Galaxy effective radius explained

Galaxy effective radius or half-light radius (

R _{e} ) is the radius at which half of the total light of a galaxy is emitted.^{[1] [2]} 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.R _{e} is an important length scale in \sqrt[ 4 ] R term in de Vaucouleurs law,^[3] which characterizes a specific rate at which surface brightness decreases as a function of radius:$$I(R)\; =\; I\_e\; \backslash cdot\; e^$$where I _{e} is the surface brightness at R = R _{e} . At R = 0 ,$$I(R=0)\; =\; I\_e\; \backslash cdot\; e^\; \backslash approx\; 2000\; \backslash cdot\; I\_e$$

Thus, the central surface brightness is approximately

2000 ⋅ I _{e} .

Notes and References

1. Web site: Half-light Radius . Swinburne University . 22 May 2013.
2. Book: James . Binney . Scott . Tremaine . Galactic Dynamics . Second . 2008 . Princeton Series in Astrophysics . 9780691130279 . 21.
3. Mazure . Alain . Exact solutions for the spatial de Vaucouleurs and Sérsic laws and related quantities. 15 February 2002 . Astronomy & Astrophysics. 383 . 2 . 384–389 . 10.1051/0004-6361:20011751 . astro-ph/0112147 . 2002A&A...383..384M . 17651247 .