E9 Quantum Degeneration and Dense Matter

Topic

The central feature of this model is the hydrogen fusion occurring within the star—the nuclear reaction that sustains it while it remains on the main sequence.

The energy released by each of these nuclear reactions corresponds to the mass defect between the reactants and the products, converted directly into energy; in the proton-proton chain—the dominant process within the Sun—four protons fuse to form a single helium nucleus, releasing a fixed amount of energy, although some of this energy escapes as neutrinos without being deposited in the star.

The rate at which this fusion occurs depends on the product of the reaction's cross-section and the quantum probability of overcoming the electrical repulsion barrier separating the nuclei. There is a specific energy range—the Gamow window—where this product is maximized; consequently, the vast majority of fusion events actually take place within this narrow window, rather than at the most probable thermal energy found in the stellar interior.

In any case, the efficiency with which this hydrogen-to-helium fusion converts mass into energy represents a small, fixed fraction. In contrast, the carbon-nitrogen-oxygen (CNO) cycle dominates fusion in stars with more than one and a half times the mass of the Sun, precisely because its rate is far more sensitive to temperature than that of the proton-proton chain: a slight rise in the star's core temperature causes the cycle's energy output to surge disproportionately.

Furthermore, a star's main-sequence lifespan decreases sharply as its mass increases; an increase in stellar mass causes the time spent on the main sequence to shrink disproportionately relative to that increase. Thus, from the hydrogen fusion within the star—with which this document begins—to the waning life on the main sequence—with which it concludes—and encompassing the proton-proton chain, the Gamow window, and the carbon-nitrogen-oxygen cycle, nuclear reactions ensure that a single star's mass simultaneously determines how its hydrogen fuses and how much time remains of its life on the main sequence.

ID:3930