Astronomy

Stars

HR diagram, fusion, lifetimes, magnitude.

Basics

Hertzsprung–Russell diagram

X: temperature (hot on the left). Y: luminosity. The main sequence is the diagonal. Giants and supergiants sit above; white dwarfs below. Mass largely sets main-sequence place and lifetime.

Fusion

The Sun’s core: proton–proton chain, H → He. More massive stars use the CNO cycle. When hydrogen is gone, the star moves toward red giant, then white dwarf, neutron star, or black hole by mass.

Formulas

Wien's displacement law

λ_max T = 2.897×10⁻³ m·K

Hotter stars peak at shorter (bluer) wavelengths.

Symbols

  • λ_max wavelength of peak emission

Stefan–Boltzmann

L = 4π R² σ T⁴

Luminosity scales as radius squared and T to the fourth. A cool, huge giant can still be bright.

Symbols

  • L luminosity (W)
  • σ Stefan–Boltzmann constant

Apparent magnitude

m₁ − m₂ = −2.5 log₁₀ (F₁ / F₂)

Smaller magnitude is brighter. Five magnitudes = 100× flux.

Symbols

  • F flux

Distance modulus

m − M = 5 log₁₀ (d / 10 pc)

Distance from apparent vs absolute magnitude.

Symbols

  • M absolute magnitude (10 pc)
  • d distance

Parallax

d(pc) = 1 / p(")

A parallax of 1 arcsecond is 1 parsec. The basic nearby-star distance.

Symbols

  • p parallax (arcseconds)

In this field