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tokens: the size of the halo scatter in GR. For the mapping defined using the effective density field, given by equation ( 17 ), it has been expected that the GR X-ray luminosity should be equal to the f ( R ) gravity value multiplied by the factor . From Fig. 6 , the rescaled data in F5 appear to be higher than in GR by on average for both the non-radiative and the full-physics simulations. A similar level of deviation is also observed for the true density results, where equation ( 22 ) predicts that the GR and f ( R ) gravity X-ray luminosity should be equal after the values in f ( R ) gravity are divided by the factor . Again, the rescaled F5 X-ray luminosity is significantly greater than in GR on average. As for the Y SZ and Y X mappings, the disparity found here can be explained by looking at the gas density profiles in Fig. 2 . For both the non-radiative and full-physics data, the gas density in the inner halo regions is greater for F5 (with appropriate rescaling applied) than for GR. Because the inner regions have a greater contribution to the X-ray luminosity than for other proxies, as described above, this causes these differences in the inner regions to become significant overall, even for the non-radiative data for which the F5 and GR profiles are converged above a lower radius. This results in the general offset for the full range of masses as shown in Fig. 6 . As described above, the X-ray luminosity is also more strongly influenced by feedback processes, which can further increase the offset between F5 and GR if the feedback behaves differently in these two models. Our observation that the mappings have a poorer performance for the X-ray luminosity than for the other proxies is consistent with He Li ( 2016 ), who observed a disparity of . Unless further corrections are applied to account for the unpredictable effects of feedback in the mappings therefore the X-ray luminosity is unlikely to be a reliable proxy for mass determination in accurate cluster tests of f ( R ) gravity. 4.1.4 Further comments As described in Section 3.2 , we have excluded the core region of r 0.15 R 500 when calculating the thermal properties of our simulated FOF groups. We have also experimented excluding core regions of size r 0.1 R 500 and r 0.2 R 500 : for the scaling relations Y SZ – M, Y X – M , and – M , the relative differences between f ( R ) gravity and GR are barely affected; on the other hand, the effect is larger for the L X – M scaling relation, because L X is more sensitive to the inner halo regions than the other proxies. However, the L X – M relation is not ideal for reliable tests of gravity anyway, as noted above, and is mainly included in this work for completeness and for comparison with the other relations. Even if the entire core is included in the calculations, we have found that the effect on the Y SZ – M and Y X – M results is still very small, providing further confirmation that these relations can be used for reliable tests of