The Simons Observatory: Quantifying the impact of beam chromaticity on large-scale B-mode science

Abstract

The Simons Observatory (SO) Small Aperture Telescopes (SATs) will observe the Cosmic Microwave Background (CMB) temperature and polarization at six frequency bands. Within these bands, the angular response of the telescope (beam) is convolved with the instrument's spectral response (commonly called bandpass) and the signal from the sky, which leads to the band-averaged telescope beam response, which is sampled and digitized. The spectral properties of the band-averaged beam depend on the natural variation of the beam within the band, referred to as beam chromaticity. In this paper, we quantify the impact of the interplay of beam chromaticity and intrinsic frequency scaling from the various components that dominate the polarized sky emission on the tensor-to-scalar ratio, $r$, and foreground parameters. We do so by employing a parametric power-spectrum-based foreground component separation algorithm, namely BBPower, to which we provide beam-convolved time domain simulations performed with the beamconv software while assuming an idealized version of the SO SAT optics. We find a small, $0.02σ$, bias on $r$, due to beam chromaticity, which seems to mostly impact the dust spatial parameters, causing a maximum $0.77 σ$ bias on the dust $B$-mode spectra amplitude, $A_{d}$, when employing Gaussian foreground simulations. However, we find all parameter biases to be smaller than $1σ$ at all times, independently of the foreground model. This includes the case where we introduce additional uncertainty on the bandpass shape, which accounts for approximately half of the total allowed gain uncertainty, as estimated in previous work for the SO SATs.

Figures (10)

• Figure 1: Logarithmic profiles of five monochromatic co-polar beam maps generated for each of the 93 (top left), 145 (top right), 225 (bottom left), and 280GHz bands (bottom right), using TICRA TOOLS software. Each set of (five) maps is produced at frequencies of uniform spacing across the full frequency range of the corresponding band. All bands are assumed to have 25$\%$ fractional width, and all beam maps are generated for a detector on the center of the focal plane of a simulated three-lens refracting telescope.
• Figure 2: The harmonic transforms of the first ten azimuthal modes of five monochromatic beam simulations sampled uniformly across a $25\%$-relative-width frequency band centered on 93GHz. The beam transfer functions have been truncated to a multipole range spanning $\ell$=30-300 and normalized with respect to the peak amplitude of the symmetric mode.
• Figure 3: Top: The first five azimuthal modes of the band-averaged 93GHz beam shown in map space. Bottom: The percent relative error between the frequency-scaled, $B_{\ell}^{\mathrm{fsc}}$, and constant-SED beam harmonic transforms, $B_{\ell}$, per mode. The different curves represent the cases where the frequency scaling matches the dust (blue), synchrotron (orange), CMB (green) and planet (red) SEDs. The band-averaged beams with and without frequency scaling are estimated from the monochromatic beam modes of $m=0..4$ shown in the first row of Figure \ref{['fig:first_10_az_modes']}.
• Figure 4: Left: Beam-convolved Stokes $Q$ map at 280GHz produced by simulating the SAT scan strategy with beamconv, assuming an input sky model including CMB and Gaussian foregrounds. Right: The apodized custom mask that is generated from the detector hits for the simulated SAT-like scan strategy. Both maps are shown in Equatorial coordinates.
• Figure 5: The posterior distributions of the nine model parameters as estimated from ten sets of six beamconv maps where the MF, UHF frequency maps were convolved with symmetric co-polar (green), symmetric co- and cross-polar (red), asymmetric co- and cross-polar (magenta) and wide asymmetric co- and cross-polar beams (blue). The true values for these parameters are also shown for reference (grey vertical lines). The component separation method is applied only to the center frequencies of each band for a net evaluation of the beam systematics impact that is decoupled from the beam chromaticity effect.