Measuring our peculiar velocity on the CMB with high-multipole off-diagonal correlations

Abstract

Our peculiar velocity with respect to the CMB rest frame is knownto induce a large dipole in the CMB. However, the motion of an observerhas also the effect of distorting the anisotropies at all scales,as shown by Challinor and Van Leeuwen (2002), due to aberration andDoppler effects. We propose to measure independently our local motionby using off-diagonal two-point correlation functions for high multipoles.We study the observability of the signal for temperature and polarizationanisotropies. We point out that Planck can measure the velocityβ with an error of about 30% and the direction with anerror of about 20°. This method constitutes a cross-check,which can be useful to verify that our CMB dipole is due mainly toour velocity or to disentangle the velocity from other possible intrinsicsources.Although in this paper we focus on our peculiar velocity, a similareffect would result also from other intrinsic vectorial distortion ofthe CMB which would induce a dipolar lensing. Measuringthe off-diagonal correlation terms is therefore a test for a preferreddirection on the CMB sky.