View source for Galaxy effective radius

{{Short description|Radius which encloses 50% of the total light of a galaxy}}
{{redirect-distinguish|Effective radius|Cloud effective radius|Effective Earth radius}}
[[File:Half light radius simple.svg|thumb|right|Half light radius ''R<sub>e</sub>'' encloses half of the total light emitted by an object]]
'''Galaxy effective radius''' or '''half-light radius''' (<math>R_e</math>) is the [[radius]] at which half of the total [[light]] of a [[galaxy]] is emitted.<ref>{{cite web|title=Half-light Radius |url=http://astronomy.swin.edu.au/cms/astro/cosmos/h/Half-light+Radius |publisher=Swinburne University |accessdate=22 May 2013}}</ref><ref>{{cite book | first1=James | last1=Binney | first2=Scott | last2=Tremaine | title=Galactic Dynamics | edition=Second | date=2008 | publisher=Princeton Series in Astrophysics | isbn=9780691130279 | page=21}}</ref> This assumes the galaxy has either intrinsic [[circular symmetry|spherical symmetry]] or is at least circularly symmetric as viewed in the plane of the sky. Alternatively, a half-light [[Contour line|contour]], or [[Contour line#Other phenomena|isophote]], may be used for spherically and circularly asymmetric objects.

<math>R_e</math> is an important length scale in <math>\sqrt[4] R</math> term in [[Gérard de Vaucouleurs|de&nbsp;Vaucouleurs]] [[De Vaucouleurs' law|law]],<ref>{{cite journal | last = Mazure | first = Alain | title = Exact solutions for the spatial de Vaucouleurs and Sérsic laws and related quantities|url= https://www.aanda.org/articles/aa/pdf/2002/08/aa1928.pdf | date = 15 February 2002 | journal = Astronomy & Astrophysics| volume = 383 | issue = 2 | pages = 384–389 |doi= 10.1051/0004-6361:20011751 | arxiv = astro-ph/0112147 | bibcode = 2002A&A...383..384M | s2cid = 17651247 }}</ref> which characterizes a specific rate at which [[surface brightness]] decreases as a function of radius:
<math display="block">
I(R) = I_e \cdot e^{-7.67 \left( \sqrt[4]{ R/ {R_e}} - 1 \right)}
</math>
where <math>I_e</math> is the surface brightness at <math>R = R_e</math>. At <math>R = 0</math>,
<math display="block">
I(R=0) = I_e \cdot e^{7.67} \approx 2000 \cdot I_e
</math>

Thus, the central surface brightness is approximately <math>2000 \cdot I_e</math>.

==See also==
{{cmn|colwidth=20em|
* [[Airy disk]]
* [[Elliptical galaxy]]
* [[Globular cluster]]
* [[Open cluster]]
* [[Point spread function]]
* [[Sérsic profile]]
}}

==References==
{{reflist}}

{{DEFAULTSORT:Effective Radius}}
[[Category:Physical quantities]]
[[Category:Length]]
[[Category:Equations of astronomy]]

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