Pairwise Transverse Velocity Measurement with the Rees-Sciama Effect
  We introduce a new estimator for the mean pairwise velocities of galaxy
clusters, which is based on the measurement of the clusters'
$\textit{transverse}$ velocity components. The Rees-Sciama (RS) effect offers
an opportunity to measure transverse peculiar velocities through its distinct
dipolar signature around the halo centers in the Cosmic Microwave Background
(CMB) temperature map. We exploit this dipolar structure to extract the
magnitude and direction of the transverse velocity vectors from CMB maps
simulated with the expected characteristics of future surveys like CMB-S4.
Although in the presence of lensed CMB and instrumental noise individual
velocities are not reliably reconstructed, we demonstrate that the mean
pairwise velocity measurement obtained using the estimator yields a
signal-to-noise ratio of $5.2$ for $\sim21,000$ halos with $M >
7\times10^{13}\rm M_\odot$ in a $40\times40$ [deg$^2$] patch at $z=0.5$. While
the proposed estimator carries promising prospects for measuring pairwise
velocities through the RS effect in CMB stage IV experiments, its applications
extend to any other potential probe of transverse velocities.
