No Arabic abstract
This paper forms the second part of our study on how the neglect of NLTE conditions in the formation of Fe I 6301.5 A and the 6302.5 A lines influences the atmosphere obtained by inverting their profiles in LTE. The main cause of NLTE effects is the line opacity deficit due to the excess ionization of the Fe I atoms by the UV photons in the Sun. In the first paper, the above photospheric lines were assumed to have formed in 1DNLTE and the effects of horizontal radiation transfer (RT) were neglected. In the present paper, the iron lines are computed in 3DNLTE. We investigate the influence of horizontal RT on the inverted atmosphere and how it can enhance or reduce the errors due to the neglect of 1DNLTE effects. The iron lines are computed in LTE, 1DNLTE and 3DNLTE. They all are inverted using an LTE inversion code. The atmosphere from the inversion of LTE profiles is taken as the reference model. The test atmospheres from the inversion of 1DNLTE and 3DNLTE profiles are compared with it. The differences between models are analysed and correspondingly attributed to NLTE and 3D effects. The effects of horizontal RT are evident in regions surrounded by strong horizontal gradients in temperature. In some regions, the 3D effects enhance the 1DNLTE effects while in some, they weaken. The errors due to neglecting the 3D effects are less than 5% in temperature while the errors are mostly less than 20% in both velocity and magnetic field strength. These errors are found to survive spatial and spectral degradation. The neglect of horizontal RT is found to introduce errors in the derived atmosphere. How large the errors are depends on how strong the local horizontal gradients are in temperature. Compared to the 1DNLTE effect, the 3D effects are more localised to specific regions in the atmosphere and overall less dominant.
Early magnetographic observations indicated that magnetic field in the solar photosphere has unresolved small-scale structure. Near-infrared and optical data with extremely high spatial resolution show that these structures have scales of few tens of kilometres, which are not resolved in the majority of solar observations. The goal of this study is to establish the effect of unresolved photospheric magnetic field structure on Stokes profiles observed with relatively low spatial resolution. Ultimately, we aim to develop methods for fast estimation of the photospheric magnetic filling factor and line-of-sight gradient of the photospheric magnetic field, which can be applied to large observational data sets. We exploit 3D MHD models of magneto-convection developed using MURAM code. Corresponding profiles of Fe I 6301.5 and 6302.5 $mathrm{AA}$ spectral lines are calculated using NICOLE radiative transfer code. The resulting I and V Stokes [x,y,$lambda$] cubes with reduced spatial resolution of 150 km are used to calculate magnetic field values as they would be obtained in observations with Hinode/SOT or SDO/HMI. Three different methods of the magnetic filling factor estimation are considered: the magnetic line ratio method, Stokes V width method and a simple statistical method. We find that the statistical method and the Stokes V width method are sufficiently reliable for fast filling factor estimations. Furthermore, we find that Stokes $Ipm V$ bisector splitting gradient can be used for fast estimation of line-of-sight gradient of the photospheric magnetic field.
We checked consistency between the copper abundance derived in six metal-poor stars using UV Cu II lines (which are assumed to form in LTE) and UV Cu I lines (treated in NLTE). Our program stars cover the atmosphere parameters which are typical for intermediate temperature dwarfs (effective temperature is in the range from approximately 5800 to 6100 K, surface garvity is from 3.6 to 4.5, metallicity is from about -1 to -2.6 dex). We obtained a good agreement between abundance from these two sets of the lines, and this testifies about reliability of our NLTE copper atomic model. We confirmed that no underabundace of this element is seen at low metallicities (the mean [Cu/Fe] value is about -0.2 dex, while as it follows from the previous LTE studies copper behaves as a secondary element and [Cu/Fe] ratio in the range of [Fe/H from -2 to -3 dex should be about -1 dex). According to our NLTE data the copper behaves as a primary element at low metallicity regime. We also conclude that our new NLTE copper abundance in metal-poor stars requires significant reconsideration of this element yields in the explosive nucleosynthesis.
We present an investigation of the velocity fields in early to late M-type star hydrodynamic models, and we simulate their influence on FeH molecular line shapes. The M star model parameters range between log g of 3.0 - 5.0 and Teff of 2500 K and 4000 K. Our aim is to characterize the Teff- and log g -dependence of the velocity fields and express them in terms of micro- and macro-turbulent velocities in the one dimensional sense. We present also a direct comparison between 3D hydrodynamical velocity fields and 1D turbulent velocities. The velocity fields strongly affect the line shapes of FeH, and it is our goal to give a rough estimate for the log g and Teff parameter range in which 3D spectral synthesis is necessary and where 1D synthesis suffices. In order to calculate M-star structure models we employ the 3D radiative-hydrodynamics (RHD) code CO5BOLD. The spectral synthesis on these models is performed with the line synthesis code LINFOR3D. We describe the 3D velocity fields in terms of a Gaussian standard deviation and project them onto the line of sight to include geometrical and limb-darkening effects. The micro- and macro-turbulent velocities are determined with the Curve of Growth method and convolution with a Gaussian velocity profile, respectively. To characterize the log g and Teff dependence of FeH lines, the equivalent width, line width, and line depth are regarded. The velocity fields in M-stars strongly depend on log g and Teff. They become stronger with decreasing log g and increasing Teff.
The copper abundances of 29 metal-poor stars are determined based on the high resolution, high signal-to-noise ratio spectra from the UVES spectragraph at the ESO VLT telescope. Our sample consists of the stars of the Galactic halo, thick- and thin-disk with [Fe/H] ranging from ~ -3.2 to ~ 0.0 dex. The non-local thermodynamic equilibrium (NLTE) effects of Cu I lines are investigated, and line formation calculations are presented for an atomic model of copper including 97 terms and 1089 line transitions. We adopted the recently calculated photo-ionization cross-sections of Cu I, and investigated the hydrogen collision by comparing the theoretical and observed line profiles of our sample stars. The copper abundances are derived for both local thermodynamic equilibrium (LTE) and NLTE based on the spectrum synthesis methods. Our results show that the NLTE effects for Cu I lines are important for metal-poor stars, in particular for very metal-poor stars, and these effects depend on the metallicity. For very metal-poor stars, the NLTE abundance correction reaches as large as ~ +0.5 dex compared to standard LTE calculations. Our results indicate that [Cu/Fe] is under-abundant for metal-poor stars (~ -0.5 dex) when the NLTE effects are included.
The Einstein spontaneous rates (A-coefficients) of Fe^+ lines have been computed by several authors, with results that differ from each other up to 40%. Consequently, models for line emissivities suffer from uncertainties which in turn affect the determination of the physical conditions at the base of line excitation. We provide an empirical determination of the A-coefficient ratios of bright [Fe II] lines, which would represent both a valid benchmark for theoretical computations and a reference for the physical interpretation of the observed lines. With the ESO-VLT X-shooter instrument between 3,000 A, and 24,700 A, we obtained a spectrum of the bright Herbig-Haro object HH1. We detect around 100 [Fe II] lines, some of which with a signal-to-noise ratio > 100. Among these latter, we selected those emitted by the same level, whose de-reddened intensity ratio is a direct function of the Einstein A-coefficient ratios. From the same X-shooter spectrum, we got an accurate estimate of the extinction toward HH1 through intensity ratios of atomic species, HI, recombination lines and H_2 ro-vibrational transitions. We provide seven reliable A-ooefficient ratios between bright [Fe II] lines, which are compared with the literature determinations. In particular, the A-coefficient ratios involving the brightest near-infrared lines (12570A/16440A and 13209A/16440A) are better in agreement with the predictions by Quinet et al. (1996) Relativistic Hartree-Fock model. However, none of the theoretical models predicts A-coefficient ratios in agreement with all our determinations. We also show that literature data of near-infrared intensity ratios better agree with our determinations than with theoretical expectations.