Ellipticity of Brightest Cluster Galaxies as tracer of halo orientation and weak-lensing mass bias

Weak-lensing measurements of the massesof galaxy clustersare commonly based on the assumption of spherically symmetric density profiles. Yet, the cold dark mattermodel predicts the shapes of dark matter halosto be triaxial. Halo triaxiality, and the orientation of the major axis with respect to the line of sight, are expected to be the leading cause of intrinsic scatter in weak-lensing massmeasurements. The shape of central cluster galaxies ( Brightest Cluster Galaxies; BCGs) is expected to follow the shape of the dark matter halo. Here we investigate the use of BCG ellipticity as predictor of the weak-lensing massbias in individual clusters compared to the mean. Using weaklensing masses$M^{\rm WL}_{500}$ from the Weighing the Giants project, and $M_{500}$ derived from gas massesas low-scatter massproxy, we find that, on average, the lensing massesof clusters with the roundest / most elliptical 25% of BCGs are biased $\sim 20$% high / low compared to the average, as qualitatively predicted by the cold dark mattermodel. For cluster cosmology projects utilizing weak-lensing massestimates, the shape of the BCG can thus contribute useful information on the effect of orientation bias in weaklensing massestimates as well as on cluster selection bias.