# Application of XFaster power spectrum and likelihood estimator to Planck

## TL;DR

This paper introduces the XFaster power spectrum and likelihood estimator tailored for the Planck CMB data, demonstrating its accuracy in extracting power spectra and estimating cosmological parameters across a wide multipole range.

## Contribution

The paper presents a new implementation of the XFaster estimator and likelihood, showing its effectiveness for Planck data analysis and comparison with other high-l likelihood methods.

## Key findings

- Accurately extracts power spectrum for high-l multipoles.
- Performs well at moderately low multipoles.
- Recovers cosmological parameters with high accuracy when low-l likelihood is included.

## Abstract

We develop the XFaster Cosmic Microwave Background (CMB) temperature and polarization anisotropy power spectrum and likelihood technique for the Planck CMB satellite mission. We give an overview of this estimator and its current implementation and present the results of applying this algorithm to simulated Planck data. We show that it can accurately extract the power spectrum of Planck data for the high-l multipoles range. We compare the XFaster approximation for the likelihood to other high-l likelihood approximations such as Gaussian and Offset Lognormal and a low-l pixel-based likelihood. We show that the XFaster likelihood is not only accurate at high-l, but also performs well at moderately low multipoles. We also present results for cosmological parameter Markov Chain Monte Carlo estimation with the XFaster likelihood. As long as the low-l polarization and temperature power are properly accounted for, e.g., by adding an adequate low-l likelihood ingredient, the input parameters are recovered to a high level of accuracy.