ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: of 90%–100% completeness, while the remainder (12%) lies in the region of 50%–90% completeness. To place an upper limit on the impact of selection biases, we adopt the lower limits of 90% and 50% on the completeness in these two regions of the R eff – H 160 plane, assign weights 2.0 (i.e., 1/0.5) and 1.1 (i.e., 1/0.9) to the galaxies in our sample in these regions, and then recompute the R eff – R 200 c relations. For R 200 c ≳ 100 kpc, we find negligible corrections to the median R eff – R 200 c relations, while for R 200 c ≲ 100 kpc, we find corrections below 0.1 dex for all galaxy types and redshifts 0 z 3. We conclude from this exercise that selection biases are likely to be subdominant sources of uncertainty in our R eff – R 200 c relations. Based on this assessment of uncertainties, most of the results of this paper appear to be robust. In particular, there is a strong, approximately linear correlation between the sizes of galaxies and their dark matter halos over the full range of redshifts examined here, 0 z 3. The coefficient of proportionality is larger for late-type galaxies than for early-type galaxies, which follow roughly parallel sequences, except possibly at the highest redshifts. For late-type galaxies, the observed R eff – R 200 c relation is generally consistent with simple models in which galactic disks grow with the same specific angular momentum as their dark matter halos. There is some evidence for a slowdown in disk growth at z 0.5, but the apparent deviation from the J / M equality line is only ∼0.2 dex. We have plotted and examined the R eff – R 200 c relations at all redshifts (0 z 3) for all four SMHM relations to determine whether or not they support the four main results discussed in Section 4 . The outcome of this test is recorded in Table 2 by a T (for true) or F (for false) for each combination of SMHM relation and result. All of the entries are Ts. Table 2 therefore reinforces our conclusion that the main scientific results of this study are robust relative to discrepancies among the SMHM relations (because of the weak dependence of R 200 c on M 200 c ). Table 2 Verification of Main Results 6. Discussion We have found that the sizes of galaxies are proportional on average to the sizes of their dark matter halos over a wide range of galaxy and halo masses and over the entire redshift range 0 z 3 studied here: R eff = αR 200 c with α ≈ 0.03. In particular, we confirm the basic relation found by Kravtsov ( 2013 ) at z = 0 with only minor adjustment, some of which is related to the difference between 2D half-light radii and 3D half-mass radii. There is some curvature at the upper end of our overall R eff – R 200 c relation, which is due to the larger abundance and smaller average size of early-type galaxies compared with late-type galaxies of the same stellar mass. Indeed, we find that early- and late-type galaxies follow distinct, roughly parallel R eff – R 200 c relations offset by a factor of ∼2 for the