An Introduction to Modern Astrophysics · Problem 10.10
The Sun — Carroll & Ostlie
Physics — Astrophysics · pp-chain-cno-cycle-energy-generation-ratio
Problem
Calculate the ratio of the energy generation rate for the pp chain to the energy generation rate for the CNO cycle given conditions characteristic of the center of the present-day (evolved) Sun, namely K, kg m, , and . Assume the pp chain screening factor is unity () and that the pp chain branching factor is unity ().Intuitive explanation
The pp chain and CNO cycle are the two main hydrogen-burning pathways in stars, and their relative importance depends sensitively on temperature through their vastly different reaction rates. The pp chain dominates at lower temperatures (like the Sun's core today) because its rate grows more slowly with , while the CNO cycle's rate scales steeply with temperature and becomes dominant in hotter, more massive stars. You'll calculate each rate using the temperature-dependent reaction coefficients and the available fuel abundances, then take their ratio to see why the pp chain still powers the Sun despite the CNO cycle's presence.
Intuitive explanation
The pp chain and CNO cycle are the two main hydrogen-burning pathways in stars, and their relative importance depends sensitively on temperature through their vastly different reaction rates. The pp chain dominates at lower temperatures (like the Sun's core today) because its rate grows more slowly with , while the CNO cycle's rate scales steeply with temperature and becomes dominant in hotter, more massive stars. You'll calculate each rate using the temperature-dependent reaction coefficients and the available fuel abundances, then take their ratio to see why the pp chain still powers the Sun despite the CNO cycle's presence.