Determine the physical alignment of centering offsets with projected halo structure

Determine the sign and magnitude of the offset–major-axis alignment statistic describing the preferred orientation of centering-offset directions relative to the projected major axis of galaxy clusters.

Background

The paper discusses evidence that centering-offset directions need not be statistically independent of projected cluster structure. The relevant alignment is quantified by the population statistic $\langle\cos 2\varphi_{\mathrm{off}}\rangle$, where positive values favor offsets along the projected major axis and negative values favor offsets along the minor axis.

The authors explore imposed alignment distributions as a diagnostic, but these calculations do not establish the sign or magnitude of the alignment statistic for actual cluster populations. Calibrating it would be necessary for predicting how offset–shape correlations affect nonlinear ring-averaging residuals and weak-lensing mass analyses.