BEYONDPLANCK

VII. Bayesian estimation of gain and absolute calibration for cosmic microwave background experiments

¹ Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
e-mail: eirik.gjerlow@astro.uio.no
² INAF-Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, Trieste, Italy
³ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, Milano, Italy
⁴ INAF-IASF Milano, Via E. Bassini 15, Milano, Italy
⁵ INFN, Sezione di Milano, Via Celoria 16, Milano, Italy
⁶ Planetek Hellas, Leoforos Kifisias 44, Marousi, 151 25 Greece
⁷ Department of Astrophysical Sciences, Princeton University, Princeton, NJ, 08544 USA
⁸ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, USA
⁹ Department of Physics, University of Helsinki, Gustaf Hällströmin katu 2, Helsinki, Finland
¹⁰ Helsinki Institute of Physics, University of Helsinki, Gustaf Hällströmin katu 2, Helsinki, Finland
¹¹ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
¹² Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, PA, 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: 19 May 2022
Accepted: 13 October 2022

Abstract

We present a Bayesian calibration algorithm for cosmic microwave background (CMB) observations as implemented within the global end-to-end BEYONDPLANCK framework and applied to the Planck Low Frequency Instrument (LFI) data. Following the most recent Planck analysis, we decomposed the full time-dependent gain into a sum of three nearly orthogonal components: one absolute calibration term, common to all detectors, one time-independent term that can vary between detectors, and one time-dependent component that was allowed to vary between one-hour pointing periods. Each term was then sampled conditionally on all other parameters in the global signal model through Gibbs sampling. The absolute calibration is sampled using only the orbital dipole as a reference source, while the two relative gain components were sampled using the full sky signal, including the orbital and Solar CMB dipoles, CMB fluctuations, and foreground contributions. We discuss various aspects of the data that influence gain estimation, including the dipole-polarization quadrupole degeneracy and processing masks. Comparing our solution to previous pipelines, we find good agreement in general, with relative deviations of −0.67% (−0.84%) for 30 GHz, 0.12% (−0.04%) for 44 GHz and −0.03% (−0.64%) for 70 GHz, compared to Planck PR4 and Planck 2018, respectively. We note that the BEYONDPLANCK calibration was performed globally, which results in better inter-frequency consistency than previous estimates. Additionally, WMAP observations were used actively in the BEYONDPLANCK analysis, which both breaks internal degeneracies in the Planck data set and results in an overall better agreement with WMAP. Finally, we used a Wiener filtering approach to smoothing the gain estimates. We show that this method avoids artifacts in the correlated noise maps as a result of oversmoothing the gain solution, which is difficult to avoid with methods like boxcar smoothing, as Wiener filtering by construction maintains a balance between data fidelity and prior knowledge. Although our presentation and algorithm are currently oriented toward LFI processing, the general procedure is fully generalizable to other experiments, as long as the Solar dipole signal is available to be used for calibration.