# How to avoid X'es around point sources in maximum likelihood CMB maps

## TL;DR

This paper examines the bias introduced by model errors in maximum likelihood CMB map-making, especially around point sources, and presents methods to mitigate leakage artifacts such as X-shaped patterns.

## Contribution

It introduces new and existing techniques to reduce point source leakage in CMB maps caused by model inaccuracies, with implementation in a Python simulator and map-maker.

## Key findings

- Leakage manifests as X-shaped artifacts around point sources.
- Mitigation methods can significantly reduce leakage artifacts.
- Implementation includes a Python simulator and map-maker for testing.

## Abstract

The maximum likelihood estimator for CMB map-making is optimal and unbiased as long as the data model is correct, but in practice it rarely is, with model errors including sub-pixel structure and instrumental problems like time-variable gain and pointing errors. In the presence of such errors, the solution is biased, with the local error in each pixel leaking outwards along the scanning pattern by a noise correlation length. The most important sources of such leakage are strong point sources, and for common scanning patterns the leakage manifests as an X around each such source. I discuss why this happens, and present several old and new methods for mitigating and/or eliminating this leakage, along with a small stand-alone TOD simulator and map-maker in Python that implements them.