Requirements on bandpass resolution and measurement precision for LiteBIRD

TL;DR

This paper assesses how inaccuracies in instrument bandpass knowledge affect the measurement of the tensor-to-scalar ratio r in the LiteBIRD satellite, establishing resolution and error thresholds to keep systematic biases below the mission's budget.

Contribution

It introduces a pipeline to evaluate the impact of bandpass uncertainties on r measurement and determines specific resolution and error limits for LiteBIRD's channels to control systematic bias.

Findings

Resolution ≤ 1.5 GHz limits bias on r

Measurement error σ ≤ 0.0089 is acceptable

NILC method allows relaxing σ to 0.05

Abstract

In this work, we study the impact of an imperfect knowledge of the instrument bandpasses on the estimate of the tensor-to-scalar ratio $r$ in the context of the next-generation LiteBIRD satellite. We develop a pipeline to integrate over the bandpass transmission in both the time-ordered data (TOD) and the map-making processing steps. We introduce the systematic effect by having a mismatch between the ``real'', high resolution bandpass $\tau$, entering the TOD, and the estimated one $\tau_s$, used in the map-making. We focus on two aspects: the effect of degrading the $\tau_s$ resolution, and the addition of a Gaussian error $\sigma$ to $\tau_s$. To reduce the computational load of the analysis, the two effects are explored separately, for three representative LiteBIRD channels (40 GHz, 140 GHz and 402 GHz) and for three bandpass shapes. Computing the amount of bias on $r$, $\Delta r$, caused by these effects on a single channel, we find that a resolution $\lesssim 1.5$ GHz and $\sigma \lesssim 0.0089$ do not exceed the LiteBIRD budget allocation per systematic effect, $\Delta r < 6.5 \times 10^{-6}$. We then check that propagating separately the uncertainties due to a resolution of 1 GHz and a measurement error with $\sigma = 0.0089$ in all LiteBIRD frequency channels, for the most pessimistic bandpass shape of the three considered, still produces a $\Delta r < 6.5 \times 10^{-6}$. This is done both with the simple deprojection approach and with a blind component separation technique, the Needlet Internal Linear Combination (NILC). Due to the effectiveness of NILC in cleaning the systematic residuals, we have tested that the requirement on $\sigma$ can be relaxed to $\sigma \lesssim 0.05$. (Abridged)