BEETROOTS: Spatially regularized Bayesian inference of physical parameter maps. Application to Orion

¹ LUX, UMR 8262, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, 92190 Meudon, France
² Univ. Lille, CNRS, Centrale Lille, UMR 9189 – CRIStAL, 59651 Villeneuve d’Ascq, France
³ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁴ Instituto de Física Fundamental (CSIC), Calle Serrano 121, 28006, Madrid, Spain
⁵ Department of Astronomy, University of Florida, PO Box 112055, Gainesville, FL 32611, USA
⁶ LUX, UMR 8262, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, 75014 Paris, France
⁷ IRAM, 300 rue de la Piscine, 38406 Saint-Martin-d’Hères, France
⁸ Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, GIPSA-Lab, Grenoble 38000, France
⁹ Univ. Toulon, Aix Marseille Univ., CNRS, IM2NP, Toulon, France
¹⁰ Department of Earth, Environment, and Physics, Worcester State University, Worcester, MA 01602, USA
¹¹ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
¹² Institut de Recherche en Astrophysique et Planétologie (IRAP), Université Paul Sabatier, Toulouse cedex 4, France
¹³ National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA
¹⁴ Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, Allée Geoffroy Saint-Hilaire, 33615 Pessac, France
¹⁵ Instituto de Astrofísica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile
¹⁶ Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Sorbonne Paris Cité, Paris, France
¹⁷ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
¹⁸ School of Physics and Astronomy, Cardiff University, Queen’s buildings, Cardiff CF24 3AA, UK

^★ Corresponding author: palud@apc.in2p3.fr

Received: 25 February 2025
Accepted: 15 April 2025

Abstract

Context. The current generation of millimeter (mm) receivers is capable of producing cubes of 800 000 pixels over 200 000 frequency channels to cover a number of square degrees over the 3 mm atmospheric window. Estimating the physical conditions of the interstellar medium (ISM) with an astrophysical model on the basis of such large datasets is challenging. Common approaches tend to converge to local minima and end up poorly reconstructing regions with a low signal-to-noise ratio (S/N) in most cases. This instrumental revolution thus calls for new scalable data analysis techniques with more advanced approaches to statistical modeling and methods.

Aims. Our aim is to design a general method to reconstruct large maps of physical conditions from the rich datasets produced by new and future instruments. The requirements of the method include the ability to scale to very large maps, to be robust to varying S/N, and to escape from the local minima. In addition, we want to quantify the uncertainties associated with our reconstructions to produce reliable analyses.

Methods. We present BEETROOTS, a PYTHON software that performs Bayesian reconstructions of maps of physical conditions based on observation maps and an astrophysical model. It relies on an accurate statistical model, exploits spatial regularization to guide estimations, and uses state-of-the-art algorithms. It can also assess the ability of the astrophysical model to explain the observations, providing feedback to improve ISM models. In this work, we demonstrate the power of BEETROOTS with the Meudon PDR code on synthetic data. We then apply it to estimate physical condition maps in the full Orion molecular cloud 1 (OMC-1) star-forming region based on Herschel molecular line emission maps.

Results. The application to the synthetic case shows that BEETROOTS can currently analyze maps with up to ten thousand pixels, addressing large variations among the S/N values within the observations while escaping from local minima and providing consistent uncertainty quantifications. On a personal laptop, the inference runtime ranges from a few minutes for maps of 100 pixels to 28 hours for maps of 8100 pixels. Regarding OMC-1, our reconstructions of the incident UV radiation field intensity, G₀, are consistent with those obtained from FIR luminosities. This demonstrates that the considered molecular tracers are able to constrain G₀ over a wide range of environments. In addition, the obtained thermal pressures are high in all dense regions of OMC-1 and positively correlated with G₀. Finally, the Meudon PDR code successfully explains the observations and the obtained G₀ values are reasonable, which indicates that UV photons control the gas physics and chemistry across the rim of OMC-1.

Conclusions. This work paves the way toward systematic and rigorous analyses of observations produced by current and future instruments. Subsequent efforts still need to be made in parallelizing the algorithm and thereby gaining two orders of magnitude for the map sizes.