luminosities

Luminosity is the total power emitted by a source in all directions per unit time. In astronomy, the term usually refers to bolometric luminosity, L, the intrinsic energy output across all wavelengths. It is commonly expressed in watts or as a multiple of the solar luminosity, L⊙, where 1 L⊙ ≈ 3.828 × 10^26 W.

Observed brightness relates to luminosity through distance. If F is the flux received at Earth from a source at distance d, then F ≈ L / (4πd^2). In cosmology, one uses the luminosity distance d_L, so L = 4π d_L^2 F. Redshift and interstellar absorption can modify the observed spectrum and flux.

Luminosity can be specified as bolometric (L across all wavelengths) or as spectral luminosity, Lν or Lλ, the luminosity per unit frequency or wavelength. The spectral energy distribution (SED) shows how L is distributed among wavelengths.

Stars and other blackbody-like objects allow L to be estimated from radius and effective temperature via L = 4πR^2 σ T_eff^4. Alternatively, L can be inferred from distance and observed flux, or from integrating the SED. Magnitude relations link bolometric luminosity to bolometric magnitude Mbol: L/L⊙ = 10^{0.4(Mbol,⊙ − Mbol)}.

Common reference values include the solar luminosity L⊙ and the Eddington luminosity, which sets an approximate maximum luminosity for accreting objects of a given mass, beyond which radiation pressure can expel infalling material.

In practice, luminosities span many orders of magnitude: stars, galaxies, quasars, and supernovae each have characteristic luminosity ranges. The term should not be confused with luminous flux or luminance (photometric quantities like lumens), which measure human-perceived brightness rather than intrinsic energy output.