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Fig. 2.

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Comparison between the 3D spherical half-mass radius, r1/2, mass, 3D, and the projected 2D effective radius, Re, for a range of Sérsic indices n and intrinsic axis ratios q0 (left, colored by q0; right, colored by n). For oblate cases, Re is the projected major axis, while for prolate cases Re is the projected minor axis. For all cases, r1/2, mass, 3D > Re. However, as q0 decreases (i.e., flatter Sérsic distributions), the 3D half-mass radius approaches the value of Re. Overall, the systematic difference between r1/2, mass, 3D and Re highlights that while half of the model mass is enclosed within a projected 2D ellipse of major axis Re (e.g., an infinite ellipsoidal cylinder), less than half the total mass is enclosed within a sphere of radius Re (ignoring any M/L gradients or optically thick regions, which would change Re, light/Re, mass).

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