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Surface brightness

Measurement of the surface brightnesses of celestial objects is called surface photometry.

The total magnitude is a measure of the brightness of an extended object such as a nebula, cluster, galaxy or comet. It can be obtained by summing up the luminosity over the area of the object. Alternatively, a photometer can be used by applying apertures or slits of different sizes of diameter.^[1] The background light is then subtracted from the measurement to obtain the total brightness.^[2] The resulting magnitude value is the same as a point-like source that is emitting the same amount of energy.^[3] The total magnitude of a comet is the combined magnitude of the coma and nucleus.

The apparent magnitude of an astronomical object is generally given as an integrated value—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, a star is so small it is effectively a point source in most observations (the largest angular diameter, that of R Doradus, is 0.057 ± 0.005 arcsec), whereas a galaxy may extend over several arcsecondsorarcminutes. Therefore, the galaxy will be harder to see than the star against the airglow background light. Apparent magnitude is a good indication of visibility if the object is point-like or small, whereas surface brightness is a better indicator if the object is large. What counts as small or large depends on the specific viewing conditions and follows from Ricco's law.^[4] In general, in order to adequately assess an object's visibility one needs to know both parameters.

This is the reason the extreme naked eye limit for viewing a star is apparent magnitude 8,^[5] but only apparent magnitude 6.9 for galaxies.^[6]

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 a total or integrated magnitude m extending over a visual area of A square arcseconds, the surface brightness S is given by $${\displaystyle S=m+2.5\cdot \log _{10}A.}$$

For astronomical objects, surface brightness is analogous to photometric luminance and is therefore constant with distance: as an object becomes fainter with distance, it also becomes correspondingly smaller in visual area. In geometrical terms, 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 or visual area (e.g. 1 square arcsecond) decreases by the same proportion, resulting in the same surface brightness.^[7] For extended objects such as nebulae or galaxies, this allows the estimation of spatial distance from surface brightness by means of the distance modulus or luminosity distance.^{[clarification needed]}

The surface brightness in magnitude units is related to the surface brightness in physical units of solar luminosity per square parsecby^{[citation needed]} $${\displaystyle S(\mathrm {mag/arcsec^{2}} )=M_{\odot }+21.572-2.5\log _{10}S(L_{\odot }/\mathrm {pc} ^{2}),}$$ where ${\displaystyle M_{\odot }}$ and ${\displaystyle L_{\odot }}$ are the absolute magnitude and the luminosity of the Sun in chosen color-band^[8] respectively.

Surface brightness can also be expressed in candela per square metre using the formula [value in cd/m²] = 10.8×10⁴ × 10^{(−0.4×[value in mag/arcsec2])}.

A truly dark sky has a surface brightness of 2×10⁻⁴  cd m⁻² or 21.8 mag arcsec⁻².^{[9][clarification needed]}

The peak surface brightness of the central region of the Orion Nebula is about 17 Mag/arcsec² (about 14 millinits) and the outer bluish glow has a peak surface brightness of 21.3 Mag/arcsec² (about 0.27 millinits).^[10]

• Araucaria Project
• Low-surface-brightness galaxy
• Limiting magnitude
• Sigma-D relation

• Binney, James; Merrifield, Michael (1998). Galactic Astronomy. Princeton University Press. ISBN 978-0-691-02565-0.
• Sparke, L.; Gallagher, J. (2000). Galaxies in the Universe: An Introduction (1st ed.). Cambridge University Press. ISBN 0-521-59241-0.

• Online calculator for mags/arcsecond² to cd/m² and vice versa

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