An empirical recipe for inelastic hydrogen-atom collisions in non-LTE calculations^⋆

¹ Laboratoire Univers et Particules de Montpellier, Université de Montpellier, CNRS, UMR 5299 Montpellier, France
² Joint Institute for Nuclear Astrophysics, Center for the Evolution of the Elements, East Lansing, MI 48824, USA
³ Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
e-mail: ranae@mit.edu
⁴ Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles, CP 226, Boulevard du Triomphe, 1050 Brussels, Belgium
⁵ Department of Physics and Astronomy, Notre Dame University-Louaize, PO Box 72, Zouk Mikaël, Lebanon
⁶ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, UMR7293, CS 34229, 06304 Nice Cedex 4, France

Received: 23 December 2016
Accepted: 27 August 2018

Abstract

Context. Determination of high-precision abundances of late-type stars has been and always will be an important goal of spectroscopic studies, which requires accurate modeling of their stellar spectra with non-local thermodynamic equilibrium (NLTE) radiative transfer methods. This entails using up-to-date atomic data of the elements under study, which are still subject to large uncertainties.

Aims. We investigate the role of hydrogen collisions in NLTE spectral line synthesis, and introduce a new general empirical recipe to determine inelastic charge transfer (CT) and bound-bound hydrogen collisional rates. This recipe is based on fitting the energy functional dependence of published quantum collisional rate coefficients of several neutral elements (BeI, Na I, Mg I, Al I, Si I and Ca I) using simple polynomial equations.

Methods. We perform thorough NLTE abundance calculation tests using our method for four different atoms, Na, Mg, Al and Si, for a broad range of stellar parameters. We then compare the results to calculations computed using the published quantum rates for all the corresponding elements. We also compare to results computed using excitation collisional rates via the commonly used Drawin equation for different fudge factors, SM_H, applied.

Results. We demonstrate that our proposed method is able to reproduce the NLTE abundance corrections performed with the quantum rates for different spectral types and metallicities for representative Na I and Al I lines to within ≤0.05 dex and ≤0.03 dex, respectively. For Mg I and Si I lines, the method performs better for the cool giants and dwarfs, while larger discrepancies up to 0.2 dex could be obtained for some lines for the subgiants and warm dwarfs. We obtained larger NLTE correction differences between models incorporating Drawin rates relative to the quantum models by up to 0.4 dex. These large discrepancies are potentially due to ignoring either or both CT and ionization collisional processes by hydrogen in our Drawin models.

Conclusions. Our general empirical fitting method (EFM) for estimating hydrogen collision rates performs well in its ability to reproduce, within narrow uncertainties, the abundance corrections computed with models incorporating quantum collisional rates. It performs generally best for the cool and warm dwarfs, with slightly larger discrepancies obtained for the giants and subgiants. It could possibly be extended in the future to transitions of the same elements for which quantum calculations do not exist, or, in the absence of published quantum calculations, to other elements as well.