Fig. 1.

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Fractional mass enclosed within a sphere of radius r = R for deprojected Sérsic models of different intrinsic axis ratios. From left to right: enclosed Msph is plotted as a function of log radius (relative to the projected 2D effective radius, Re), assuming intrinsic axis ratios of q0 = 1, 0.4, 0.2, respectively. The colored curves denote the enclosed mass profiles for Sérsic indices from n = 0.5 to n = 8 (yellow to purple). The vertical lines denote R = Re (grey dashed) and R = 1.3Re (≈r1/2, mass, 3D for q0 = 1; grey dash-dotted), and the horizontal colored lines denote the fraction of the mass enclosed within r = Re for n = 1, 4 (lime, teal dashed, respectively) and 50% of the total mass (grey dashed dotted). For q0 = 1, the half-mass 3D spherical radius is indeed r1/2, mass, 3D ≈ 1.3Re regardless of n, as in Ciotti (1991). For flattened (i.e., oblate) systems, the half-mass 3D spherical radius is smaller, and approaches Re as q0 decreases. See also Fig. 2.
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