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.

Radiative transfer

Methods: data analysis

Methods: statistical

ISM: clouds

Line: profiles

ISM: general

Author

Antoine Roueff

University of Toulon

J. Pety

Institut de Radioastronomie Millimétrique (IRAM)

Paris Observatory

M. Gerin

Paris Observatory

L. Segal

University of Toulon

Institut de Radioastronomie Millimétrique (IRAM)

J.R. Goicoechea

CSIC - Instituto de Fisica Fundamental (IFF)

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

Paris Observatory

University of Lille

Miriam G. Santa-Maria

CSIC - Instituto de Fisica Fundamental (IFF)

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

Environment Environment

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 A255

Subject Categories

Astronomy, Astrophysics and Cosmology

Atom and Molecular Physics and Optics

Probability Theory and Statistics

DOI

10.1051/0004-6361/202449148

More information

Latest update

8/8/2024 1