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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.

Galaxy cluster masses, rich with cosmological information, can be estimated from internal dark matter (DM) velocity dispersions, which in turn can be observationally inferred from satellite galaxy velocities. However, galaxies are biased tracers of the DM, and the bias can vary over host halo and galaxy properties as well as time. We precisely calibrate the velocity bias, bv – defined as the ratio of galaxy and DM velocity dispersions – as a function of redshift, host halo mass, and galaxy stellar mass threshold ($M_{\rm \star , sat}$), for massive haloes ($M_{\rm 200c}\gt 10^{13.5} \, {\rm M}_\odot$) from five cosmological simulations: IllustrisTNG, Magneticum, Bahamas + Macsis, The Three Hundred Project, and MultiDark Planck-2. We first compare scaling relations for galaxy and DM velocity dispersion across simulations; the former is estimated using a new ensemble velocity likelihood method that is unbiased for low galaxy counts per halo, while the latter uses a local linear regression. The simulations show consistent trends of bv increasing with M200c and decreasing with redshift and $M_{\rm \star , sat}$. The ensemble-estimated theoretical uncertainty in bv is 2–3 per cent, but becomes percent-level when considering only the three highest resolution simulations. We update the mass–richness normalization for an SDSS redMaPPer cluster sample, and find our improved bv estimates reduce the normalization uncertainty from 22 to 8 per cent, demonstrating that dynamical mass estimation is competitive with weak lensing mass estimation. We discuss necessary steps for further improving this precision. Our estimates for $b_v(M_{\rm 200c}, M_{\rm \star , sat}, z)$ are made publicly available.