BEYONDPLANCK

X. Planck Low Frequency Instrument frequency maps with sample-based error propagation

¹ Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029, Blindern, 0315 Oslo, Norway
e-mail: artem.basyrov@astro.uio.no
² Department of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
³ Helsinki Institute 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 INAF-IASF Milano, Via E. Bassini 15, Milano, Italy
⁶ INFN, Sezione di Milano, Via Celoria 16, Milano, Italy
⁷ INAF-Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, Trieste, Italy
⁸ Planetek Hellas, Leoforos Kifisias 44, Marousi, 151 25 Greece
⁹ Department of Astrophysical Sciences, Princeton University, Princeton, NJ, 08544 USA
¹⁰ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109 USA
¹¹ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 USA
¹² Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, PA, 19041 USA
¹³ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
¹⁴ Dipartimento di Fisica, Università degli Studi di Trieste, Via A. Valerio 2, Trieste, Italy

Received: 25 August 2022
Accepted: 16 November 2022

Abstract

We present Planck Low Frequency Instrument (LFI) frequency sky maps derived within the BEYONDPLANCK framework. This framework draws samples from a global posterior distribution that includes instrumental, astrophysical, and cosmological parameters, and the main product is an entire ensemble of frequency sky map samples, each of which corresponds to one possible realization of the various modeled instrumental systematic corrections, including correlated noise, time-variable gain, as well as far sidelobe and bandpass corrections. This ensemble allows for computationally convenient end-to-end propagation of low-level instrumental uncertainties into higher-level science products, including astrophysical component maps, angular power spectra, and cosmological parameters. We show that the two dominant sources of LFI instrumental systematic uncertainties are correlated noise and gain fluctuations, and the products presented here support – for the first time – full Bayesian error propagation for these effects at full angular resolution. We compared our posterior mean maps with traditional frequency maps delivered by the Planck Collaboration, and find generally good agreement. The most important quality improvement is due to significantly lower calibration uncertainties in the new processing, as we find a fractional absolute calibration uncertainty at 70 GHz of Δg₀/g₀ = 5 × 10⁻⁵, which is nominally 40 times smaller than that reported by Planck 2018. However, we also note that the original Planck 2018 estimate has a nontrivial statistical interpretation, and this further illustrates the advantage of the new framework in terms of producing self-consistent and well-defined error estimates of all involved quantities without the need of ad hoc uncertainty contributions. We describe how low-resolution data products, including dense pixel-pixel covariance matrices, may be produced from the posterior samples directly, without the need for computationally expensive analytic calculations or simulations. We conclude that posterior-based frequency map sampling provides unique capabilities in terms of low-level systematics modeling and error propagation, and may play an important role for future Cosmic Microwave Background (CMB) B-mode experiments aiming at nanokelvin precision.