astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

, surface brightness (SB) quantifies the

apparent brightness Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's ...

flux density Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...

per unit

angular area In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The poi ...

of a spatially extended object such as a

galaxy A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. ...

nebula A nebula ('cloud' or 'fog' in Latin; pl. nebulae, nebulæ or nebulas) is a distinct luminescent part of interstellar medium, which can consist of ionized, neutral or molecular hydrogen and also cosmic dust. Nebulae are often star-forming regio ...

, or of the

night sky The night sky is the nighttime appearance of celestial objects like stars, planets, and the Moon, which are visible in a clear sky between sunset and sunrise, when the Sun is below the horizon. Natural light sources in a night sky include ...

background. An object's surface brightness depends on its surface luminosity density, i.e., its

luminosity Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object over time. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a st ...

emitted per unit surface area. In

visible Visibility, in meteorology, is a measure of the distance at which an object or light can be seen. Visibility may also refer to: * A measure of turbidity in water quality control * Interferometric visibility, which quantifies interference contrast ...

and

infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...

astronomy, surface brightness is often quoted on a

magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...

scale, in magnitudes per square

arcsecond A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...

(MPSAS) in a particular filter band or

photometric system In astronomy, a photometric system is a set of well-defined passbands (or optical filters), with a known sensitivity to incident radiation. The sensitivity usually depends on the optical system, detectors and filters used. For each photometric sy ...

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

photometry Photometry can refer to: * Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision * Photometry (astronomy), the measurement of the flux or intensity of an astronomical object's electrom ...

General description

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 A photometer is an instrument that measures the strength of electromagnetic radiation in the range from ultraviolet to infrared and including the visible spectrum. Most photometers convert light into an electric current using a photoresistor, ph ...

can be used by applying apertures or slits of different sizes of diameter. The background light is then subtracted from the measurement to obtain the total brightness. The resulting magnitude value is the same as a point-like source that is emitting the same amount of energy. The total magnitude of a

comet A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail. These phenomena ar ...

is the combined magnitude of the

coma A coma is a deep state of prolonged unconsciousness in which a person cannot be awakened, fails to respond normally to painful stimuli, light, or sound, lacks a normal wake-sleep cycle and does not initiate voluntary actions. Coma patients exhi ...

and

nucleus Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA Nucle ...

. The

apparent magnitude Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's li ...

of an astronomical object is generally given as an integrated value—if a

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 A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...

is so small it is effectively a

point source A point source is a single identifiable ''localised'' source of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because in mathematical modeling, these sources can ...

in most observations (the largest

angular diameter The angular diameter, angular size, apparent diameter, or apparent size is an angular distance describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is ...

, that of

R Doradus R Doradus (HD 29712 or P Doradus) is a red giant variable star in the far-southern constellation Dorado. Its distance from Earth is . Having a uniform disk diameter of , it is thought to be the extrasolar star with the largest apparent ...

, is 0.057 ± 0.005 arcsec), whereas a galaxy may extend over several

s or

arcminute A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...

s. Therefore, the galaxy will be harder to see than the star against the

airglow Airglow (also called nightglow) is a faint emission of light by a planetary atmosphere. In the case of Earth's atmosphere, this optical phenomenon causes the night sky never to be completely dark, even after the effects of starlight and diff ...

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 Riccò's law, discovered by astronomer Annibale Riccò, is one of several laws that describe a human's ability to visually detect targets on a uniform background. This law explains the visual relationship between a target angular area ''A'' and targ ...

. In general, in order to adequately assess an object's visibility one needs to know both parameters.

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 a total or integrated magnitude ''m'' extending over a visual area of ''A'' square arcseconds, the surface brightness ''S'' is given by

S = m + 2.5 \cdot \log_ A.

For astronomical objects, surface brightness is analogous to photometric

luminance Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls withi ...

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 Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...

decreases with the square of the distance to the object, but the physical area corresponding to a given

solid angle In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The poi ...

or visual area (e.g. 1 square arcsecond) decreases by the same proportion, resulting in the same surface brightness. 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 Luminosity distance ''DL'' is defined in terms of the relationship between the absolute magnitude ''M'' and apparent magnitude ''m'' of an astronomical object. : M = m - 5 \log_\!\, which gives: : D_L = 10^ where ''DL'' is measured in parsecs. F ...

Relationship to physical units

The surface brightness in magnitude units is related to the surface brightness in physical units of

solar luminosity The solar luminosity (), 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 s ...

per square

parsec The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, and ...

S(\mathrm) = M_ + 21.572-2.5\log_ S (L_/\mathrm^2),

where

M_

and

L_

are the

absolute magnitude Absolute magnitude () is a measure of the luminosity of a celestial object on an inverse Logarithmic scale, logarithmic Magnitude (astronomy), astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent mag ...

and the luminosity of the Sun in chosen color-band respectively. Surface brightness can also be expressed in

candela per square metre The candela per square metre (symbol: cd/m2) is the unit of luminance in the International System of Units (SI). The unit is based on the candela, the SI unit of luminous intensity, and the square metre, the SI unit of area. The nit (symbol: n ...

using the formula alue in cd/m²= 10.8×10⁴ × 10^{(-0.4* alue in mag/arcsec2}. There is an online calculator available here http://unihedron.com/projects/darksky/magconv.php?ACTION=SOLVE&txtMAGSQA=21.83

Examples

A truly dark sky has a surface brightness of cd m⁻² or 21.8 mag arcsec⁻².Based on the equivalence 21.83 mag arcsec⁻² = cd m⁻², from description of a "truly dark sky", Section 1.3 of Crumey, A. (2014)
Human contrast threshold and astronomical visibility.
MNRAS 442, 2600–2619. The peak surface brightness of the central region of the

Orion Nebula The Orion Nebula (also known as Messier 42, M42, or NGC 1976) is a diffuse nebula situated in the Milky Way, being south of Orion's Belt in the constellation of Orion. It is one of the brightest nebulae and is visible to the naked eye in the nig ...

is about 17 Mag/arcsec² (about 14

milli ''Milli'' (symbol m) is a unit prefix in the metric system denoting a factor of one thousandth (10−3). Proposed in 1793, and adopted in 1795, the prefix comes from the Latin , meaning ''one thousand'' (the Latin plural is ). Since 1960, the pre ...

nits The National Institutes of Technology (NITs) are the central government-owned-public technical institutes under the ownership of Ministry of Education, Government of India. They are governed by the National Institutes of Technology, Science ...

) and the outer bluish glow has a peak surface brightness of 21.3 Mag/arcsec² (about 0.27 millinits).. The conversion to nits is based on 0 magnitude being 2.08 microlux.

References

General references