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Galaxy clusters have a triaxial matter distribution. The weak-lensing signal, an important part in cosmological studies, measures the projected mass of all matter along the line of sight, and therefore changes with the orientation of the cluster. Studies suggest that the shape of the brightest cluster galaxy (BCG) in the centre of the cluster traces the underlying halo shape, enabling a method to account for projection effects. We use 324 simulated clusters at four redshifts between 0.1 and 0.6 from ‘The Three Hundred Project’ to quantify correlations between the orientation and shape of the BCG and the halo. We find that haloes and their embedded BCGs are aligned, with an average ∼20 degree angle between their major axes. The bias in weak lensing cluster mass estimates correlates with the orientation of both the halo and the BCG. Mimicking observations, we compute the projected shape of the BCG, as a measure of the BCG orientation, and find that it is most strongly correlated to the weak-lensing mass for relaxed clusters. We also test a 2D cluster relaxation proxy measured from BCG mass isocontours. The concentration of stellar mass in the projected BCG core compared to the total stellar mass provides an alternative proxy for the BCG orientation. We find that the concentration does not correlate to the weak-lensing mass bias, but does correlate with the true halo mass. These results indicate that the BCG shape and orientation for large samples of relaxed clusters can provide information to improve weak-lensing mass estimates.

We present updated cosmological constraints from measurements of the gas mass fractions (fgas) of massive, dynamically relaxed galaxy clusters. Our new data set has greater leverage on models of dark energy, thanks to the addition of the Perseus cluster at low redshifts, two new clusters at redshifts z ≳ 1, and significantly longer observations of four clusters at 0.6 < z < 0.9. Our low-redshift (z < 0.16) fgas data, combined with the cosmic baryon fraction measured from the cosmic microwave background (CMB), imply a Hubble constant of h = 0.722 ± 0.067. Combining the full fgas data set with priors on the cosmic baryon density and the Hubble constant, we constrain the dark energy density to be ΩΛ = 0.865 ± 0.119 in non-flat Lambda cold dark matter (cosmological constant) models, and its equation of state to be $w=-1.13_{-0.20}^{+0.17}$ in flat, constant-w models, respectively 41 per cent and 29 per cent tighter than our previous work, and comparable to the best constraints available from other probes. Combining fgas, CMB, supernova, and baryon acoustic oscillation data, we also constrain models with global curvature and evolving dark energy. For the massive, relaxed clusters employed here, we find the scaling of fgas with mass to be consistent with a constant, with an intrinsic scatter that corresponds to just ∼3 per cent in distance.