Effects of boosting on extragalactic components: methods and statistical studies

TL;DR

This paper investigates how our motion relative to the CMB rest frame affects various statistical measures of CMB and SZ maps, introducing new analytical tools and corrections to improve accuracy in cosmological analyses.

Contribution

It derives a new analytical formula for boosted power spectra with frequency dependence and validates boosting codes for CMB and SZ statistics, including bias corrections for estimators.

Findings

Boosting correction increases power spectrum accuracy by ~30% at 150 GHz.

Boosting effects are generally small on SZ power spectra, except near the tSZ null frequency.

Quadratic estimators for the convergence field can be biased at the 1% level due to boosting, but this bias can be corrected.

Abstract

In this work we examine the impact of our motion with respect to the CMB rest frame on statistics of CMB maps by examining the one-, two-, three- and four- point statistics of simulated maps of the CMB and Sunyaev-Zeldovich (SZ) effects. We validate boosting codes by comparing their outcomes for temperature and polarization power spectra up to $\ell \simeq 6000$. We derive and validate a new analytical formula for the computation of the boosted power spectrum of a signal with a generic frequency dependence. As an example we show how this increases the boosting correction to the power spectrum of CMB intensity measurements by $\sim 30\%$ at 150 GHz. We examine the effect of boosting on thermal and kinetic SZ power spectra from semianalytical and hydrodynamical simulations; the boosting correction is generally small for both simulations, except when considering frequencies near the tSZ null. For the non-Gaussian statistics, in general we find that boosting has no impact with two exceptions. We find that, whilst the statistics of the CMB convergence field are unaffected, quadratic estimators that are used to measure this field can become biased at the $O(1)\%$ level by boosting effects. We present a simple modification to the standard estimators that removes this bias. Second, bispectrum estimators can receive a systematic bias from the Doppler induced quadrupole when there is anisotropy in the sky -- in practice this anisotropy comes from masking and inhomogenous noise. This effect is unobservable and already removed by existing analysis methods.