Astrophysics and Stellar Structure
Core concepts
Stellar structure balances hydrostatic equilibrium (pressure gradient versus gravity), energy transport (radiative and convective), and nuclear fusion in the core. The Hertzsprung–Russell diagram plots luminosity against temperature; the main sequence runs from hot, luminous O stars to cool, dim M dwarfs. Luminosity follows L = 4πR²σT⁴, and the mass–luminosity relation L ∝ M^3.5 for main-sequence stars. Fusion via the proton–proton chain dominates in Sun-like stars; the CNO cycle dominates in massive stars. Stellar endpoints depend on mass: white dwarfs (Chandrasekhar limit ≈ 1.4 M☉), neutron stars, and black holes. Spectra reveal composition and radial velocity via Doppler shifts.
Traps
Questions mix up apparent and absolute magnitude-distance modulus m − M = 5 log₁₀(d/10 pc). Hotter stars are not always more luminous; radius matters. The main sequence is a band of hydrogen-burning stars, not an evolutionary track. Red giants are cool but luminous because of large radius. Remember the inverse-square law when comparing brightness at different distances.
Worked example
A star has twice the Sun's radius and twice its temperature. Since L ∝ R²T⁴, L = 4 × 16 = 64 L☉. Rule of thumb: use ratios-doubling radius quadruples luminosity; doubling temperature multiplies it by 16.