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Weak-lensing measurements of the masses of galaxy clusters are commonly basedon the assumption of spherically symmetric density profiles. Yet, the cold darkmatter model predicts the shapes of dark matter halos to be triaxial. Halotriaxiality, and the orientation of the major axis with respect to the line ofsight, are expected to be the leading cause of intrinsic scatter inweak-lensing mass measurements. The shape of central cluster galaxies(Brightest Cluster Galaxies; BCGs) is expected to follow the shape of the darkmatter halo. Here we investigate the use of BCG ellipticity as predictor of theweak-lensing mass bias 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 masses as low-scatter mass proxy, we find that, onaverage, the lensing masses of clusters with the roundest / most elliptical 25%of BCGs are biased $\sim 20$% high / low compared to the average, asqualitatively predicted by the cold dark matter model. For cluster cosmologyprojects utilizing weak-lensing mass estimates, the shape of the BCG can thuscontribute useful information on the effect of orientation bias in weak lensingmass estimates as well as on cluster selection bias.

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