal, and verify your answer is consistent with the value quoted in Lecture 06.
- Using Sirius A's schematic core-temperature estimate, classify Sirius A as pp-dominated or CNO-dominated, and state whether this is consistent with real stellar models for a star of Sirius A's mass and spectral type.
Analysis and Uncertainty
The Sirius A core-temperature estimate uses a schematic mass-scaling relation (T_core ∝ M^0.7), not a precision stellar model; state explicitly why this is sufficient for a qualitative pp-versus-CNO classification but would not be sufficient for a precise nuclear-burning-rate calculation.
Deliverables
- Both Gamow-peak calculations with a comparison to kT.
- The crossover-temperature calculation, reproduced independently of the lecture's own numbers.
- Sirius A's pp/CNO classification with supporting arithmetic.
Assessment Criteria
- Correct Gamow-peak arithmetic for both reactions.
- Correct, independently reproduced crossover-temperature calculation.
- Correct pp/CNO classification for Sirius A with supporting numbers, not just an assertion.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 16.3.
- Sirius A mass and spectral type: standard published values, carried forward from ASTR 230/ASTR 310.
- Generated by
materials/ASTR330/src/generate_astr330_content.py.