tokens: correlations between the measurements when using a common analysis aperture, the intrinsic scatter between X-ray and lensing masses, and the cosmology dependence of both. For a fixed cosmology and a sample of 12 clusters, we measure a lensing-to-X-ray mass ratio of r = 0.96 within the Chandra -determined r 2500 aperture with a statistical precision of 9 per cent and additional systematic uncertainty from lensing of 9 per cent, for a combined precision of ≈12 per cent. These results are for the specific Chandra calibrations tested, and cannot be easily extrapolated to other versions of the Chandra calibration. We find that our results are robust to perturbations in the sample selection and lensing analysis. We interpret the measured lensing-to-X-ray mass ratio as ruling out large departures from hydrostatic equilibrium, on the order of tens of percent, at the measurement radii in our relaxed target clusters. Since the effects of biases in the X-ray effective area calibration are degenerate with biases due to non-thermal pressure support, more robust constraints on the level of non-thermal support from lensing and X-ray data will not be possible without an independent constraint on the X-ray calibration, e.g. from precisely measured emission line ratios. By measuring the lensing-to-X-ray mass ratio within the cosmological framework of Paper II , we are able to render the results of that work independent of overall shifts in the Chandra temperature calibration. We are also able to naturally capture the cosmology dependence of the lensing-to-X-ray mass ratio by simultaneously modelling the lensing signal for the 12 clusters in this sample with the rest of the f gas data set. The improvements to cosmological constraints that the lensing enables are significant, as discussed in detail in Paper II . There are clear opportunities for improvement of the lensing-based calibration for the f gas experiment (as well as cluster counts; see discussion in Mantz et al. 2015a ) in the next few years. Efforts are under way to improve key lensing systematics, most notably with measuring shear (Kitching et al. 2011 ) and with mass modelling of clusters (LSST Dark Energy Science Collaboration 2012 ). With these improvements coming into place, the remaining limitation to an improved measurement of the lensing to X-ray mass ratio is the number of clusters with sufficient optical filter coverage for P ( z ) measurements, which eliminate a key systematic in the lensing masses used in this work (see Applegate et al. 2014 ). Expanding the sample of P ( z ) cluster masses from the current six clusters to ∼24 clusters would already improve the mass ratio precision, and thus constraints on Ω m , by ≈30 per cent. APPENDIX A: RATIO MODEL WITH INTRINSIC SCATTER AND COMMON APERTURES There are multiple, mathematically equivalent ways to implement a ratio model that includes intrinsic scatter and accounts for correlations induced from a shared measurement aperture. For
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