Non-LTE radiative transfer in cool stars. Theory and applications to the abundance analysis for 24 chemical elements

The interpretation of observed spectra of stars in terms of fundamental stellar properties is a key problem in astrophysics. For FGK-type stars, the radiative transfer models are often computed using the assumption of local thermodynamic equilibrium (LTE). Its validity is often questionable and needs to be supported by detailed studies, which build upon the consistent framework of non-LTE. In this review, we outline the theory of non-LTE. The processes causing departures from LTE are introduced qualitatively by their physical interpretation, as well as quantitatively by their impact on the models of stellar spectra and element abundances. We also compile and analyse the most recent results from the literature. In particular, we examine the non-LTE effects for 24 chemical elements for six late-studied FGK-type stars.Comment: 19 pages, accepted for publication as a chapter in "Determination of Atmospheric Parameters of B, A, F and G Type Stars", Springer (2014), eds. E. Niemczura, B. Smalley, W. Pyc

Non-LTE aluminium abundances in late-type stars

Aluminium plays a key role in studies of the chemical enrichment of the Galaxy and of globular clusters. However, strong deviations from LTE (non-LTE) are known to significantly affect the inferred abundances in giant and metal-poor stars. We present NLTE modeling of aluminium using recent and accurate atomic data, in particular utilizing new transition rates for collisions with hydrogen atoms, without the need for any astrophysically calibrated parameters. For the first time, we perform 3D NLTE modeling of aluminium lines in the solar spectrum. We also compute and make available extensive grids of abundance corrections for lines in the optical and near-infrared using one-dimensional model atmospheres, and apply grids of precomputed departure coefficients to direct line synthesis for a set of benchmark stars with accurately known stellar parameters. Our 3D NLTE modeling of the solar spectrum reproduces observed center-to-limb variations in the solar spectrum of the 7835 {\AA} line as well as the mid-infrared photospheric emission line at 12.33 micron. We infer a 3D NLTE solar photospheric abundance of A(Al) = 6.43+-0.03, in exact agreement with the meteoritic abundance. We find that abundance corrections vary rapidly with stellar parameters; for the 3961 {\AA} resonance line, corrections are positive and may be as large as +1 dex, while corrections for subordinate lines generally have positive sign for warm stars but negative for cool stars. Our modeling reproduces the observed line profiles of benchmark K-giants, and we find abundance corrections as large as -0.3 dex for Arcturus. Our analyses of four metal-poor benchmark stars yield consistent abundances between the 3961 {\AA} resonance line and lines in the UV, optical and near-infrared regions. Finally, we discuss implications for the galactic chemical evolution of aluminium.Comment: 20 pages, 15 figures. Accepted for publication in A&

Atomic Diffusion and Mixing in Old Stars V: A deeper look into the Globular Cluster NGC 6752

Abundance trends in heavier elements with evolutionary phase have been shown to exist in the globular cluster NGC 6752 [Fe/H]=-1.6. These trends are a result of atomic diffusion and additional (non-convective) mixing. Studying such trends can provide us with important constraints on the extent to which diffusion modifies the internal structure and surface abundances of solar-type, metal-poor stars. Taking advantage of a larger data sample, we investigate the reality and the size of these abundance trends and address questions and potential biases associated with the various stellar populations that make up NGC6752. Based on uvby Str\"omgren photometry, we are able to separate three stellar populations in NGC 6752 along the evolutionary sequence from the base of the red giant branch down to the turnoff point. We find weak systematic abundance trends with evolutionary phase for Ca, Ti, and Fe which are best explained by stellar-structure models including atomic diffusion with efficient additional mixing. We derive a new value for the initial lithium abundance of NGC 6752 after correcting for the effect of atomic diffusion and additional mixing which falls slightly below the predicted standard BBN value. We find three stellar populations by combining photometric and spectroscopic data of 194 stars in the globular cluster NGC 6752. Abundance trends for groups of elements, differently affected by atomic diffusion and additional mixing, are identified. Although the statistical significance of the individual trends is weak, they all support the notion that atomic diffusion is operational along the evolutionary sequence of NGC 6752.Comment: 15 pages, 11 figures, 2 online table

Dynamics of passing-stars-perturbed binary star systems

In this work, we investigate the dynamical effects of a sequence of close encounters over 200 Myr varying in the interval of 10000 -- 100000 au between a binary star system and passing stars with masses ranging from 0.1$M_{\odot}$ to 10$M_{\odot}$. We focus on binaries consisting of two Sun-like stars with various orbital separations $a_{\scriptscriptstyle 0}$ from 50 au to 200 au initially on circular-planar orbits. We treat the problem statistically since each sequence is cloned 1000 times. Our study shows that orbits of binaries initially at $a_{\scriptscriptstyle 0}$ = 50 au will slightly be perturbed by each close encounter and exhibit a small deviation in eccentricity (+0.03) and in periapsis distance (+1 and -2 au) around the mean value. However increasing $a_{\scriptscriptstyle 0}$ will drastically increase these variances: up to +0.45 in eccentricity and between +63 au and -106 au in periapsis, leading to a higher rate of disrupted binaries up to 50% after the sequence of close encounters. Even though the secondary star can remain bound to the primary, $\sim$20% of the final orbits will have inclinations greater than 10$^{\circ}$. As planetary formation already takes place when stars are still members of their birth cluster, we show that the variances in eccentricity and periapsis distance of Jupiter- and Saturn-like planets will inversely decrease with $a_{\scriptscriptstyle 0}$ after successive fly-bys. This leads to higher ejection rate at $a_{\scriptscriptstyle 0}$ = 50 au but to a higher extent for Saturn-likes (60%) as those planets' apoapsis distances cross the critical stability distance for such binary separation.Comment: Accepted for publication (MNRAS

A method for identifying metal-poor stars with Gaia BP/RP spectra

Context. The study of the oldest and most metal-poor stars in our Galaxy promotes our understanding of the Galactic chemical evolution and the beginning of Galaxy and star formation. However, they are notoriously difficult to find, with only five stars at $\mathrm{[Fe/H]<-5.0}$ having been detected to date. Thus, the spectrophotometric data of 219 million sources which became available in the third Gaia Data Release comprise a very promising dataset for the identification of metal-poor stars. Aims. We want to use the low-resolution Gaia Blue Photometer / Red Photometer (BP/RP) spectra to identify metal-poor stars. Our primary aspiration is to help populate the poorly constrained tail of the metallicity distribution function of the stellar halo of the Galaxy. Methods. We developed a metal-poor candidate selection method based on flux ratios from the BP/RP Gaia spectra, using simulated synthetic spectra. Results. We found a relation between the relative iron abundance and the flux ratio of the Ca H \& K region to that of the $\mathrm{H\beta}$ line. This relation is temperature and surface gravity dependent, and it holds for stars with $\mathrm{4800\,K \leq T_{eff}\leq6300\,K}$. We applied it to noisy simulated synthetic spectra and inferred $\mathrm{[Fe/H]}$ with an uncertainty of $\sigma_{\mathrm{[Fe/H]}}\lessapprox0.65$ dex for $\mathrm{-3\leq[Fe/H]}\leq 0.5$ and G=15-17mag, which is sufficient to identify stars at $\mathrm{[Fe/H]<-2.0 }$ reliably. We predict that by selecting stars with inferred $\mathrm{[Fe/H]}\leq-2.5$ dex, we can retrieve 80% of the stars with $\mathrm{[Fe/H]}\leq-3$ and have a success rate of about 50%, that is one in two stars we select would have $\mathrm{[Fe/H]}\leq-3$. We do not take into account the effect of reddening, so our method should only be applied to stars which are located in regions of low extinction.Comment: 11 pages, 15 figures, to be published in A&

Non-LTE aluminium abundances in late-type stars

Aims. Aluminium plays a key role in studies of the chemical enrichment of the Galaxy and of globular clusters. However, strong deviations from LTE (non-LTE) are known to significantly affect the inferred abundances in giant and metal-poor stars. Methods. We present non-local thermodynamic equilibrium (NLTE) modeling of aluminium using recent and accurate atomic data, in particular utilizing new transition rates for collisions with hydrogen atoms, without the need for any astrophysically calibrated parameters. For the first time, we perform 3D NLTE modeling of aluminium lines in the solar spectrum. We also compute and make available extensive grids of abundance corrections for lines in the optical and near-infrared using one-dimensional model atmospheres, and apply grids of precomputed departure coefficients to direct line synthesis for a set of benchmark stars with accurately known stellar parameters. Results. Our 3D NLTE modeling of the solar spectrum reproduces observed center-to-limb variations in the solar spectrum of the 7835 Å line as well as the mid-infrared photospheric emission line at 12.33 μm. We infer a 3D NLTE solar photospheric abundance of A(Al) = 6.43 ± 0.03, in exact agreement with the meteoritic abundance. We find that abundance corrections vary rapidly with stellar parameters; for the 3961 Å resonance line, corrections are positive and may be as large as +1 dex, while corrections for subordinate lines generally have positive sign for warm stars but negative for cool stars. Our modeling reproduces the observed line profiles of benchmark K-giants, and we find abundance corrections as large as −0.3 dex for Arcturus. Our analyses of four metal-poor benchmark stars yield consistent abundances between the 3961 Å resonance line and lines in the UV, optical and near-infrared regions. Finally, we discuss implications for the galactic chemical evolution of aluminium.T.N. acknowledges support from the Swedish National Space Board (Rymdstyrelsen), and funding from Australian Research Council (grant DP150100250). K.L. acknowledges funds from the Alexander von Humboldt Foundation in the framework of the Sofja Kovalevskaja Award endowed by the Federal Ministry of Education and Research as well as funds from the Swedish Research Council (Grant No. 2015-00415_3) and Marie Sklodowska Curie Actions (Cofund Project INCA 600398). The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at High Performance Computing Center North (HPC2N) under projects SNIC2015/1-309 and SNIC2016/1-400

A high-resolution spectroscopic search for multiple populations in the 2 Gyr old cluster NGC 1846

We present detailed C, O, Na, Mg, Si, Ca, Ti, V, Fe, Zr, Ba, and Eu abundance measurements for 20 red giant branch (RGB) stars in the LMC star cluster NGC 1846 ([Fe/H] = -0.59). This cluster is 1.95 Gyr old and lies just below the supposed lower age limit (2 Gyr) for the presence of multiple populations in massive star clusters. Our measurements are based on high and low-resolution VLT/FLAMES spectra combined with photometric data from HST. Corrections for non-local thermodynamic equilibrium effects are also included for O, Na, Mg, Si, Ca, Fe and Ba. Our results show that there is no evidence for multiple populations in this cluster based on the lack of any intrinsic star-to-star spread in the abundances of Na and O: we place 95 \% confidence limits on the intrinsic dispersion for these elements of $\leq 0.07$ and $\leq 0.09$ dex, respectively. However, we do detect a significant spread in the carbon abundances, indicating varying evolutionary mixing occurring on the RGB that increases with luminosity. Overall, the general abundance patterns for NGC 1846 are similar to those seen in previous studies of intermediate-age LMC star clusters and field stars

The destruction of an Oort Cloud in a rich stellar cluster

Context. It is possible that the formation of the Oort Cloud dates back to the earliest epochs of solar system history. At that time, the Sun was almost certainly a member of the stellar cluster where it was born. Since the solar birth cluster is likely to have been massive (103−104ℳ⊙), and therefore long-lived, an issue concerns the survival of such a primordial Oort Cloud. Aims. We have investigated this issue by simulating the orbital evolution of Oort Cloud comets for several hundred Myr, assuming the Sun to start its life as a typical member of such a massive cluster. Methods. We have devised a synthetic representation of the relevant dynamics, where the cluster potential is represented by a King model, and about 20 close encounters with individual cluster stars are selected and integrated based on the solar orbit and the cluster structure. Thousands of individual simulations are made, each including 3000 comets with orbits with three different initial semi-major axes. Results. Practically the entire initial Oort Cloud is found to be lost for our choice of semi-major axes (5000−20 000 au), independent of the cluster mass, although the chance of survival is better for the smaller cluster, since in a certain fraction of the simulations the Sun orbits at relatively safe distances from the dense cluster centre. Conclusions. For the range of birth cluster sizes that we investigate, a primordial Oort Cloud will likely survive only as a small inner core with semi-major axes ≲3000 au. Such a population of comets would be inert to orbital diffusion into an outer halo and subsequent injection into observable orbits. Some mechanism is therefore needed to accomplish this transfer, in case the Oort Cloud is primordial and the birth cluster did not have a low mass. From this point of view, our results lend some support to a delayed formation of the Oort Cloud, that occurred after the Sun had left its birth cluste

3D Stagger model atmospheres with FreeEOS I. Exploring the impact of microphysics on the Sun

Three-dimensional radiation-hydrodynamics (3D RHD) simulations of stellar surface convection provide valuable insights into many problems in solar and stellar physics. However, almost all 3D near-surface convection simulations to date are based on solar-scaled chemical compositions, which limit their application on stars with peculiar abundance patterns. To overcome this difficulty, we implement the robust and widely-used FreeEOS equation of state and our Blue opacity package into the Stagger 3D radiation-magnetohydrodynamics code. We present a new 3D RHD model of the solar atmosphere, and demonstrate that the mean stratification as well as the distributions of key physical quantities are in good agreement with those of the latest Stagger solar model atmosphere. The new model is further validated by comparing against solar observations. The new model atmospheres reproduce the observed flux spectrum, continuum centre-to-limb variation, and hydrogen line profiles at a satisfactory level, thereby confirming the realism of the model and the underlying input physics. These implementations open the prospect for studying other stars with different $\alpha$-element abundance, carbon-enhanced metal-poor stars and population II stars with peculiar chemical compositions using 3D Stagger model atmospheres.Comment: 24 pages, 20 figures, accepted for publication in A&

The relationship between photometric and spectroscopic oscillation amplitudes from 3D stellar atmosphere simulations

We establish a quantitative relationship between photometric and spectroscopic detections of solar-like oscillations using ab initio, three-dimensional (3D), hydrodynamical numerical simulations of stellar atmospheres. We present a theoretical derivation as proof of concept for our method. We perform realistic spectral line formation calculations to quantify the ratio between luminosity and radial velocity amplitude for two case studies: the Sun and the red giant $\epsilon$ Tau. Luminosity amplitudes are computed based on the bolometric flux predicted by 3D simulations with granulation background modelled the same way as asteroseismic observations. Radial velocity amplitudes are determined from the wavelength shift of synthesized spectral lines with methods closely resembling those used in BiSON and SONG observations. Consequently, the theoretical luminosity to radial velocity amplitude ratios are directly comparable with corresponding observations. For the Sun, we predict theoretical ratios of 21.0 and 23.7 ppm/[m/s] from BiSON and SONG respectively, in good agreement with observations 19.1 and 21.6 ppm/[m/s]. For $\epsilon$ Tau, we predict K2 and SONG ratios of 48.4 ppm/[m/s], again in good agreement with observations 42.2 ppm/[m/s], and much improved over the result from conventional empirical scaling relations which gives 23.2 ppm/[m/s]. This study thus opens the path towards a quantitative understanding of solar-like oscillations, via detailed modelling of 3D stellar atmospheres.Comment: 16 pages, 7 figures, accepted for publication in MNRA