[Paper Review] The Crab Nebula as a Calibrator for Wide-beam Cosmic Microwave Background Polarization Surveys

S. Masi, P. de Bernardis+6 more|arXiv (Cornell University)|Jan 1, 2021

Cosmology and Gravitation TheoriesPhysics and Astronomy68 references5 citations

TL;DR

This paper demonstrates that diffuse polarized Galactic emission significantly biases calibration of wide-beam CMB polarimeters using the Crab Nebula as a reference, requiring high-precision, wide-area (≥1.5° radius) polarization maps at ∼20 µK_CMB arcmin accuracy to achieve the sub-arcminute calibration accuracy needed for detecting B-mode signals with tensor-to-scalar ratio r ∼ 0.001.

ABSTRACT

We analyze the effect of polarized diffuse emission in the calibration of wide-beam mm-wave polarimeters, when using the Crab Nebula as a reference source for both polarized brightness and polarization angle. We show that, for CMB polarization experiments aiming at detecting B-mode in a scenario with a tensor to scalar ratio $r \sim 0.001$, wide (a few degrees in diameter), precise ($\sigma_Q$ , $\sigma_U$ $\sim$ 20 $\mu$$K_{CMB}$ arcmin), high angular resolution ($< \mathrm{FWHM}$) reference maps are needed to properly take into account the effects of diffuse polarized emission and avoid significant bias in the calibration.

Motivation & Objective

• Address the challenge of systematic errors in wide-beam CMB polarization surveys due to unaccounted diffuse polarized emission near calibration sources.
• Assess the feasibility of using the Crab Nebula as a polarization calibrator for future CMB experiments targeting B-mode signals with r ∼ 0.001.
• Quantify the impact of diffuse Galactic polarized emission on polarization angle and flux measurements in wide beams.
• Determine the required accuracy and spatial extent of reference maps to achieve sub-arcminute calibration precision.
• Evaluate the sensitivity of calibration results to beam response uncertainties, particularly sidelobe errors.

Proposed method

• Utilized multi-frequency Planck Legacy Archive Stokes I, Q, U maps (HEALPix Nside=2048) to model wide-beam observations of the Crab Nebula.
• Performed beam-weighted aperture photometry using Gaussian beam approximations (FWHM 69′ to 17′) to simulate LSPE and LiteBIRD surveys.
• Computed measured polarization angle ψm and polarized flux Pm as functions of integration radius to assess contamination from diffuse emission.
• Injected 10,000 realizations of uncorrelated Gaussian noise (σ = 10 µK_CMB per pixel) to estimate statistical uncertainty in ψm and Pm.
• Simulated systematic beam errors (solid angle, FWHM, first sidelobe amplitude) to assess their impact on ψm and Pm convergence.
• Used equations (1) to model the transformation of angular power spectra under polarization angle error ∆α, linking it to calibration bias.

Experimental results

Research questions

• RQ1 To what extent does diffuse polarized Galactic emission bias the measured polarization angle and flux when using the Crab Nebula as a calibration source in wide-beam CMB surveys?
• RQ2 What spatial extent and angular resolution are required for reference maps to mitigate contamination from diffuse foregrounds?
• RQ3 How precise must the polarization angle calibration be to avoid significant bias in B-mode power spectrum measurements for r ∼ 0.001?
• RQ4 What level of beam response uncertainty (e.g., FWHM, sidelobe amplitude) is tolerable for achieving sub-arcminute calibration accuracy?
• RQ5 Can the Crab Nebula remain a viable calibration source if diffuse emission dominates the signal in wide beams?

Key findings

• The measured polarization angle ψm and polarized flux Pm converge to values different from the Crab Nebula’s intrinsic signal when integrating over radii >0.5°, due to contamination from diffuse polarized emission.
• For the LSPE-SWIPE 210 GHz channel, diffuse dust emission dominates the signal at large radii, causing a significant angular offset of ∼1° in ψm.
• Even at high frequencies (e.g., 337 GHz), the diffuse foreground contribution leads to a ψm bias of |ψm − ψCN| ∼1°, indicating persistent contamination.
• To achieve sub-arcminute calibration accuracy (required for r ∼ 0.001), reference maps must cover at least 1.5° in radius around the Crab Nebula with ∼20 µK_CMB arcmin precision.
• Statistical uncertainty in ψm is <1 arcmin at 40 GHz and <3 arcmin at higher frequencies, setting a stringent requirement for map depth and accuracy.
• A 1% variation in beam FWHM induces a ∼1 arcmin shift in ψm, indicating standard beam measurements are sufficient; however, a 10% sidelobe amplitude error affects ψm by >1 arcmin only at 337 GHz, highlighting the need for high-accuracy sidelobe characterization.