Stellar Structure and Evolution
Core concepts
Master the four stellar structure equations (hydrostatic equilibrium, mass continuity, energy transport, and energy generation), the equation of state across regimes, opacity sources, and the Hertzsprung-Russell diagram. Know the main sequence's mass-luminosity relation (roughly L ∝ M^3.5), the proton-proton chain versus the CNO cycle, and the endpoints of evolution: white dwarfs, neutron stars, and black holes, with the Chandrasekhar limit near 1.4 solar masses.
Traps
Distinguish the Kelvin-Helmholtz timescale from the nuclear timescale; the former governs pre-main-sequence contraction. Do not apply the mass-luminosity relation to giants. Remember that more massive stars burn hotter and die younger, so clusters' turnoff mass dates them. Watch for confusion between convective and radiative zones and their effect on surface abundances.
Worked example
A star with 4 solar masses: using L ∝ M^3.5, L ≈ 4^3.5 ≈ 128 solar luminosities. Its main-sequence lifetime scales as M/L ≈ 4/128 ≈ 1/32 of the Sun's roughly 10 Gyr, giving about 0.3 Gyr. Rule of thumb: doubling the mass shortens the main-sequence life by roughly a factor of five.
Rule of thumb
The main sequence is a mass sequence; position on it encodes mass, not age, for single stars.