Inastronomy,surface brightness (SB) quantifies theapparent brightness orflux density per unitangular area of a spatially extended object such as agalaxy ornebula, or of thenight sky background. An object's surface brightness depends on its surface luminosity density, i.e., itsluminosity emitted per unit surface area. Invisible andinfrared astronomy, surface brightness is often quoted on amagnitude scale, inmagnitudes per squarearcsecond (MPSAS) in a particularfilter band orphotometric system.
Measurement of the surface brightnesses of celestial objects is called surfacephotometry.
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, aphotometer 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 acomet is the combined magnitude of thecoma andnucleus.
Theapparent magnitude of an astronomical object is generally given as an integrated value—if agalaxy 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, astar is so small it is effectively apoint source in most observations (the largestangular diameter, that ofR Doradus, is 0.057 ± 0.005arcsec), whereas a galaxy may extend over severalarcseconds orarcminutes. Therefore, the galaxy will be harder to see than the star against theairglow 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 fromRicco'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 extremenaked eye limit for viewing a star isapparent magnitude 8,[5] but onlyapparent magnitude 6.9 for galaxies.[6]
| Object | apmag |
|---|---|
| Andromeda Galaxy (M31) | 3.4 |
| Orion Nebula (M42) | 4 |
| Triangulum Galaxy (M33) | 5.7 |
| Bode's Galaxy (M81) | 6.9 |
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 magnitudem extending over a visual area ofA square arcseconds, the surface brightnessS is given by
For astronomical objects, surface brightness is analogous to photometricluminance 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, radiativeflux decreases with the square of the distance to the object, but the physical area corresponding to a givensolid 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 orluminosity distance.[clarification needed]
The surface brightness in magnitude units is related to the surface brightness in physical units ofsolar luminosity per squareparsec by[citation needed]where and are theabsolute magnitude and the luminosity of the Sun in chosencolor-band[8] respectively.
Surface brightness can also be expressed incandela per square metre using the formula [value in cd/m2] =10.8864×104 × 10(−0.4×[value in mag/arcsec2]).[9]
A truly dark sky has a surface brightness of2×10−4 cd m−2 or 21.8 mag arcsec−2.[10][clarification needed]
The peak surface brightness of the central region of theOrion Nebula is about 17 Mag/arcsec2 (about 14millinits) and the outer bluish glow has a peak surface brightness of 21.3 Mag/arcsec2 (about 0.27 millinits).[11]
