Fig. 7.

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Ratio between the composite disk+bulge 3D half-mass radius and the 2D projected disk effective radius (r1/2, 3D, baryons/Re, disk; left) and the difference between the dark matter fraction estimators at these radii (; right), as a function of B/T, for a range of disk intrinsic axis ratios (colored lines, from q0, disk = 0.05 to 2) and ratio between the bulge and disk Re (solid, dashed, and dotted lines, for Re, bulge/Re, disk = 0.2, 0.5, 1, respectively). The adopted galaxy values are the same as in Fig. 6, except Re, disk is now determined by Re, bulge/Re, disk. With a non-zero bulge contribution, r1/2, 3D, baryons/Re, disk deviates from the single-component ratio (Fig. 2), decreasing with increasing B/T for Re, disk = 2, 5 kpc for all q0, disk (increasing, however, with B/T when q0 < 1, Re, disk = Re, bulge = 1 kpc). For large B/T and Re, disk = 5 kpc, the composite r1/2, 3D, baryons is less than 50% of Re, disk. If the dark matter fractions are measured at different radii, the mismatch of the aperture sizes will lead to much larger fDM differences than those found for the simple estimator mismatch (
vs
at the same radius; Fig. 6). Here, we show
, as might be adopted for modeling of observations, and
, representing a simple option for simulations (where spherical curves of growth separating gas, star, and DM particles could be used to find both the composite baryon r1/2, 3D, baryons within, e.g., Rvir and then
). For small B/T,
is larger than
, but for large B/T, the trend reverses (excepting the Re, disk = Re, bulge = 1 kpc case), and
can be up to 50%–400% larger than
as B/T → 1 (for Re, disk = 2, 5 kpc, respectively). This example illustrates how, depending on galaxy structures, quoted “half-mass” fDM values can be very different – but that this is primarily driven by the aperture radii definitions and not by estimator mismatches.
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