Beyondplanck VI. Noise Characterization and Modelling
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Astronomy & Astrophysics manuscript no. noise_paper ©ESO 2020 November 16, 2020 BeyondPlanck VI. Noise characterization and modelling H. T. Ihle11?, M. Bersanelli4; 9; 10, C. Franceschet4; 10, E. Gjerløw11, K. J. Andersen11, R. Aurlien11, R. Banerji11, S. Bertocco8, M. Brilenkov11, M. Carbone14, L. P. L. Colombo4, H. K. Eriksen11, J. R. Eskilt11, M. K. Foss11, U. Fuskeland11, S. Galeotta8, M. Galloway11, S. Gerakakis14, B. Hensley2, D. Herman11, M. Iacobellis14, M. Ieronymaki14, H. T. Ihle11, J. B. Jewell12, A. Karakci11, E. Keihänen3; 7, R. Keskitalo1, G. Maggio8, D. Maino4; 9; 10, M. Maris8, A. Mennella4; 9; 10, S. Paradiso4; 9, B. Partridge6, M. Reinecke13, M. San11, A.-S. Suur-Uski3; 7, T. L. Svalheim11, D. Tavagnacco8; 5, H. Thommesen11, D. J. Watts11, I. K. Wehus11, and A. Zacchei8 1 Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, California, U.S.A. 2 Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, U.S.A. 3 Department of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland 4 Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, Milano, Italy 5 Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, Trieste, Italy 6 Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, Pennsylvania, U.S.A. 7 Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland 8 INAF - Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, Trieste, Italy 9 INAF-IASF Milano, Via E. Bassini 15, Milano, Italy 10 INFN, Sezione di Milano, Via Celoria 16, Milano, Italy 11 Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway 12 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, U.S.A. 13 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany 14 Planetek Hellas, Leoforos Kifisias 44, Marousi 151 25, Greece November 16, 2020 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 n time-domain, ncorr, and to sample the noise PSD spectral parameters, ξ = fσ0; fknee; αg. 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 fknee. 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. Key words. ISM: general – Cosmology: observations, polarization, cosmic microwave background, diffuse radiation – Galaxy: general Contents 3.1.2 Handling masking through a conjugate arXiv:2011.06650v1 [astro-ph.CO] 12 Nov 2020 gradient solver . .5 1 Introduction2 3.1.3 Gap-filling by polynomial interpolation .5 3.2 Sampling noise PSD parameters, P(ξn j ncorr)..6 2 The BeyondPlanck data model and framework3 3.2.1 Sampling the white noise level, σ0 ....6 3.2.2 Sampling correlated noise parameters, f and α ................6 3 Methods4 knee 3.2.3 Priors on α and f ...........7 corr n knee 3.1 Sampling correlated noise, P(n j d; ξ ; stot; g).4 3.1.1 Ideal data . .4 4 Mitigation of modelling errors and degeneracies7 4.1 Signal modelling errors and processing masks . .7 ? Corresponding author: H. T. Ihle; [email protected] 4.2 Degeneracies with the gain . .8 Article number, page 1 of 26 A&A proofs: manuscript no. noise_paper 5 Results 10 minimized by introducing the 4 K reference loads and gain mod- 5.1 Posterior distributions and Gibbs chains . 10 ulation factor to optimize the receiver balance; see, e.g., Planck 5.2 Time variability and goodness-of-fit . 11 Collaboration II(2014, 2016) and BeyondPlanck Collaboration (2020) for further details. 6 Systematic effects 18 Regarding stationarity, the two most common assumptions 6.1 Temperature changes in the 20 K stage . 18 are either that the statistical properties remain constant through- 6.2 Temperature fluctuations and 1= f parameters . 19 out the entire observation period (e.g., Planck Collaboration II 6.3 Seasonal effects and slow drifts . 20 2020), or that it may at least be modelled as piece-wise station- 6.4 Inter-radiometer correlations . 20 ary within for instance one hour of observations (e.g., QUIET 6.5 Correlation with housekeeping data . 22 Collaboration et al. 2011). Given such basic assumptions, the ef- 6.6 Issues with individual radiometers . 23 fect of the instrumental noise on higher-order data products has then traditionally been assessed, and propagated, either through 7 Conclusions 24 the use of detailed end-to-end simulations (e.g., Planck Collabo- ration XII 2016) or in the form of explicit noise covariance ma- trices (e.g., Tegmark et al. 1997; Page et al. 2007; Planck Col- 1. Introduction laboration V 2020). The importance of accurate noise modelling is intimately One of the main algorithmic achievements made within the field tied to the overall signal-to-noise ratio of the science target in of CMB analysis during the last few decades is accurate and question. For applications with very high signal-to-noise ratios, nearly lossless data compression. Starting from data sets that detailed noise modelling is essentially irrelevant, since other typically comprise O(108 − 1011) time-ordered measurements, sources of systematic errors dominate the total error budget. One we are now able to routinely produce sky maps that contain prominent example of this is the CMB temperature power spec- O(103 − 107) pixels (e.g., Tegmark 1997; Ashdown et al. 2007). trum as measured by Planck on large angular scales (Planck From these, we may constrain the angular CMB power spectrum, Collaboration IV 2020; Planck Collaboration V 2020). Its white which spans O(103) multipoles (e.g., Gorski 1994; Hivon et al. noise contribution can be misestimated by orders of magnitude 2002; Wandelt et al. 2004). Finally, from these we may derive without making any difference in terms of cosmological parame- tight constraints on a small set of cosmological parameters (e.g., ters, because the full error budget is vastly dominated by cosmic Bond et al. 2000; Lewis & Bridle 2002; Planck Collaboration variance. V 2020; Planck Collaboration VI 2020), which typically is the ultimate goal of any CMB experiment. The cases for which accurate noise modelling is critically Two fundamental assumptions underlying this radical com- important are those with signal-to-noise ratios of order unity. pression process are that the instrumental noise may be mod- For these, noise misestimation may be the difference between elled to a sufficient precision, and that the corresponding induced obtaining a tantalizing, but ultimately unsatisfying, 2 σ result, uncertainties may be propagated faithfully to higher-order data and claiming a ground-breaking and decisive 5 σ discovery; or, products. The starting point for this process is typically to as- the worst-case scenario, erroneously reporting a baseless posi- sume that the noise is Gaussian and random in time, and does tive detection. not correlate with the true sky signal at any given time. Under This regime is precisely where the CMB field is expected to the Gaussianp hypothesis, the net noise contribution therefore de- find itself in only a few years from now, as the next-generation creases as 1= Nobs, where Nobs is the number of observations of CMB experiments (e.g., CMB-S4, LiteBIRD, PICO, Simons Ob- the given pixel, while the signal contribution is independent of servatory, and many others; Abazajian et al. 2019; Suzuki et al. Nobs. 2018; Sugai et al. 2020; Hanany et al. 2019; Ade et al. 2019) are However, it is not sufficient to assume that the noise is sim- currently being planned, built and commissioned in the search ply Gaussian and random. One must also assume something for primordial gravitational waves imprinted in B-mode polar- about its statistical properties, both in terms of its correlation ization. The predicted magnitude of this signal is expected to be structure in time and its stationarity period.