Bias versus variance when fitting multi-species molecular lines with a non-LTE radiative transfer model: Application to the estimation of the gas temperature and volume density
Journal article, 2024
Context. Robust radiative transfer techniques are requisite for efficiently extracting the physical and chemical information from molecular rotational lines. Aims. We study several hypotheses that enable robust estimations of the column densities and physical conditions when fitting one or two transitions per molecular species. We study the extent to which simplifying assumptions aimed at reducing the complexity of the problem introduce estimation biases and how to detect them. Methods. We focus on the CO and HCO+ isotopologues and analyze maps of a 50 square arcminutes field. We used the RADEX escape probability model to solve the statistical equilibrium equations and compute the emerging line profiles, assuming that all species coexist. Depending on the considered set of species, we also fixed the abundance ratio between some species and explored different values. We proposed a maximum likelihood estimator to infer the physical conditions and considered the effect of both the thermal noise and calibration uncertainty. We analyzed any potential biases induced by model misspecifications by comparing the results on the actual data for several sets of species and confirmed with Monte Carlo simulations. The variance of the estimations and the efficiency of the estimator were studied based on the Cramér-Rao lower bound. Results. Column densities can be estimated with 30% accuracy, while the best estimations of the volume density are found to be within a factor of two. Under the chosen model framework, the peak 12CO (1 -0) is useful for constraining the kinetic temperature. The thermal pressure is better and more robustly estimated than the volume density and kinetic temperature separately. Analyzing CO and HCO+ isotopologues and fitting the full line profile are recommended practices with respect to detecting possible biases. Conclusions. Combining a non-local thermodynamic equilibrium model with a rigorous analysis of the accuracy allows us to obtain an efficient estimator and identify where the model is misspecified. We note that other combinations of molecular lines could be studied in the future.
Methods: statistical
Radiative transfer
ISM: clouds
Methods: data analysis
Line: profiles
ISM: general
Author
Antoine Roueff
University of Toulon
J. Pety
Paris Observatory
Institut de Radioastronomie Millimétrique (IRAM)
M. Gerin
Paris Observatory
L. Segal
Institut de Radioastronomie Millimétrique (IRAM)
University of Toulon
J.R. Goicoechea
Spanish National Research Council (CSIC)
Harvey Liszt
National Radio Astronomy Observatory
P. Gratier
Laboratoire d'Astrophysique de Bordeaux
Ivana Bešlić
Paris Observatory
Lucas Einig
Institut de Radioastronomie Millimétrique (IRAM)
Grenoble Alpes University
Mathilde Gaudel
Paris Observatory
Jan Orkisz
Chalmers, Space, Earth and Environment, Astronomy and Plasmaphysics
Pierre Palud
University of Lille
Paris Observatory
Miriam G. Santa-Maria
Spanish National Research Council (CSIC)
Victor De Souza Magalhaes
Institut de Radioastronomie Millimétrique (IRAM)
Antoine Zakardjian
Institut de Recherche en Astrophysique et Planétologie (IRAP)
Sébastien Bardeau
Institut de Radioastronomie Millimétrique (IRAM)
E. Bron
Paris Observatory
Pierre Chainais
University of Lille
Simon Coudé
Worcester State University
Harvard-Smithsonian Center for Astrophysics
K. Demyk
Institut de Recherche en Astrophysique et Planétologie (IRAP)
Viviana Guzman
Pontificia Universidad Catolica de Chile
A. Hughes
Institut de Recherche en Astrophysique et Planétologie (IRAP)
David Languignon
Paris Observatory
F. Levrier
Laboratoire de Physique de l’Ecole Normale Supérieure
D. C. Lis
California Institute of Technology (Caltech)
Jacques Le Bourlot
Paris Observatory
Franck Le Petit
Paris Observatory
Nicolas Peretto
Cardiff University
Evelyne Roueff
Paris Observatory
A. Sievers
Institut de Radioastronomie Millimétrique (IRAM)
Pierre Antoine Thouvenin
University of Lille
Astronomy and Astrophysics
0004-6361 (ISSN) 1432-0746 (eISSN)
Vol. 686 A255Subject Categories (SSIF 2011)
Astronomy, Astrophysics and Cosmology
Atom and Molecular Physics and Optics
Probability Theory and Statistics
DOI
10.1051/0004-6361/202449148