# Pairwise Transverse Velocity Measurement with the Rees-Sciama Effect

## TL;DR

This paper proposes a new method to measure the mean pairwise velocities of galaxy clusters using the Rees-Sciama effect in CMB maps, demonstrating promising results for future surveys despite noise challenges.

## Contribution

It introduces a novel estimator for transverse velocities based on the dipolar signature in the CMB, enabling pairwise velocity measurements with future CMB experiments.

## Key findings

- Achieves a signal-to-noise ratio of 5.2 for ~21,000 halos at z=0.5
- Demonstrates the estimator's effectiveness in simulated CMB maps with future survey characteristics
- Shows potential for measuring transverse velocities beyond the Rees-Sciama effect

## Abstract

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.