Effective radius

This article is about astronomy. For cloud drops, see Cloud drop effective radius.
Half light radius Re encloses half of the total light emitted by an object

The effective radius (R_e) of a galaxy is the radius at which half of the total light of the system 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 de Vaucouleurs \sqrt[4] R law, 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]{\frac R {R_e}} - 1 \right)}

where I_e is the surface brightness at R = R_e. Note that 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.

See also

References

  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.