Galaxy effective radius

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}\cdot e^{-7.67\left({\sqrt[{4}]{R/{R_{e}}}}-1\right)}

where

I_{e}

is the surface brightness at

R=R_{e}

. At

R=0

,

I(R=0)=I_{e}\cdot e^{7.67}\approx 2000\cdot I_{e}

Thus, the central surface brightness is approximately $2000\cdot I_{e}$ .

References[edit]

^ "Half-light Radius". Swinburne University. Retrieved 22 May 2013.
^ Binney, James; Tremaine, Scott (2008). Galactic Dynamics (Second ed.). Princeton Series in Astrophysics. p. 21. ISBN 9780691130279.
^ 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.

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[1] "Half-light Radius". Swinburne University. Retrieved 22 May 2013.

[2] Binney, James; Tremaine, Scott (2008). Galactic Dynamics (Second ed.). Princeton Series in Astrophysics. p. 21. ISBN 9780691130279.

[3] 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.

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