Bias versus variance when fitting multi-species molecular lines with a non-LTE radiative transfer model
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| Format: | Preprint |
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2024
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| author | Roueff, Antoine Pety, Jérôme Gerin, Maryvonne Ségal, Léontine Goicoechea, Javier Liszt, Harvey Gratier, Pierre Bešlić, Ivana Einig, Lucas Gaudel, M. Orkisz, Jan Palud, Pierre Santa-Maria, Miriam Magalhaes, Victor de Souza Zakardjian, Antoine Bardeau, Sebastien Bron, Emeric E. Chainais, Pierre Coudé, Simon Demyk, Karine Veloso, Viviana Guzman Hughes, Annie Languignon, David Levrier, François Lis, Dariusz C Bourlot, Jacques Le Petit, Franck Le Peretto, Nicolas Roueff, Evelyne Sievers, Albrecht Thouvenin, Pierre-Antoine |
| author_facet | Roueff, Antoine Pety, Jérôme Gerin, Maryvonne Ségal, Léontine Goicoechea, Javier Liszt, Harvey Gratier, Pierre Bešlić, Ivana Einig, Lucas Gaudel, M. Orkisz, Jan Palud, Pierre Santa-Maria, Miriam Magalhaes, Victor de Souza Zakardjian, Antoine Bardeau, Sebastien Bron, Emeric E. Chainais, Pierre Coudé, Simon Demyk, Karine Veloso, Viviana Guzman Hughes, Annie Languignon, David Levrier, François Lis, Dariusz C Bourlot, Jacques Le Petit, Franck Le Peretto, Nicolas Roueff, Evelyne Sievers, Albrecht Thouvenin, Pierre-Antoine |
| contents | Robust radiative transfer techniques are requisite for efficiently extracting the physical and chemical information from molecular rotational lines.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.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 Cram{é}r-Rao lower bound.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.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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_20057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bias versus variance when fitting multi-species molecular lines with a non-LTE radiative transfer model Roueff, Antoine Pety, Jérôme Gerin, Maryvonne Ségal, Léontine Goicoechea, Javier Liszt, Harvey Gratier, Pierre Bešlić, Ivana Einig, Lucas Gaudel, M. Orkisz, Jan Palud, Pierre Santa-Maria, Miriam Magalhaes, Victor de Souza Zakardjian, Antoine Bardeau, Sebastien Bron, Emeric E. Chainais, Pierre Coudé, Simon Demyk, Karine Veloso, Viviana Guzman Hughes, Annie Languignon, David Levrier, François Lis, Dariusz C Bourlot, Jacques Le Petit, Franck Le Peretto, Nicolas Roueff, Evelyne Sievers, Albrecht Thouvenin, Pierre-Antoine Astrophysics of Galaxies Applications Robust radiative transfer techniques are requisite for efficiently extracting the physical and chemical information from molecular rotational lines.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.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 Cram{é}r-Rao lower bound.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.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. |
| title | Bias versus variance when fitting multi-species molecular lines with a non-LTE radiative transfer model |
| topic | Astrophysics of Galaxies Applications |
| url | https://arxiv.org/abs/2403.20057 |