# Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: Statistical and systematic error budgets for future experiments

## TL;DR

This paper introduces an optimal Maximum Likelihood estimator for measuring galaxy cluster masses via CMB lensing, demonstrating improved accuracy over traditional methods and analyzing systematic errors and experimental sensitivities.

## Contribution

The paper develops a new MLE approach for CMB lensing mass measurements, outperforming quadratic estimators and assessing systematic biases and experimental requirements.

## Key findings

- MLE outperforms quadratic estimator at low noise levels
- Polarization maps can replace E- and B-modes without information loss
- Predicted mass uncertainties are 3-6% for current experiments and below 1% for CMB-S4

## Abstract

We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential systematic errors. Using realistic simulations, we examine the cluster mass uncertainties from CMB-cluster lensing as a function of an experiment's beam size and noise level. We predict the cluster mass uncertainties will be 3 - 6% for SPT-3G, AdvACT, and Simons Array experiments with 10,000 clusters and less than 1% for the CMB-S4 experiment with a sample containing 100,000 clusters. The mass constraints from CMB polarization are very sensitive to the experimental beam size and map noise level: for a factor of three reduction in either the beam size or noise level, the lensing signal-to-noise improves by roughly a factor of two.