tokens: ] sample, we notice that although the measurements are consistent with each other at a given stellar mass for all redshifts, the slope of the trend decreases such that by z ≳ 2.2, the trend is flat. Interestingly, these measurements occur in the same mass range (9.2 log 10 M stellar /M ⊙ 11.0) where for all redshifts, the trend is flat and then increases for higher stellar masses. A similar flat, redshift-independent trend is seen for [O ii ] emitters within the stellar mass range of10 9.75–11.0 M ⊙ . Figure 6. The minimum halo mass dependency with stellar mass. We find a strong relationship at all redshift slices for our H β + [O iii ] samples and for the z = 1.47 [O ii ] sample. The z = 2.25 [O ii ] sample also shows an increasing trend, but is limited only to two stellar mass bins. The other [O ii ] samples are limited due to sample size and could not be separated in stellar mass bins. We find no redshift evolution in the relationship. Interestingly, at stellar masses >10 9.75 M ⊙ , the halo mass is found to be constant at ∼10 12.3 M ⊙ for H β + [O iii ] emitters and ∼10 12 M ⊙ for [O ii ] emitters. Fig. 7 shows the SHM ratio as a function of stellar mass, where we find it to be redshift-independent for all stellar masses. We find the SHM ratio for z = 0.84 and 1.42 H β + [O iii ] emitters to be constant between 8.5 log 10 M stellar /M ⊙ 9.75 and increasing for all redshift slices at M stellar > 10 9.75 M ⊙ . The [O ii ] emitters show a continuous increase in the SHM ratio from the lowest masses to the highest masses probed. Figure 7. The SHM ratio as a function of stellar mass. We find our [O ii ] measurements show a continuous, redshift-independent increase in the SHM ratio for the full stellar mass range. The H β + [O iii ] measurements show a constant ratio up to ∼10 9.75 M ⊙ followed by a continuous, redshift-independent increase in the ratio. We compare our measurements with the abundance matching measurements of Behroozi, Wechsler Conroy ( 2013b ) overlaid in grey. We find that our [O ii ] and H β + [O iii ] measurements are in agreement within 1σ except for our H β + [O iii ] 10 9.75–10.00 M ⊙ measurements. Overlaid in Fig. 7 are the measurements of Behroozi et al. ( 2013b ), which used abundance matching along with constraints from observational measurements of global stellar mass functions to calculate the SHM ratio up to z ∼ 8. Behroozi et al. ( 2013b ) found that the ratio is redshift-independent and we therefore only highlight in Fig. 7 the 1σ confidence region of their measurements that correspond to the redshifts of our sample. We find that all four redshift slices for the [O ii ] samples are in agreement with the Behroozi et al. ( 2013b ) measurements. Our H β + [O iii ] measurements are also in agreement for M stellar 10 9.5 M ⊙ and >10 10 M ⊙ . Note that the Behroozi et al. ( 2013b ) measurements are based on ‘global’ (passive+active galaxy) stellar mass functions, while our samples are comprised of ‘active’ galaxies
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