Context. Magnesium is an element of significant astrophysical importance, often traced in late-type stars using lines of neutral magnesium, which is expected to be subject to departures from local thermodynamic equilibrium (LTE). The importance of Mg, together with the unique range of spectral features in late-type stars probing different parts of the atom, as well as its relative simplicity from an atomic physics point of view, makes it a prime target and test bed for detailed ab initio non-LTE modelling in stellar atmospheres. Previous non-LTE modelling of spectral line formation has, however, been subject to uncertainties due to lack of accurate data for inelastic collisions with electrons and hydrogen atoms. Aims. In this paper we build and test a Mg model atom for spectral line formation in late-type stars with new or recent inelastic collision data and no associated free parameters. We aim to reduce these uncertainties and thereby improve the accuracy of Mg non-LTE modelling in late-type stars.Methods. For the low-lying states of Mg i, electron collision data were calculated using the R-matrix method. Hydrogen collision data, including charge transfer processes, were taken from recent calculations by some of us. Calculations for collisional broadening by neutral hydrogen were also performed where data were missing. These calculations, together with data from the literature, were used to build a model atom. This model was then employed in the context of standard non-LTE modelling in 1D (including average 3D) model atmospheres in a small set of stellar atmosphere models. First, the modelling was tested by comparisons with observed spectra of benchmark stars with well-known parameters. Second, the spectral line behaviour and uncertainties were explored by extensive experiments in which sets of collisional data were changed or removed. Results. The modelled spectra agree well with observed spectra from benchmark stars, showing much better agreement with line profile shapes than with LTE modelling. The line-to-line scatter in the derived abundances shows some improvements compared to LTE (where the cores of strong lines must often be ignored), particularly when coupled with averaged 3D models. The observed Mg emission features at 7 and 12 μm in the spectra of the Sun and Arcturus, which are sensitive to the collision data, are reasonably well reproduced. Charge transfer with H is generally important as a thermalising mechanism in dwarfs, but less so in giants. Excitation due to collisions with H is found to be quite important in both giants and dwarfs. The R-matrix calculations for electron collisions also lead to significant differences compared to when approximate formulas are employed. The modelling predicts non-LTE abundance corrections ΔA(Mg) NLTE−LTE in dwarfs, both solar metallicity and metal-poor, to be very small (of order 0.01 dex), even smaller than found in previous studies. In giants, corrections vary greatly between lines, but can be as large as 0.4 dex. Conclusions. Our results emphasise ...

We report full quantum scattering calculations for low-energy near-threshold inelastic cross sections in Mg + H and Mg + + H − collisions. The calculations include all transitions between the eight lowest adiabatic MgH( 2 + ) molecular states, with the uppermost of those diabatically extended to the ionic molecular state in the asymptotic region. This allows us to treat the excitation processes between the seven lowest atomic states of magnesium in collisions with hydrogen atoms, as well as the ion-pair production and the mutual neutralization processes. The collision energy range is from threshold up to 10 eV. These results are important for astrophysical modeling of spectra in stellar atmospheres. The processes in question are carefully examined and several process mechanisms are found. Some mechanisms are determined by interactions between ionic and covalent configurations at relatively large internuclear distances, while others are based on short-range nonadiabatic regions due to interactions between covalent configurations.

The influence of inelastic hydrogen atom collisions on non-LTE spectral line formation has been, and remains to be, a significant source of uncertainty for stellar abundance analyses, due to the difficulty in obtaining accurate data for low-energy atomic collisions either experimentally or theoretically. For lack of a better alternative, the classical "Drawin formula" is often used. Over recent decades, our understanding of these collisions has improved markedly, predominantly through a number of detailed quantum mechanical calculations. In this paper, the Drawin formula is compared with the quantum mechanical calculations both in terms of the underlying physics and the resulting rate coefficients. It is shown that the Drawin formula does not contain the essential physics behind direct excitation by H atom collisions, the important physical mechanism being quantum mechanical in character. Quantitatively, the Drawin formula compares poorly with the results of the available quantum mechanical calculations, usually significantly overestimating the collision rates by amounts that vary markedly between transitions.

Rate coefficients for inelastic Mg+H collisions are calculated for all transitions between the lowest seven levels and the ionic state (charge transfer), namely Mg(3s 2 1 S, 3s3p 3 P, 3s3p 1 P, 3s4s 3 S, 3s4s 1 S, 3s3d 1 D, 3s4p 3 P)+H(1s) and Mg + (3s 2 S)+H − . The rate coefficients are based on cross-sections from full quantum scattering calculations, which are themselves based on detailed quantum chemical calculations for the MgH molecule. The data are needed for non-LTE applications in cool astrophysical environments, especially cool stellar atmospheres, and are presented for a temperature range of 500−8000 K. From consideration of the sensitivity of the cross-sections to various uncertainties in the calculations, most importantly input quantum chemical data and the numerical accuracy of the scattering calculations, a measure of the possible uncertainties in the rate coefficients is estimated.

Full quantum scattering calculations of cross sections for low-energy near-threshold inelastic Mg + H collisions are reported, such processes being of interest for modelling of Mg spectral lines in stellar atmospheres. The calculations are made for three transitions between the ground and two lowest excited Mg states, Mg(3s2 1S0), Mg(3s3p 3P) and Mg(3s3p 1P). The calculations are based on adiabatic potentials and nonadiabatic couplings for the three low-lying 2Σ+ and the first two 2Π states, calculated using large active spaces and basis sets. Non-adiabatic regions associated with radial couplings at avoided ionic crossings in the 2Σ+ molecular potentials are found to be the main mechanism for excitation. Cross sections of similar order of magnitude to those obtained in Li + H and Na + H collisions are found. This, together with the fact that the same mechanism is important, suggests that as has been found earlier for Li and Na, processes such as ion pair production may be important in astrophysical modelling of Mg, and motivates continued study of this system including all states up to and including the ionic limit.

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Context. Departures from local thermodynamic equilibrium (LTE) distort the calcium abundance derived from stellar spectra in various ways, depending on the lines used and the stellar atmospheric parameters. The collection of atomic data adopted in non-LTE (NLTE) calculations must be sufficiently complete and accurate. Aims. We derive NLTE abundances from high-quality observations and reliable stellar parameters using a model atom built afresh for this work, and check the consistency of our results over a wide wavelength range with transitions of atomic and singly ionised calcium.Methods. We built and tested Ca i and Ca ii model atoms with state-of-the-art radiative and collisional data, and tested their performance deriving the Ca abundance in three benchmark stars: Procyon, the Sun, and Arcturus. We have excellent-quality observations and accurate stellar parameters for these stars. Two methods to derive the LTE / NLTE abundances were used and compared. The LTE / NLTE centre-to-limb variation (CLV) of Ca lines in the Sun was also investigated. Results. The two methods used give similar results in all three stars. Several discrepancies found in LTE do not appear in our NLTE results; in particular the agreement between abundances in the visual and infra-red (IR) and the Ca i and Ca ii ionisation balance is improved overall, although substantial line-to-line scatter remains. The CLV of the calcium lines around 6165 Å can be partially reproduced. We suspect differences between our modelling and CLV results are due to inhomogeneities in the atmosphere that require 3D modelling.

The accurate highly correlated ab initio calculations for ten low lying covalent Σ+2 states of CaH molecule, and one ionic CaH state, are performed using large active space and extended basis set, with special attention to the long-range (6-20 Å) region where a number of avoided crossings between ionic and covalent states occur. These states are further transformed to a diabatic representation using a numerical diabatization scheme based on the minimization of derivative coupling. This results in a smooth diabatic Hamiltonian which can be easily fit to an analytic form. The diagonal elements of the diabatic potentials were then empirically corrected to reproduce experimental dissociation energies. Though the emphasis is on the asymptotic region, the obtained spectroscopic constants are in good agreement with available experimental and theoretical data. The resulting analytical Hamiltonian, after back transformation to adiabatic representation, is used to obtain cross sections for different inelastic processes using both the multichannel and the branching probability current approaches. It is shown that while for most intense transitions both approaches provide very close results, the multichannel approach underestimates the cross sections of weak transitions, as a consequence of the short-range avoided crossings that are accounted for only in the branching probability current method.