Physics:Galaxy effective radius

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Short description: Radius which encloses 50% of the total light of a galaxy
Half light radius Re encloses half of the total light emitted by an object

Galaxy effective radius or half-light radius ([math]\displaystyle{ R_e }[/math]) 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.

[math]\displaystyle{ R_e }[/math] is an important length scale in [math]\displaystyle{ \sqrt[4] R }[/math] term in de Vaucouleurs law,[3] which characterizes a specific rate at which surface brightness decreases as a function of radius: [math]\displaystyle{ I(R) = I_e \cdot e^{-7.67 \left( \sqrt[4]{ R/ {R_e}} - 1 \right)} }[/math] where [math]\displaystyle{ I_e }[/math] is the surface brightness at [math]\displaystyle{ R = R_e }[/math]. At [math]\displaystyle{ R = 0 }[/math], [math]\displaystyle{ I(R=0) = I_e \cdot e^{7.67} \approx 2000 \cdot I_e }[/math]

Thus, the central surface brightness is approximately [math]\displaystyle{ 2000 \cdot I_e }[/math].

See also

References

  1. "Half-light Radius". Swinburne University. http://astronomy.swin.edu.au/cms/astro/cosmos/h/Half-light+Radius. 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". Astronomy & Astrophysics 383 (2): 384–389. doi:10.1051/0004-6361:20011751. Bibcode2002A&A...383..384M. https://www.aanda.org/articles/aa/pdf/2002/08/aa1928.pdf.