Large-scale power loss in ground-based CMB mapmaking

TL;DR

This work reveals that data-model biases in ground-based CMB mapmaking can induce substantial large-scale power loss, driven by subpixel errors and detector gain miscalibration. Through 1D and 2D toy models, the authors show that traditional methods (ML, filter+bin, destriping) can be biased on large scales, while bilinear pointing mitigates subpixel bias and reduces overall bias with manageable costs. They explain why such biases evade many simulations and propose practical detection strategies and mitigation approaches, highlighting the vulnerability of TT measurements to atmospheric-correlated noise. The results have direct implications for upcoming ground-based CMB experiments, emphasizing the need for explicit model-error checks and robust subpixel handling to avoid false conclusions at large scales.

Abstract

CMB mapmaking relies on a data model to solve for the sky map, and this process is vulnerable to bias if the data model cannot capture the full behavior of the signal. We demonstrate that this bias is not just limited to small-scale effects in high-contrast regions of the sky, but can manifest as $\mathcal{O}(1)$ power loss on large scales in the map under conditions and assumptions realistic for ground-based CMB telescopes. This bias is invisible to simulation-based tests that do not explicitly model them, making it easy to miss. We identify two different mechanisms that both cause suppression of long-wavelength modes: sub-pixel errors and detector gain calibration mismatch. We show that the specific case of subpixel bias can be eliminated using bilinear pointing matrices, but also provide simple methods for testing for the presence of large-scale model error bias in general.

Figures (16)

• Figure 1: Preview of the model error bias we will discuss in the following sections. Despite the standard expectations that maximum-likelihood mapmaking is optimal and unbiased, the maximum-likelihood solution (right) for a simple toy example is strongly power-deficient on large scales compared to the input signal (left). As we shall see this bias is not unique to maximum-likelihood methods, and can be triggered by several subtle types of model error.
• Figure 2: a: Example path (red) of a detector across a few pixels. The area closest to each pixel center (black dots) is shown with dotted lines. In the nearest neighbor model, the value associated with each sample is simply that of the closest pixel, regardless of where inside that pixel it is. b: Example detector signal (red) for the same path. The closest matching model (green) leaves a jagged residual (blue) that has power on all length scales despite the signal itself being very smooth. For comparison, if our model were a constant zero, then the residual would just be the signal itself (red), and hence smooth. If smooth residuals are much cheaper in the likelihood than jagged ones, then a zero model will be preferred to one that hugs the signal as tightly as possible like the green curve.
• Figure 3: The noise model/inverse weights/inverse filter used in the subpixel bias demonstration in figures \ref{['fig:subpix-bias']} and \ref{['fig:subpix-noerr']}. It is a simple Fourier-diagonal 1/f + white noise spectrum typical for ground-based CMB observations. The frequency axis is in dimensionless units in this toy example, but for real telescopes the transition from white noise is typically a few Hz, corresponding to multipoles of hundreds on the sky. The power axis is dimensionless here, but for a real-world case could have units like $\micro$K$^2$/Hz.
• Figure 4: Demonstration of large loss of power in long-wavelength mode caused by the poor subpixel treatment in the standard nearest-neighbor pointing matrix. The vertical axis is dimensionless in this toy example, but could have units like $\micro$K or Jy/sr for a real-world case. Figure \ref{['fig:ps']} shows the noise model/inverse weights/inverse filter used in the various methods. signal: The input signal, a smooth long-wavelength mode, sampled at 10 samples per output pixel. binned: Simple binned map (the unweighted average per pixel). Very suboptimal in the presence of correlated noise, but unbiased. ML: Maximum-likelihood map. 2/3 of the signal amplitude is lost despite the naive expectation of biaslessness for this estimator. FB deobs: Filter+bin map debiased using an observation matrix. Identical to ML. FB detrans: Filter+bin map debiased by deconvolving a transfer function measured from simulations. Even more biased than the others due to ignoring mode coupling. destripe: Destriper in the maximum-likelihood limit (1-sample baselines with optimal baseline prior). Identical to ML.
• Figure 5: Like figure \ref{['fig:subpix-bias']}, but with the input signal having the same nearest-neighbor pixelization as the models. In this case all models except FB detrans are unbiased.