Editing Surface brightness

{{Short description|Astronomical term for luminosity per area}}
In [[astronomy]], '''surface brightness''' (SB) quantifies the [[apparent brightness]] or [[spectral flux density|flux density]] per unit [[Solid angle|angular area]] of a spatially extended object such as a [[galaxy]] or [[nebula]], or of the [[night sky]] background.  An object's surface brightness depends on its surface luminosity density, i.e., its [[luminosity]] emitted per unit surface area. In [[Visible-light astronomy|visible]] and [[Infrared astronomy|infrared]] astronomy, surface brightness is often quoted on a [[Astronomical magnitude|magnitude]] scale, in '''magnitudes per square [[Minute and second of arc|arcsecond]]''' (MPSAS) in a particular [[Astronomical filter|filter band]] or [[photometric system]].

Measurement of the surface brightnesses of celestial objects is called surface [[Photometry (astronomy)|photometry]].

==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]] can be used by applying apertures or slits of different sizes of diameter.<ref name=daintith_gould2005>{{cite book
 | author=Daintith, John
 | author2=Gould, William | date=2006
 | title=The Facts on File dictionary of astronomy
 | page=489 | series=Facts on File science library
 | edition=5th | publisher=[[Infobase Publishing]]
 | isbn=0-8160-5998-5 }}</ref> The background light is then subtracted from the measurement to obtain the total brightness.<ref name=sa12_164>{{cite journal
 | last=Palei | first=A. B.
 | title=Integrating Photometers
 | journal=Soviet Astronomy | volume=12 | page=164
 |date=August 1968
 | bibcode=1968SvA....12..164P
 }}</ref> The resulting magnitude value is the same as a point-like source that is emitting the same amount of energy.<ref name=sherrod_koed2003>{{cite book
 | author=Sherrod, P. Clay
 | author2=Koed, Thomas L. | date=2003
 | title=A Complete Manual of Amateur Astronomy: Tools and Techniques for Astronomical Observations
 | page=266 | series=Astronomy Series
 | publisher=Courier Dover Publications
 | isbn=0-486-42820-6 }}</ref> The total magnitude of a [[comet]] is the combined magnitude of the [[coma (cometary)|coma]] and [[comet nucleus|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 [[wikt:point source|point source]] in most observations (the largest [[angular diameter]], that of [[R Doradus]], is 0.057&nbsp;± 0.005 [[Arcsecond|arcsec]]), whereas a galaxy may extend over several [[arcsecond]]s or [[arcminute]]s. 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]].<ref>{{cite journal | doi= 10.1093/mnras/stu992  | author=Crumey, Andrew | title= Human contrast threshold and astronomical visibility | journal=Monthly Notices of the Royal Astronomical Society | date=2014 | volume=442 | issue=3 | pages=2600–2619 | doi-access=free | bibcode=2014MNRAS.442.2600C | arxiv=1405.4209}}</ref> 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#extremestar|apparent magnitude 8]],<ref name="Bortle">{{cite web |date=February 2001 |title=The Bortle Dark-Sky Scale |publisher=Sky & Telescope |author=John E. Bortle |url=https://skyandtelescope.org/astronomy-resources/light-pollution-and-astronomy-the-bortle-dark-sky-scale/ |access-date=2009-11-18 |archive-url=https://web.archive.org/web/20090323232806/http://www.skyandtelescope.com/resources/darksky/3304011.html |archive-date=23 March 2009 |url-status=live }}</ref> but only [[apparent magnitude#extremegalaxy|apparent magnitude 6.9]] for galaxies.<ref name="SEDS">{{cite web|url=http://messier.seds.org/m/m081.html|title=Messier 81|date=2007-09-02|publisher=SEDS (Students for the Exploration and Development of Space)|access-date=2009-11-28|archive-url=https://web.archive.org/web/20170714113244/http://messier.seds.org/m/m081.html|archive-date=2017-07-14|url-status=live}}</ref>

{| class="wikitable" style="text-align: center; font-size: 0.9em;"
|+Diffuse objects visible to the naked eye
! Object
! [[Apparent Magnitude|apmag]]
|-
| [[Andromeda Galaxy]] (M31) || 3.4
|-
| [[Orion Nebula]] (M42) || 4
|-
| [[Triangulum Galaxy]] (M33) || 5.7
|-
| [[Messier 81|Bode's Galaxy]] (M81) || 6.9
|}

==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
<math display="block">S = m + 2.5 \cdot \log_{10} A.</math>

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.<ref>{{harvtxt|Sparke|Gallagher|2000|loc=§ 5.1.2}}</ref> 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]].{{Clarify|date=February 2018|reason=How can we get a distance from the surface brightness if it doesn't depend on distance?}}

==Relationship to physical units==
The surface brightness in magnitude units is related to the surface brightness in physical units of [[solar luminosity]] per square [[parsec]] by{{Citation needed|date=April 2023}}
<math display="block">S(\mathrm{mag/arcsec^2}) = M_{\odot} + 21.572-2.5\log_{10} S (L_{\odot}/\mathrm{pc}^2),</math>
where <math>M_{\odot}</math> and <math> L_{\odot} </math> are the [[absolute magnitude]] and the luminosity of the Sun in chosen [[Photometric system|color-band]]<ref>Absolute magnitudes of the Sun in different color-bands can be obtained from {{harvtxt|Binney|Merrifield|1998}} or [http://www.ucolick.org/~cnaw/sun.html Absolute Magnitude of the Sun in Several Bands] {{webarchive|url=https://web.archive.org/web/20070718015507/http://www.ucolick.org/~cnaw/sun.html |date=2007-07-18 }}</ref> respectively.

Surface brightness can also be expressed in [[candela per square metre]] using the formula [value in cd/m<sup>2</sup>] = {{val|10.8e4}} × 10<sup>(−0.4×[value in mag/arcsec<sup>2</sup>])</sup>.

==Examples==
A truly dark sky has a surface brightness of {{val|2|e=-4}} &nbsp;cd&nbsp;m<sup>−2</sup> or 21.8&nbsp;mag&nbsp;arcsec<sup>−2</sup>.<ref name="Crumey">Based on the equivalence 21.83&nbsp;mag&nbsp;arcsec<sup>−2</sup> = {{val|2|e=-4}} &nbsp;cd&nbsp;m<sup>−2</sup>, from description of a "truly dark sky", Section 1.3 of Crumey, A. (2014). [http://mnras.oxfordjournals.org/content/442/3/2600.full.pdf+html Human contrast threshold and astronomical visibility.] MNRAS 442, 2600–2619.</ref>
{{Clarify|date=February 2018|reason=A surface brightness in mag/arcsec^2 is only meaningful if a filter band or wavelength band is specified. Also useful to specify Vega or AB mag.}}

The peak surface brightness of the central region of the [[Orion Nebula]] is about 17 Mag/arcsec<sup>2</sup> (about 14 [[milli]][[nit (unit)|nits]]) and the outer bluish glow has a peak surface brightness of 21.3 Mag/arcsec<sup>2</sup> (about 0.27 millinits).<ref>{{cite web
 |url        = http://www.clarkvision.com/astro/surface-brightness-profiles/introduction.html
 |title      = Surface Brightness of Deep Sky Objects
 |date       = 2004-03-28
 |first      = Roger
 |last       = Clark
 |access-date = 2013-06-29
}}. The conversion to nits is based on 0 magnitude being 2.08 microlux.</ref>

==See also==
* [[Araucaria Project]]
* [[Low-surface-brightness galaxy]]
* [[Limiting magnitude]]
* [[Sigma-D relation]]

==References==
{{Reflist}}

===General references===
* {{Cite book | last1=Binney | first1=James | last2=Merrifield | first2=Michael | title= Galactic Astronomy | publisher=[[Princeton University Press]] | date=1998 | isbn= 978-0-691-02565-0 }}
* {{Cite book | last1=Sparke | first1=L.|author1-link=Linda Sparke | last2=Gallagher | first2=J. | date=2000 | title=Galaxies in the Universe: An Introduction | edition=1st | publisher=[[Cambridge University Press]] | isbn=0-521-59241-0 }}

== External links ==
* [http://unihedron.com/projects/darksky/magconv.php?ACTION=SOLVE&txtMAGSQA=21.83 Online calculator for mags/arcsecond<sup>2</sup> to cd/m<sup>2</sup> and vice versa]

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[[Category:Observational astronomy]]