Luminosity ($L$)

Luminosity is emitted radiative power: the energy carried away by electromagnetic radiation per unit time, measured in watts. Bolometric luminosity includes all wavelengths; a measurement through one photometric passband captures only part of it. Spectral luminosity records how that power is distributed over frequency. Received observed radiative flux has different units, watts per square metre, because it measures what crosses an observer's collecting area. ^[ref].

For example, an ideal source with luminosity $10^{26}\mathrm{W}$ emits $10^{26}\mathrm{J}$ each second regardless of whether it is viewed from $20$ or $40$ parsecs. Its observed radiative flux changes with distance, while its luminosity remains fixed. Combining stellar parallax with observed radiative flux therefore lets us compare the actual outputs of stars rather than their apparent brightnesses.

The bolometric luminosity of a star is its total radiated power integrated over all wavelengths. A band or spectral luminosity instead specifies a restricted spectral range. The Hertzsprung-Russell diagram compares total luminosity with effective temperature.

A logarithmic luminosity or measured radiative flux scale using radiation integrated over all wavelengths, in contrast to a measurement in one observing band. Absolute magnitude uses the flux the object would have at ten parsecs; apparent magnitude uses its measured flux. Neglecting extinction, $m_{\mathrm{bol}}-M_{\mathrm{bol}}=5{\log }_{10}(d/10\mathrm{pc})$.

The radiant power emitted by the Sun. A reaction-rate estimate must use the energy deposited in visible radiation per reaction, excluding energy lost in escaping neutrinos.

The adjustment from an astronomical magnitude in a particular observational band to the bolometric magnitude, accounting for energy outside that band. It depends on the stellar spectrum, hence on effective temperature, composition and surface gravity. A ratio of observed single-band luminosities should not be inserted into the Stefan–Boltzmann law as a bolometric ratio without allowing for different corrections.

The luminosity per unit spatial volume. For a spherical source, its enclosed luminosity is $L(r)=4\pi {\int }_0^r\lambda (s)s^{2}ds$, and its projected surface brightness is $\mu (R)=2{\int }_R^{\infty }\lambda (r)rdr/\sqrt{r^2-R^2}$.

Comoving spectral emissivity is emitted spectral luminosity per comoving volume, measured using source-rest-frame time and frequency. For identical sources with comoving number density $n_c$, it is ${ϵ}_{\nu }=n_c{L}_{\nu }$. For a population with a luminosity function, integrate its rest-frame spectral luminosity over that distribution. Multiplying a proper-volume emissivity by $a^3$ gives this comoving convention for dimensionless scale factor $a$.

Spectral luminosity is energy radiated per unit time per unit frequency. Its frequency integral is the total luminosity. For an isotropic source at small distance $r$, neglecting attenuation and cosmological effects, the spectral flux density is $L_{\nu }/(4\pi r^2)$.

For photon energy $\epsilon =h\nu$, equating radiated energy in corresponding spectral intervals gives $L_{\nu }d\nu =\epsilon L_{\epsilon }^{N}d\epsilon$. Thus $L_{\epsilon }^N=L_{\nu }/(h\epsilon )$. A quoted rate per joule must be multiplied by the number of joules per electronvolt or per $\mathrm{keV}$ to express it in that spectral unit. For homogeneous optically thin emission, $L_{\nu }=4\pi V{j}_{\nu }$ if $j_{\nu }$ is defined per solid angle.