# Surface brightness

Surface brightness is a concept used in astronomy when describing extended astronomical objects such as galaxies and nebulae.

General description

The apparent magnitude of an astronomical object is generally given as an integrated value&mdash;if a galaxy is quoted as having a magnitude of 12.5, it means we see the same total amount of light from the galaxy as we would from a star with magnitude 12.5. However, while a star is so small it is effectively a in most observations, the galaxy may extend over several arcseconds or arcminutes. Therefore, the galaxy will be harder to see than the star against the airglow background light. Quoting an object's surface brightness gives an indication of how easily observable it is.

Calculating surface brightness

Surface brightnesses are usually quoted in magnitudes per square arcsecond. Because the magnitude is logarithmic, calculating surface brightness cannot be done by simple division of magnitude by area. Instead, for a source with magnitude "m" extending over an area of "A" square arcseconds, the surface brightness "S" is given by

$S = m + 2.5 cdot log A.$

Surface brightness is constant with luminosity distance. For nearby objects, the luminosity distance is equal to the physical distance of the object. For a nearby object emitting a given amount of light, radiative flux decreases with the square of the distance to the object, but the physical area corresponding to a given solid angle (e. g. 1 square arcsecond) increases in the same fashion, resulting in the same surface brightness. [harvtxt|Sparke|Gallagher|2000|loc=&sect; 5.1.2]

Relationship to physical units

The surface brightness in magnitude units is related to the surface brightness in physical units of solar luminosities per square parsec by

$S\left(mag/arcsec^2\right)=M_\left\{V,odot\right\}+21.57-2.5log S \left(L_\left\{odot\right\}/pc^2\right),$

where $M_\left\{V,odot\right\}$ is the absolute magnitude of the sun in V band. [Other absolute magnitudes of the sun can be obtained from harvtxt|Binney|Merrifield|1998 or [http://www.ucolick.org/~cnaw/sun.html Absolute Magnitude of the Sun in Several Bands] ]

References

General references

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ee also

* Low surface brightness galaxy

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