# Solar luminosity

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Unit of Luminosity L☉ or Lsun
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 radiative (power emitted in the form of photons) conventionally used by astronomers to measure the luminosity of stars.

One needs to distinguish between the Sun's actual measured radiative luminosity (${\displaystyle L_{\odot }}$), which is variable at the ±0.1% level, and the Sun's long-term average luminosity which has been adopted by astronomers as a standard unit of power for quoting the luminosities of celestial objects (e.g. stars, galaxies, etc.). The latter was recently defined by the International Astronomical Union as the nominal solar luminosity (${\displaystyle L_{\odot }^{N}}$) which corresponds to a power of exactly 3.828×1026 W or 3.828×1033 erg/s.[2][3]

Values of the solar radiative luminosity do not include the solar neutrino luminosity, which would add 0.023 L.[4] The Sun is a weakly variable star, and its luminosity therefore fluctuates.[5] The major fluctuation is the eleven-year solar cycle (sunspot cycle) which produces ±0.04% amplitude variations on decade timescales, however ±0.1% variations on timescales of centuries have been inferred from solar irradiance reconstructions based on sunspot numbers.[6] The IAU's nominal solar luminosity value corresponds to the Sun's luminosity averaged over the past few solar cycles.[3]

## Determination

Solar luminosity is related to solar irradiance (the so-called "solar constant"). The value of the solar irradiance measured from spacecraft near Earth is always varying as the Earth's orbit is not exactly circular (eccentricity is approximately 0.017) and the Sun appears to be variable at the ±0.1% level. Quoted total solar irradiance (TSI) values are corrected to the standard distance of 1 astronomical unit to take into account the slight changes in heliocentric distances experienced by radiometry experiments on spacecraft in the course of their orbits (measured irradiances from an isotropically emitting power source decrease as the inverse of the distance squared). The average total solar irradiance measured at 1 au is ${\displaystyle S_{\odot }=1361Wm^{-2}}$.[3][6] As irradiance is defined as power per unit area, the solar luminosity (total power emitted by the Sun) can be calculated as the total solar irradiance corrected to distance 1 astronomical unit, multiplied by the area of the sphere whose radius of 1 astronomical unit:

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

To calculate the luminosity in SI units of Watts, A is the unit distance is meters and ${\displaystyle S_{\odot }}$ is the total solar irradiance in ${\displaystyle Wm^{-2}}$. Note that the astronomical unit is now defined by the International Astronomical Union as an exact number of meters, and recent total solar irradiance experiments are calibrated to ground-based irradiance standards to the ~0.03% level (absolute accuracy). Irradiance reconstructions based on tying modern TSI measurements to modern and historical sunspot observations indicate that the Sun's total solar irradiance has meandered between about 1360 and 1362 ${\displaystyle Wm^{-2}}$ over the past four centuries,[6] and hence the Sun's actual luminosity ${\displaystyle L_{\odot }}$ has varied between about 3.825×1026 W and 3.830×1026 W (with 1${\displaystyle \sigma }$ absolute uncertainties of approximately 0.013×1026 W).

## Nominal Solar Luminosity

As the Sun is a variable star, and the luminosities of stars are usually quoted in units of the solar luminosity, astronomers needed a standard value. At the 2015 International Astronomical Union General Assembly in Honolulu, the international astronomical community adopted IAU 2015 Resolution B3, which defined a set of nominal solar and planetary conversion factors ("nominal units"). Based on an extensive review of the solar radiometry literature by the IAU Working Group on Nominal Units for Stellar & Planetary Astronomy, Resolution B3 adopted a nominal total solar irradiance (${\displaystyle S_{\odot }^{N}}$) equal to exactly ${\displaystyle 1361Wm^{-2}}$, the average value of Sun's electromagnetic power per unit area measured by spacecraft corrected to exactly 1 astronomical unit away from the Sun. Combining the nominal total solar irradiance (${\displaystyle S_{\odot }^{N}}$) with the IAU definition of the astronomical unit (IAU 2012 Resolution B1 defined the ${\displaystyle AU}$ to be exactly 149597870700 meters[7]), Resolution B3 then defined the nominal solar luminosity (${\displaystyle L_{\odot }^{N}}$) to be an exact power in Watts: ${\displaystyle L_{\odot }^{N}}$ = 3.828×1026 W. The symbol for the nominal solar luminosity (${\displaystyle L_{\odot }^{N}}$) has a superscript N (for "nominal") so as to distinguish it from the Sun's actual radiative luminosity (which is variable), whose symbol is ${\displaystyle L_{\odot }}$.

## 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, arXiv:0911.4872, Bibcode:2010IAUS..264....3R, doi:10.1017/S1743921309992298
2. ^ International Astronomical Union, ed. (14 August 2015), "RESOLUTION B3 on recommended nominal conversion constants for selected solar and planetary properties" (PDF), RESOLUTION B3, Honolulu, USA: International Astronomical Union
3. ^ a b c Mamajek, E.E.; Prsa, A.; Torres, G.; et, al., IAU 2015 Resolution B3 on Recommended Nominal Conversion Constants for Selected Solar and Planetary Properties, arXiv:1510.07674, Bibcode:2015arXiv151007674M
4. ^ Bahcall, John N. (1989). Neutrino Astrophysics. Cambridge University Press. p. 79. ISBN 978-0-521-37975-5.
5. ^ 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): n/a. Bibcode:2012GeoRL..3916104V. doi:10.1029/2012GL052950.
6. ^ a b c Kopp, G.; Krivova, N.; Lean, J.; Wu, C.J. (2016). "The Impact of the Revised Sunspot Record on Solar Irradiance Reconstructions". Solar Physics: in press. doi:10.1007/s11207-016-0853.
7. ^ International Astronomical Union, ed. (31 August 2012), "RESOLUTION B2 on the re-definition of the astronomical unit of length" (PDF), RESOLUTION B2, Beijing, Kina: International Astronomical Union, The XXVIII General Assembly of International Astronomical Union recommends [adopted] that the astronomical unit be re-defined to be a conventional unit of length equal to exactly 149597870700 metres, in agreement with the value adopted in IAU 2009 Resolution B2