Marginalized posteriors for quadrupolar modulation parameter g_*, using SMICA data for the TT+EE asymmetry constraints (orange curves) and Planck TT,TE,EE+lowE for the isotropic constraints (blue curves), which probe the modification to the power spectrum via Eq. (114). Top: constraints for q = 2 and 1 (left and right, respectively). Bottom: constraints for q = −1 and −2 (left and right, respectively). Strongly negative g_* is suppressed for q <  0, due to the unphysical prediction of negative power.