This is the fourth in a series of papers studying the astrophysics and cosmology of massive , dynamically relaxed galaxy clusters .
Here , we use measurements of weak gravitational lensing from the Weighing the Giants project to calibrate Chandra X-ray measurements of total mass that rely on the assumption of hydrostatic equilibrium .
This comparison of X-ray and lensing masses provides a measurement of the combined bias of X-ray hydrostatic masses due to both astrophysical and instrumental sources .
Assuming a fixed cosmology , and within a characteristic radius ( r _ { 2500 } ) determined from the X-ray data , we measure a lensing to X-ray mass ratio of 0.96 \pm 9 \% \mathrm { ( stat ) } \pm 9 \% \mathrm { ( sys ) } .
We find no significant trends of this ratio with mass , redshift or the morphological indicators used to select the sample .
In accordance with predictions from hydro simulations for the most massive , relaxed clusters , our results disfavor strong , tens-of-percent departures from hydrostatic equilibrium at these radii .
In addition , we find a mean concentration of the sample measured from lensing data of c _ { 200 } = 3.0 _ { -1.8 } ^ { +4.4 } .
Anticipated short-term improvements in lensing systematics , and a modest expansion of the relaxed lensing sample , can easily increase the measurement precision by 30–50 % , leading to similar improvements in cosmological constraints that employ X-ray hydrostatic mass estimates , such as on \Omega _ { m } from the cluster gas mass fraction .