Quick questions on Stellar evolution and nucleosynthesis: HSC Physics Module 8

The H-R diagram plots stars by their luminosity (vertical, increasing upward) against their surface temperature (horizontal, increasing to the left, by historical convention). Stars do not fill the diagram uniformly; they cluster in well-defined regions.

1. Pre-main-sequence. A protostar contracts under gravity, heats, and ignites hydrogen fusion when the core reaches about 10 million K. 2. Main sequence (about 10 billion years). Hydrogen burns to helium in the core via the proton-proton chain.

The first stages are the same (main sequence, red supergiant), but the higher core mass allows successive ignitions of heavier elements:

The binding energy per nucleon as a function of mass number $A$ has a maximum at iron-56 (and the closely competing nickel-62). Below iron, fusion of light nuclei releases energy because the product has higher binding energy per nucleon. Above iron, fusion costs energy. Therefore stellar cores cannot produce elements heavier than iron by exothermic fusion.

During the supernova explosion, the collapsing core releases a flood of free neutrons. Heavy seed nuclei (already present from earlier stages) absorb many neutrons in quick succession, far faster than the timescale for beta decay. This is the r-process (rapid neutron capture). The neutron-rich nuclei subsequently beta-decay to stable isotopes of elements up to and beyond uranium.

The continuous part of a stellar spectrum is a near-blackbody curve from the dense photosphere (see the Module 7 dot point on spectra and stars). The cooler outer atmosphere imprints absorption lines whose pattern reveals composition and (with line-ratio analysis) temperature. Nebulae and hot rarefied gas glow with emission lines instead. Together these spectra are the observational tool by which stellar nucleosynthesis is checked: the predicted abundances of elements in the surfaces of stars (and in interstellar gas clouds) can be matched against observations.

A star has surface temperature 25000 K and luminosity 10000 $L_{\odot}$. Where is it on the H-R diagram, and what is its evolutionary stage?

Temperature increases to the left, by convention.

Red dwarfs (cool, dim, lower right of main sequence) are also red but are not red giants. The size or luminosity distinguishes them.

Iron formation requires high core temperatures only reached in massive stars. Sun-like stars stop at carbon and oxygen.

Stars fuse light elements into heavier ones, releasing energy up to iron. Fission of heavy elements (uranium, plutonium) is not a stellar energy source.

Up to iron: ordinary stellar fusion. Beyond iron: rapid neutron capture during supernovae and neutron star mergers.