BeyondPlanck VI. Noise characterization and modelling

Abstract

We present a Bayesian method for estimating instrumental noise parameters and propagating noise uncertainties within the global BeyondPlanck Gibbs sampling framework, and apply this to Planck LFI time-ordered data. Following previous literature, we adopt a simple 1/ f model for the noise power spectral density (PSD), and implement an optimal Wiener-filter (or constrained realization) gap-filling procedure to account for masked data. We then use this procedure to both estimate the gapless correlated noise in the time-domain, n corr , and to sample the noise PSD spectral parameters, ξ n = {σ 0 , f knee , α}. In contrast to previous Planck analyses, we only assume piecewise stationary noise within each pointing period (PID), not throughout the full mission, but we adopt the LFI DPC results as priors on α and f knee . On average, we find best-fit correlated noise parameters that are mostly consistent with previous results, with a few notable exceptions. However, a detailed inspection of the time-dependent results reveals many important findings. First and foremost, we find strong evidence for statistically significant temporal variations in all noise PSD parameters, many of which are directly correlated with satellite housekeeping data. Second, while the simple 1/ f model appears to be an excellent fit for the LFI 70 GHz channel, there is evidence for additional correlated noise not described by a 1/ f model in the 30 and 44 GHz channels, including within the primary science frequency range of 0.1-1 Hz. In general, most 30 and 44 GHz channels exhibit excess noise at the 2-3 σ level in each one hour pointing period. For some periods of time, we also find evidence of strong common mode noise fluctuations across the entire focal plane. Finally, we find a number of strong stripes when binning the 44 GHz correlated noise into a sky map, and we hypothesize that these may be associated with deficiencies in the gain model for this channel. Overall, we conclude that a simple 1/ f profile is not adequate to fully characterize the Planck LFI noise, even when fitted hour-by-hour, and a more general model is required. These findings have important implications for large-scale CMB polarization reconstruction with the Planck LFI data, and understanding and mitigating these issues should be a high-priority task for future studies.

BeyondPlanck XIV. Intensity foreground sampling, degeneracies and priors

“…This methodology allows us to characterize degeneracies between instrumental and astrophysical parameters in a statistically welldefined framework, with uncertainties propagating consistently through all stages of the pipeline. It also seamlessly connects low-level instrumental quantities like gain (Gjerløw et al 2022) and correlated noise (Ihle et al 2022), bandpasses (Svalheim et al 2022a), and far sidelobes (Galloway et al 2022b) via Galactic parameters such as the synchrotron amplitude and spectral index (current paper and Svalheim et al 2022b), to the angular CMB power spectrum and cosmological parameters (Colombo et al 2022;Paradiso et al 2022). In this section, we provide a brief review of the BeyondPlanck sky model, data selection, and sampling scheme, and we refer the interested reader to the various companion papers for full details.…”

“…In this case, we instead adopt a noise rms model that is the sum of an isotropic 0.8 K term (representing statistical uncertainties) and 1 % of the actual map itself, representing multiplicative uncertainties; this is the same approach as taken by Planck Collaboration X (2016). For LFI, correlated noise is accounted for on all angular scales through explicit time-domain sampling, as discussed by Ihle et al (2022).…”

From BeyondPlanck to Cosmoglobe: Preliminary $\mathit{WMAP}$ $\mathit Q$-band analysis

“…This does have some important sampling technical implications for the noise PSD Gibbs step, as defined in Eq. ( 15) and discussed by Ihle et al (2022). The current LFI implementation assumes that the noise is white at the sampling frequency, and explicitly uses this to break a degeneracy between the correlated and white noise components.…”

“…To address this, the WMAP team applied a whitening filter using an estimate of the 1/ f noise spectrum, and iteratively solved for the baseline. In contrast, no priors are imposed on the offset at all in the Commander pipeline, as the inverse noise covariance matrix for the zeroth component is set to zero by hand (Ihle et al 2022). -Solar dipole: While the WMAP team subtracted an estimate of the Solar dipole from the time-ordered data before mapmaking, resulting in dipole-free frequency maps (Hinshaw et al 2003), Commander retains it for calibration and component separation purposes, following Planck DR4 (Planck Collaboration Int.…”

“…-Mapmaking: The WMAP team accounted for correlated noise weighting by estimating a two-point correlation function in time-domain, and used this to pre-whiten the TOD prior to mapmaking. In contrast, we assume a 1/ f noise model, and sample correlated noise explicitly as a stochastic field in (Ihle et al 2022). We note again that this noise PSD model will be generalized in the future to fully capture the temporal behaviour of the WMAP noise, as discussed in Sec.…”