Requirements on bandpass resolution and measurement precision for LiteBIRD

TL;DR

This work analyzes how uncertainties in instrument bandpasses affect LiteBIRD's ability to measure the tensor-to-scalar ratio $r$ via $B$-mode polarization. By propagating bandpass uncertainties through both TOD and map-making, and by testing three representative bandpass shapes across three reference channels, the authors derive concrete requirements on bandpass sampling resolution ($\lesssim 1.5$ GHz) and Gaussian measurement error ($\sigma \lesssim 0.0089$ at 0.5 GHz resolution) to keep the bias $\Delta r$ beneath $6.5\times 10^{-6}$. They validate these requirements across the full LiteBIRD frequency configuration and with blind component separation (NILC), finding that NILC can relax the $\sigma$ requirement to $\lesssim 0.05$ while maintaining a negligible bias on $r$. The results emphasize the robustness of NILC to bandpass distortions and provide actionable specification targets for LiteBIRD bandpass characterization and sampling.

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 $τ$, entering the TOD, and the estimated one $τ_s$, used in the map-making. We focus on two aspects: the effect of degrading the $τ_s$ resolution, and the addition of a Gaussian error $σ$ to $τ_s$. 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 $r$, $Δr$, caused by these effects on a single channel, we find that a resolution $\lesssim 1.5$ GHz and $σ\lesssim 0.0089$ do not exceed the LiteBIRD budget allocation per systematic effect, $Δr < 6.5 \times 10^{-6}$. We then check that propagating separately the uncertainties due to a resolution of 1 GHz and a measurement error with $σ= 0.0089$ in all LiteBIRD frequency channels, for the most pessimistic bandpass shape of the three considered, still produces a $Δr < 6.5 \times 10^{-6}$. 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 $σ$ can be relaxed to $σ\lesssim 0.05$. (Abridged)

Figures (7)

• Figure 1: Mueller matrix elements of the LFT, MFT and HFT HWPs as functions of the frequency. These are the components of HWP Mueller matrix in its rest frame. $M_{i}^{TX}(\nu)$ in Eq. \ref{['eq:dobsnu']} can be obtained from a combination of these rest-frame components as shown in Ref. Giardiello:2021uxq. The noisy pattern in the LFT HWP elements is caused by its configuration (five-layers sapphire HWP): due to the high refractive index of sapphire, the thickness of the HWP results in fast oscillations of the transmission spectrum. We refer to Giardiello:2021uxqMonelli:2023wmv for further details.
• Figure 2: Left: Bandpass transmissions with a Chebyshev filter of different order parameters for the MFT channel centered at 140 GHz (MFT 140). Right: Bandpass transmissions for the same channel, using different bandpass shapes. The transmission is plotted in log scale to highlight the bandpass tails and the level of the shoulders in the top-hat profile. In both figures the ripple is 0.2 dB.
• Figure 3: Chebyshev order 5 bandpass profiles for the LFT 40 GHz channel (left) and the HFT 402 GHz one (right) reconstructed with different resolutions. The coarser the resolution, the worse is the reconstruction of the bandpass shape (which becomes more stable with finer resolutions of the order of a few tenths of GHz), especially for narrower bandwidths and more complicated shapes such as the Chebyshev ones. The effect is clearly worse in the left panel compared to the right one, since the bandwidth of channel LFT 40 is the narrowest.
• Figure 4: $\Delta r$ as function of different values of $\tau_s$ resolution for the three reference channels considered. We use blue dots for top-hat bandpass profiles, orange stars for Chebyshev order 5 and green crosses for Chebyshev order 3. We conclude that, as a single requirement for all channels, a resolution $\lesssim 1.5$ GHz is needed not to exceed the threshold $\Delta r = 6.5 \times 10^{-6}$ (marked by the blue horizontal line).
• Figure 5: Example of bandpasses $\tau_s$ when perturbed by a Gaussian distributed error, with respect to the unperturbed and high resolution $\tau$ (in blue). The bandpasses are renormalized, to have max($\tau_s$) = 1. We show one case with resolution 0.5 GHz and $\sigma = 0.02$ (orange), and one with resolution 1 GHz and $\sigma = 0.03$ (green). They have two different bandpass error realizations.