Galaxy effective radius
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>"Half-light Radius". Swinburne University. Retrieved 22 May 2013.</ref><ref>Binney, James; Tremaine, Scott (2008). Galactic Dynamics (Second ed.). Princeton Series in Astrophysics. p. 21. ISBN 9780691130279.</ref> This assumes the galaxy has either intrinsic spherical symmetry or is at least circularly symmetric as viewed in the plane of the sky. Alternatively, a half-light contour, or 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 de Vaucouleurs law,<ref>Mazure, Alain (15 February 2002). "Exact solutions for the spatial de Vaucouleurs and Sérsic laws and related quantities" (PDF). Astronomy & Astrophysics. 383 (2): 384–389. arXiv:astro-ph/0112147. Bibcode:2002A&A...383..384M. doi:10.1051/0004-6361:20011751. 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
References
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