Quantifying the informativity of emission lines to infer physical conditions in giant molecular clouds

I. Application to model predictions

¹ IRAM, 300 rue de la Piscine, 38406 Saint-Martin-d’Hères, France
² LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, 92190 Meudon, France
³ Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, GIPSA-Lab, Grenoble 38000, France
⁴ Univ. Lille, CNRS, Centrale Lille, UMR 9189 – CRIStAL, 59651 Villeneuve d’Ascq, France
⁵ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁶ Univ. Toulon, Aix Marseille Univ., CNRS, IM2NP, Toulon, France
⁷ LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, 75014 Paris, France
⁸ Department of Earth, Environment, and Physics, Worcester State University, Worcester, MA 01602, USA
⁹ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
¹⁰ Instituto de Física Fundamental (CSIC), Calle Serrano 121, 28006 Madrid, Spain
¹¹ Department of Astronomy, University of Florida, PO Box 112055, Gainesville, FL 32611, 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; einig@iram.fr;pierre.palud@obspm.fr

Received: 19 July 2024
Accepted: 18 September 2024

Abstract

Context. Observations of ionic, atomic, or molecular lines are performed to improve our understanding of the interstellar medium (ISM). However, the potential of a line to constrain the physical conditions of the ISM is difficult to assess quantitatively, because of the complexity of the ISM physics. The situation is even more complex when trying to assess which combinations of lines are the most useful. Therefore, observation campaigns usually try to observe as many lines as possible for as much time as possible.

Aims. We have searched for a quantitative statistical criterion to evaluate the full constraining power of a (combination of) tracer(s) with respect to physical conditions. Our goal with such a criterion is twofold. First, we want to improve our understanding of the statistical relationships between ISM tracers and physical conditions. Secondly, by exploiting this criterion, we aim to propose a method that helps observers to make their observation proposals; for example, by choosing to observe the lines with the highest constraining power given limited resources and time.

Methods. We propose an approach based on information theory, in particular the concepts of conditional differential entropy and mutual information. The best (combination of) tracer(s) is obtained by comparing the mutual information between a physical parameter and different sets of lines. The presented analysis is independent of the choice of the estimation algorithm (e.g., neural network or χ² minimization). We applied this method to simulations of radio molecular lines emitted by a photodissociation region similar to the Horsehead Nebula. In this simulated data, we considered the noise properties of a state-of-the-art single dish telescope such as the IRAM 30m telescope. We searched for the best lines to constrain the visual extinction, A_V^tot, or the ultraviolet illumination field, G₀. We ran this search for different gas regimes, namely translucent gas, filamentary gas, and dense cores.

Results. The most informative lines change with the physical regime (e.g., cloud extinction). However, the determination of the optimal (combination of) line(s) to constrain a physical parameter such as the visual extinction depends not only on the radiative transfer of the lines and chemistry of the associated species, but also on the achieved mean signal-to-noise ratio. The short integration time of the CO isotopologue J = 1 − 0 lines already yields much information on the total column density for a large range of (A_V^tot, G₀) space. The best set of lines to constrain the visual extinction does not necessarily combine the most informative individual lines. Precise constraints on the radiation field are more difficult to achieve with molecular lines. They require spectral lines emitted at the cloud surface (e.g., [CII] and [CI] lines).

Conclusions. This approach allows one to better explore the knowledge provided by ISM codes, and to guide future observation campaigns.