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

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 (Be i, 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, S 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.

Ultra-metal-poor Stars: Spectroscopic Determination of Stellar Atmospheric Parameters Using Iron Non-LTE Line Abundances

“…All levels in the atom are coupled via an extensive linelist of radiative bound-bound (extracted from VALD3 2 database) and photoionization transitions (extracted from the NORAD 3 database). A detailed description of the iron model atom can be found in Ezzeddine et al (2016b).…”

“…This enhances the role that inelastic hydrogen collision rates can play for a NLTE abundance determination. Recently, it has been shown that the chargetransfer (i.e., ion-pair production 4 ) processes can domi-nate over excitation processes (Osorio et al 2015;Osorio & Barklem 2016;Ezzeddine et al 2016b). Cross-section calculations for Li+H and Na+H (Barklem et al 2010), for example, have shown that the largest cross sections for excitation are small compared with those for ion-pair production from certain energy states.…”

“…A new semi-empirical quantum fitting method (QFM) to estimate the hydrogen collision rates, including the ion-pair production process, was developed by Ezzeddine et al (2016b). This method is based on a general fitting recipe deduced from the quantum collision rates of several elements (Be, Na, Mg, Al, Si and Ca) and then applied to Fe.…”

“…To obtain more accurate collision rates, a new semiempirical recipe was proposed by Ezzeddine et al (2016b) who developed a quantum fitting method (QFM) to estimate the hydrogen collision rates involved in iron line formation and other elements in the lack of available published quantum rates. Transition energies dependent recipes for charge transfer and excitation rates were introduced to determine more reliable Fe abundances.…”

Excitation and charge transfer in low-energy hydrogen atom collisions with neutral iron

“…∼ 30 to 50 au, corresponding to crossings about 1 eV (∼ 0.04 au) below the asymptotic limit for the ionic state. Ezzeddine et al (2016) have exploited this regular behaviour by fitting the data for simple atoms to permit extrapolation to complex atoms such as Fe. The same structure for the ion-pair production processes is seen in Fig.…”