Mitigating half-wave plate systematics at the map-making level: calibration requirements for LiteBIRD

Abstract

Although half-wave plates (HWPs) are becoming a popular choice of polarization modulators for cosmic microwave background (CMB) experiments, their non-idealities can introduce systematic effects that should be carefully characterized and mitigated. One possible mitigation strategy is to incorporate information about the non-idealities at the map-making level, which helps to reduce the HWP-induced distortions of the reconstructed CMB. Nevertheless, the non-idealities can only be known with finite precision. In this paper we investigate the consequences of discrepancies between their true frequency profiles and those assumed by the map-maker. We present an end-to-end framework, including a blind component-separation step, and use it to translate these discrepancies into a bias on the tensor-to-scalar ratio, $r$, for the LiteBIRD satellite mission. We subsequently derive realistic and conservative measurement requirements for accurately characterizing the HWP non-idealities to ensure they do not compromise LiteBIRD's ambitious scientific goals. We find that the obtained results are robust against sky models with varying complexity.

Figures (9)

• Figure 1: Frequency profiles of HWP systematics for the two types of HWPs used by LiteBIRD: the 5-layer achromatic HWP with anti-reflective coating for LFT (left) Komatsu_2021; and the metal-mesh HWP for HFT (right) Pisano_2022. The profiles are illustrated for the "L1-078" and "H2-235" channels. The rows display, in order: phase-shift (first), absorption (second), and cross-polarization module and phase (third and fourth). Each panel shows the estimated response (thick blue) alongside the true response for different miscalibrations ($m={1,2,3,4,5}$). Injection of the miscalibration is performed by fixing the seed (for the set of $m$ going from 1 to 5) per single systematic. Two distinct seeds are used for the real and imaginary parts of the cross-polarization.
• Figure 2: Configuration of needlet harmonic bands used for component separation in this work. Each color represents a different needlet scale, with bandpass filters $b(\ell)$ plotted as a function of multipole $\ell$.
• Figure 3: Methodology used in this study to determine the requirements for the mismatch factor, $m_\text{req}$, associated with HWP systematics, including non-unitary transmission, phase-shift, and cross-polarization, for a given foreground model. For each value of the mismatch factor $m \in \{1, 2, \dots, 5\}$, we simulate 200 realizations (denoted by the index $i$ running over all realizations, represented by light green boxes) of the band-integrated maps and evaluate the distortion to the tensor-to-scalar ratio, $dr_{m,i}$, for each realization. These $dr_{m,i}$ values are then used to calculate the set of $\Delta r_m$ for different $m$ (shown in shaded pink), which is subsequently used to derive the best-fit function $\tilde{\Delta}r(m)$. The final step involves determining the value $m_\text{req}$ (light blue box), such that $\Delta r(m_\text{req}) = \delta r^\text{req} = 6.5 \times 10^{-6}$.
• Figure 4: Outcome of the propagation of the miscalibration of HWP unitary-transmission (top), phase-shift (middle) and cross-polarization (bottom) through the component-separation step. Left: average $B$-mode power spectrum (over 200 simulations) of residual foregrounds and noise (solid and dashed orange lines) and systematic distortions (dotted) for different amplitude of the systematic effect ($m=0,1,...,5$). Foreground and noise residuals are reported just for the ideal case ($m=0$) because those affected by systematics would be superimposed when considering the adopted scales. The distortions' power spectrum is computed as the absolute value of the average difference between output angular power spectra with and without the systematic effect ($\left|\langle C_{\ell}^{\text{obs}}(m\neq0)-C_{\ell}^{\text{obs}}(m= 0)\rangle\right|$). For comparison, the mean input CMB $B$-mode power spectrum (grey solid line) and a range of primordial tensor $B$-mode spectra with $r\in [0.001,0.004]$ (gray shaded area) are shown. Right: trend of $\Delta r$ (computed according to Eq. \ref{['eq:Delta_r']}) as a function of the amplitude of the systematic mismatch factor $m$. The red solid lines represent the best-fit analytical expression, the blue dashed lines the threshold $\delta r^{\textrm{req}}=6.5\times 10^{-6}$ (horizontal), and the derived requirements $m_{\text{req}}$ (vertical).
• Figure 5: Trend of the bias on the tensor-to-scalar ratio $r$ as a function of the sky complexity, while simultaneously combining all the three kinds of systematic miscalibrations (see table \ref{['table:HWP_requirements_d0s0']} for the miscalibration accuracy used).