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 O O O O O O O B-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 B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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: mass profiles are extrapolated based on the best-fitting temperature profile model beyond the extent of the temperature profile. The median extent of the temperature profiles is 1.25 R 500 . Profiles of the mass ratios beyond that point are less robust. In Fig. 4 , the ratio of the hydrostatic to caustic masses at the radius R 500 determined from the hydrostatic mass profile is shown for each cluster. Again, the ratios are computed as . At this radius, the two mass estimators agree well, with κ = 0.080 ± 0.046, corresponding to . The intrinsic scatter between the hydrostatic and caustic mass estimators at this radius is , corresponding to an intrinsic scatter of . The RCC and NRCC subsamples show consistent results, albeit with weaker constraints. Figure 4. Ratio of hydrostatic to caustic masses at the hydrostatic R 500 for each cluster (computed as ). Points are coloured to indicate RCC (blue triangles) and NRCC (red circles) clusters. The solid line and shaded band show the mean bias between the hydrostatic and caustic masses and its uncertainty. These summary statistics are captured in Table 3 , along with the same quantities derived in a fixed aperture of for each cluster. The parameter values are insensitive to the choice of aperture, demonstrating that our results are not significantly influenced by scaling the caustic profiles to the hydrostatic estimate of R 500 . Table 3. Summary statistics of the ratio of the mean bias between hydrostatic and caustic masses, measured in the hydrostatic estimate of R 500 and in a fixed aperture of . The second column gives the subset being considered and the third column gives the mean bias. The mean bias is expressed as the mean ratio of masses in column four, and the intrinsic scatter between the mass estimators (converted to a percentage) is given in column five. Note that the quantities in columns four and five are summaries of a lognormal distribution using a median and percentiles as described in Section 3.3 . 5 DISCUSSION 5.1 Biases in hydrostatic and caustic masses We have performed one of the first comparisons between mass profiles of galaxy clusters determined from their hot gas via hydrostatic assumptions, and the dynamics of their galaxies via the caustic method. These two methods are completely independent, and are subject to different assumptions and systematics. We found that, while significant scatter is present between the two estimators, the average agreement is good. As demonstrated in Fig. 2 , the masses agree to better than ≈20 per cent on average over the full radial range sampled by both techniques. Importantly, neither of the mass measurement techniques assumed a functional form for the mass profile (although the hydrostatic analysis did use parametric temperature and density profiles). The agreement we find is not a consequence of a common parametrization of the mass profile. This good average agreement is somewhat surprising given that various observational and