Rearuh

Half light radius R_e encloses half of the total light emitted by an object

The effective radius (Re{displaystyle 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.

Re{displaystyle R_{e}} is an important length scale in de Vaucouleurs R4{displaystyle {sqrt[{4}]{R}}} law, which characterizes a specific rate at which surface brightness decreases as a function of radius:

I(R)=Ie⋅e−7.67(RRe4−1){displaystyle I(R)=I_{e}cdot e^{-7.67left({sqrt[{4}]{frac {R}{R_{e}}}}-1right)}}

where Ie{displaystyle I_{e}} is the surface brightness at R=Re{displaystyle R=R_{e}}. At R=0{displaystyle R=0},

I(R=0)=Ie⋅e7.67≈2000⋅Ie{displaystyle I(R=0)=I_{e}cdot e^{7.67}approx 2000cdot I_{e}}

Thus, the central surface brightness is approximately 2000⋅Ie{displaystyle 2000cdot I_{e}}.

See also

References

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