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I am studying ellipticity distributions of galaxies and am having trouble moving from the second central moment matrix (covariance matrix) to properties for an object such as its half-light radius.

I already know how to obtain $e1$ and $e2$

They are given by the following:

$e = \frac{Q_{xx} - Q_{yy} + 2iQ_{12}}{N}$

Where $N = N(Q)$ and is just the normalization. The real component is $e1$ and the imaginary component is $e2$

I am wondering how to obtain the half-light radius, as well.

I have seen:

$2r^2 = Q_{xx} + Q_{yy}$ for a circular profile, then one can obtain the HLR from $r^2$ but what about for non-circular profiles? Is the above equation even valid?

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