# Astronomy:Solar luminosity

Evolution of the solar luminosity, radius and effective temperature compared to the present-day Sun. After Ribas (2010)[1]

The solar luminosity, L, is a unit of radiant flux (power emitted in the form of photons) conventionally used by astronomers to measure the luminosity of stars, galaxies and other celestial objects in terms of the output of the Sun.

One nominal solar luminosity is defined by the International Astronomical Union to be 3.828×1026 W.[2] This does not include the solar neutrino luminosity, which would add 0.023 L,[3] or 8.8 x 1024 W, i.e. a total of 3.916 x 1026 W (the mean energy of the solar photons is 26 MeV and that of the solar neutrinos 0.59 MeV, i.e. 2.27%; the Sun emits 9.2 x 1037 photons and as many neutrinos each second, of which 6.5 x 1014 per m² reach the Earth each second). The Sun is a weakly variable star, and its actual luminosity therefore fluctuates.[4] The major fluctuation is the eleven-year solar cycle (sunspot cycle) that causes a quasi-periodic variation of about ±0.1%. Other variations over the last 200–300 years are thought to be much smaller than this.[5]

## Determination

Solar luminosity is related to solar irradiance (the solar constant). Solar irradiance is responsible for the orbital forcing that causes the Milankovitch cycles, which determine Earthly glacial cycles. The mean irradiance at the top of the Earth's atmosphere is sometimes known as the solar constant, I. Irradiance is defined as power per unit area, so the solar luminosity (total power emitted by the Sun) is the irradiance received at the Earth (solar constant) multiplied by the area of the sphere whose radius is the mean distance between the Earth and the Sun:

$\displaystyle{ L_\odot = 4\pi kI_\odot A^2\, }$

where A is the unit distance (the value of the astronomical unit in metres) and k is a constant (whose value is very close to one) that reflects the fact that the mean distance from the Earth to the Sun is not exactly one astronomical unit.

## References

1. Ribas, Ignasi (February 2010), "The Sun and stars as the primary energy input in planetary atmospheres", Solar and Stellar Variability: Impact on Earth and Planets, Proceedings of the International Astronomical Union, IAU Symposium, 264, pp. 3–18, doi:10.1017/S1743921309992298, Bibcode2010IAUS..264....3R
2. "Resolution B3 on recommended nominal conversion constants for selected solar and planetary properties". International Astronomical Union. 2015.
3. Bahcall, John N. (1989). Neutrino Astrophysics. Cambridge University Press. p. 79. ISBN 978-0-521-37975-5.
4. Vieira, L. E. A.; Norton, A.; Dudok De Wit, T.; Kretzschmar, M.; Schmidt, G. A.; Cheung, M. C. M. (2012). "How the inclination of Earth's orbit affects incoming solar irradiance". Geophysical Research Letters 39 (16): L16104 (8 pp.). doi:10.1029/2012GL052950. insu-01179873. Bibcode2012GeoRL..3916104V.
5. Noerdlinger, Peter D. (2008). "Solar Mass Loss, the Astronomical Unit, and the Scale of the Solar System". Celestial Mechanics and Dynamical Astronomy 801: 3807. Bibcode2008arXiv0801.3807N.