Opacity Distribution Functions Research Articles

Hydrodynamic simulations of cool stellar atmospheres with MANCHA

Three-dimensional time-dependent simulations of stellar atmospheres are essential to study the surface of stars other than the Sun. These simulations require the opacity binning method to reduce the computational cost of solving the radiative transfer equation down to viable limits. The method depends on a series of free parameters, among which the location and number of bins are key to set the accuracy of the resulting opacity. Our aim is to test how different binning strategies previously studied in one-dimensional models perform in three-dimensional radiative hydrodynamic simulations of stellar atmospheres. Realistic box-in-a-star simulations of the near-surface convection and photosphere of three spectral types (G2V, K0V, and M2V) were run with the MANCHA $-bins. These rates were compared with the ones computed with opacity distribution functions. Then, stellar simulations were run with grey, four-bin, and 18-bin opacities to see the impact of the opacity setup on the mean stratification of the temperature and its gradient after time evolution. The simulations of main sequence cool stars with the MANCHA code are consistent with those in the literature. For the three stars, the radiative energy exchange rates computed with 18 bins are remarkably close to the ones computed with the opacity distribution functions. The rates computed with four bins are similar to the rates computed with 18 bins, and present a significant improvement with respect to the rates computed with the Rosseland opacity, especially above the stellar surface. The Rosseland mean can reproduce the proper rates in sub-surface layers, but produces large errors for the atmospheric layers of the G2V and K0V stars. In the case of the M2V star, the Rosseland mean fails even in sub-surface layers, owing to the importance of the contribution from molecular lines in the opacity, underestimated by the harmonic mean. Similar conclusions are reached studying the mean stratification of the temperature and its gradient after time evolution.

Opacity for realistic 3D MHD simulations of cool stellar atmospheres

Context. Realistic three-dimensional time-dependent simulations of stellar near-surface convection employ the opacity binning method for the efficient and accurate computation of the radiative energy exchange. The method provides several orders of magnitude of speedup, but its implementation includes a number of free parameters. Aims. Our aim is to evaluate the accuracy of the opacity binning method as a function of the choice of these free parameters. Methods. The monochromatic opacities computed with the SYNSPEC code were used to construct opacity distribution function (ODF) that was then verified through detailed comparison with the results of the ATLAS code. The opacity binning method was implemented with the SYNSPEC opacities for four representative cool main-sequence stellar spectral types (F3V, G2V, K0V, and M2V). Results. The ODFs from SYNSPEC and ATLAS show consistent results for the opacity and bolometric radiative energy exchange rate Q in the case of the F-, G-, and K-type stars. Significant differences, coming mainly from the molecular line lists, are found for the M-type star. It is possible to optimise a small number of bins to reduce the deviation of the results coming from the opacity grouping with respect to the ODF for the F-, G-, and K-type stars. In the case of the M-type star, the inclusion of splitting in wavelength is needed in the grouping to get similar results, with a subsequent increase in computing time. In the limit of a large number of bins, the deviation for all the binning configurations tested saturates and the results do not converge to the ODF solution. Due to this saturation, the Q rate cannot be improved by increasing the number of bins to more than about 20 bins. The more effective strategy is to select the optimal location of fewer bins.

MPS-ATLAS: A fast all-in-one code for synthesising stellar spectra

Context. Stellar spectral synthesis is essential for various applications, ranging from determining stellar parameters to comprehensive stellar variability calculations. New observational resources as well as advanced stellar atmosphere modelling, taking three dimensional effects from radiative magnetohydrodynamics calculations into account, require a more efficient radiative transfer. Aims. For accurate, fast and flexible calculations of opacity distribution functions (ODFs), stellar atmospheres, and stellar spectra, we developed an efficient code building on the well-established ATLAS9 code. The new code also paves the way for easy and fast access to different elemental compositions in stellar calculations. Methods. For the generation of ODF tables, we further developed the well-established DFSYNTHE code by implementing additional functionality and a speed-up by employing a parallel computation scheme. In addition, the line lists used can be changed from Kurucz’s recent lists. In particular, we implemented the VALD3 line list. Results. A new code, the Merged Parallelised Simplified ATLAS, is presented. It combines the efficient generation of ODF, atmosphere modelling, and spectral synthesis in local thermodynamic equilibrium, therefore being an all-in-one code. This all-in-one code provides more numerical functionality and is substantially faster compared to other available codes. The fully portable MPS-ATLAS code is validated against previous ATLAS9 calculations, the PHOENIX code calculations, and high-quality observations.

Radiative Transfer with Opacity Distribution Functions: Application to Narrowband Filters

Abstract Modeling of stellar radiative intensities in various spectral passbands plays an important role in stellar physics. At the same time, direct calculation of the high-resolution spectrum and then integration of it over the given spectral passband is computationally demanding due to the vast number of atomic and molecular lines. This is particularly so when employing three-dimensional (3D) models of stellar atmospheres. To accelerate the calculations, one can employ approximate methods, e.g., the use of opacity distribution functions (ODFs). Generally, ODFs provide a good approximation of traditional spectral synthesis, i.e., computation of intensities through filters with strictly rectangular transmission functions. However, their performance strongly deteriorates when the filter transmission noticeably changes within its passband, which is the case for almost all filters routinely used in stellar physics. In this context, the aims of this paper are (a) to generalize the ODFs method for calculating intensities through filters with arbitrary transmission functions, and (b) to study the performance of the standard and generalized ODFs methods for calculating intensities emergent from 3D models of stellar atmospheres. For this purpose we use the newly developed MPS-ATLAS radiative transfer code to compute intensities emergent from 3D cubes simulated with the radiative magnetohydrodynamics code MURaM. The calculations are performed in the 1.5D regime, i.e., along many parallel rays passing through the simulated cube. We demonstrate that the generalized ODFs method allows accurate and fast syntheses of spectral intensities and their center-to-limb variations.

Opacity distribution functions for stellar spectra synthesis

Context. Stellar spectra synthesis is essential for the characterization of potential planetary hosts. In addition, comprehensive stellar variability calculations with fast radiative transfer are needed to disentangle planetary transits from stellar magnetically driven variability. The planet-hunting space telescopes, such as CoRoT, Kepler, and TESS, bring vast quantities of data, rekindling the interest in fast calculations of the radiative transfer. Aims. We revisit the opacity distribution functions (ODF) approach routinely applied to speed up stellar spectral synthesis. To achieve a considerable speedup relative to the state of the art, we further optimize the approach and search for the best ODF configuration. Furthermore, we generalize the ODF approach for fast calculations of flux in various filters often used in stellar observations. Methods. In a parameter-sweep fashion, we generated ODF in the spectral range from UV to IR with different setups. The most accurate ODF configuration for each spectral interval was determined. We adapted the wavelength grid based on the transmission curve for calculations of the radiative fluxes through filters before performing the normal ODF procedure. Results. Our optimum ODF configuration allows for a three-fold speedup, compared to the previously used ODF configurations. The ODF generalization to calculate fluxes through filters results in a speedup of more than two orders of magnitude.

Stellar Atmospheric Parameterization Based on Deep Learning

Deep learning is a typical learning method widely studied in the fields of machine learning, pattern recognition, and artificial intelligence. This work investigates the problem of stellar atmospheric parameterization by constructing a deep neural network with five layers, and the node number in each layer of the network is respectively 3821-500-100-50-1. The proposed scheme is verified on both the real spectra measured by the Sloan Digital Sky Survey (SDSS) and the theoretic spectra computed with the Kurucz's New Opacity Distribution Function (NEWODF) model, to make an automatic estimation for three physical parameters: the effective temperature (Teff), surface gravitational acceleration (lg g), and metallic abundance (Fe/H). The results show that the stacked autoencoder deep neural network has a better accuracy for the estimation. On the SDSS spectra, the mean absolute errors (MAEs) are 79.95 for Teff/K, 0.0058 for (lg Teff/K), 0.1706 for lg (g/(cm·s−2)), and 0.1294 dex for the [Fe/H], respectively; On the theoretic spectra, the MAEs are 15.34 for Teff/K, 0.0011 for lg (Teff/K), 0.0214 for lg(g/(cm · s−2)), and 0.0121 dex for [Fe/H], respectively.

Application of Multi-task Sparse Lasso Feature Extraction and Support Vector Machine Regression in the Stellar Atmospheric Parameterization

The multi-task learning takes the multiple tasks together to make analysis and calculation, so as to dig out the correlations among them, and therefore to improve the accuracy of the analyzed results. This kind of methods have been widely applied to the machine learning, pattern recognition, computer vision, and other related fields. This paper investigates the application of multi-task learning in estimating the stellar atmospheric parameters, including the surface temperature (Teff), surface gravitational acceleration (lg g), and chemical abundance ([Fe/H]). Firstly, the spectral features of the three stellar atmospheric parameters are extracted by using the multi-task sparse group Lasso algorithm, then the support vector machine is used to estimate the atmospheric physical parameters. The proposed scheme is evaluated on both the Sloan stellar spectra and the theoretical spectra computed from the Kurucz's New Opacity Distribution Function (NEWODF) model. The mean absolute errors (MAEs) on the Sloan spectra are: 0.0064 for lg (Teff /K), 0.1622 for lg (g/(cm · s−2)), and 0.1221 dex for [Fe/H]; the MAEs on the synthetic spectra are 0.0006 for lg (Teff /K), 0.0098 for lg (g/(cm · s−2)), and 0.0082 dex for [Fe/H]. Experimental results show that the proposed scheme has a rather high accuracy for the estimation of stellar atmospheric parameters.

Parameterizing Stellar Spectra Using Deep Neural Networks

Large-scale sky surveys are observing massive amounts of stellar spectra. The large number of stellar spectra makes it necessary to automatically parameterize spectral data, which in turn helps in statistically exploring properties related to the atmospheric parameters. This work focuses on designing an automatic scheme to estimate effective temperature (), surface gravity () and metallicity [Fe/H] from stellar spectra. A scheme based on three deep neural networks (DNNs) is proposed. This scheme consists of the following three procedures: first, the configuration of a DNN is initialized using a series of autoencoder neural networks; second, the DNN is fine-tuned using a gradient descent scheme; third, three atmospheric parameters , and [Fe/H] are estimated using the computed DNNs. The constructed DNN is a neural network with six layers (one input layer, one output layer and four hidden layers), for which the number of nodes in the six layers are 3821, 1000, 500, 100, 30 and 1, respectively. This proposed scheme was tested on both real spectra and theoretical spectra from Kurucz’s new opacity distribution function models. Test errors are measured with mean absolute errors (MAEs). The errors on real spectra from the Sloan Digital Sky Survey (SDSS) are 0.1477, 0.0048 and 0.1129 dex for , and [Fe/H] (64.85 K for ), respectively. Regarding theoretical spectra from Kurucz’s new opacity distribution function models, the MAE of the test errors are 0.0182, 0.0011 and 0.0112 dex for , and [Fe/H] (14.90 K for ), respectively.

NON-GREY RADIATIVE TRANSFER IN THE PHOTOSPHERIC CONVECTION : VALIDITY OF THE EDDINGTON APPROXIMATION

The aim of this study is to describe the physical processes taking place in the solar photosphere. Based on 3D hydrodynamic simulations including a detailed radiation transfer scheme, we investigate thermodynamic structures and radiation fields in solar surface convection. As a starting model, the initial stratification in the outer envelope calculated using the solar calibrations in the context of the standard stellar theory. When the numerical fluid becomes thermally relaxed, the thermodynamic structure of the steady-state turbulent flow was explicitly collected. Particularly, a non-grey radiative transfer incorporating the opacity distribution function was considered in our calculations. In addition, we evaluate the classical approximations that are usually adopted in the onedimensional stellar structure models. We numerically reconfirm that radiation fields are well represented by the asymptotic characteristics of the Eddington approximation (the diffusion limit and the streaming limit). However, this classical approximation underestimates radiation energy in the shallow layers near the surface, which implies that a reliable treatment of the non-grey line opacities is crucial for the accurate description of the photospheric convection phenomenon.

An autoencoder of stellar spectra and its application in automatically estimating atmospheric parameters

This article investigates the problem of estimating stellar atmospheric parameters from spectra. Feature extraction is a key procedure in estimating stellar parameters automatically. We propose a scheme for spectral feature extraction and atmospheric parameter estimation using the following three procedures: firstly, learn a set of basic structure elements (BSE) from stellar spectra using an autoencoder; secondly, extract representative features from stellar spectra based on the learned BSEs through some procedures of convolution and pooling; thirdly, estimate stellar parameters ($T_{eff}$, log$~g$, [Fe/H]) using a back-propagation (BP) network. The proposed scheme has been evaluated on both real spectra from Sloan Digital Sky Survey (SDSS)/Sloan Extension for Galactic Understanding and Exploration (SEGUE) and synthetic spectra calculated from Kurucz's new opacity distribution function (NEWODF) models. The best mean absolute errors (MAEs) are 0.0060 dex for log$~T_{eff}$, 0.1978 dex for log$~g$ and 0.1770 dex for [Fe/H] for the real spectra and 0.0004 dex for log$~T_{eff}$, 0.0145 dex for log$~g$ and 0.0070 dex for [Fe/H] for the synthetic spectra.

THE LTE SOLAR ABUNDANCE OF NEODYMIUM

We study the solar photospheric abundance of singly ionized neodymium (Nd II) using high resolution spectroscopic dataobtained by Fourier transform spectrograph (FTS). Based on the Local Thermodynamical Equilibrium (LTE) assumption,a new value of Nd abundance is derived. We succeed to select of 51 solar Nd II lines with accurate transition probabilitiesmeasured experimentally by Den Hartog et al. (2003) and with accurate damping parameters are determined from literature.Relying on atomic data of Opacity Distribution Function (ODF), we construct theoretical photospheric solar model.The meansolar photospheric abundance obtained from all 51Nd II lines is log eNd= , which is mostly similar to the meteoricvalue.

A new library of theoretical stellar spectra with scaled-solar and α-enhanced mixtures

Theoretical stellar libraries have been increasingly used to overcome limitations of empirical libraries, e.g. by exploring atmospheric parameter spaces not well represented in the latter. This work presents a new theoretical library which covers 3000 ≤ Teff ≤ 25 000 K, −0.5 ≤ log g ≤ 5.5 and 12 chemical mixtures covering 0.0017 ≤ Z ≤ 0.049 at both scaled-solar and α-enhanced compositions. This library complements previous ones by providing: (i) homogeneous computations of opacity distribution functions, models atmospheres, statistical surface fluxes and high-resolution spectra; (ii) high-resolution spectra with continua slopes corrected by the effect of predicted lines and (iii) two families of α-enhanced mixtures for each scaled-solar iron abundance, to allow studies of the α-enhancement both at ‘fixed iron’ and ‘fixed Z’ cases. Comparisons to observed spectra were performed and confirm that the synthetic spectra reproduce well the observations, although there are wavelength regions which should be still improved. The atmospheric parameter scale of the model library was compared to one derived from a widely used empirical library, and no systematic difference between the scales was found. This is particularly reassuring for methods which use synthetic spectra for deriving atmospheric parameters of stars in spectroscopic surveys.

NEW ATLAS9 AND MARCS MODEL ATMOSPHERE GRIDS FOR THE APACHE POINT OBSERVATORY GALACTIC EVOLUTION EXPERIMENT (APOGEE)

We present a new grid of model photospheres for the SDSS-III/APOGEE survey of stellar populations of the Galaxy, calculated using the ATLAS9 and MARCS codes. New opacity distribution functions were generated to calculate ATLAS9 model photospheres. MARCS models were calculated based on opacity sampling techniques. The metallicity ([M/H]) spans from -5 to 1.5 for ATLAS and -2.5 to 0.5 for MARCS models. There are three main differences with respect to previous ATLAS9 model grids: a new corrected H2O linelist, a wide range of carbon ([C/M]) and alpha element [alpha/M] variations, and solar reference abundances from Asplund et al. 2005. The added range of varying carbon and alpha element abundances also extends the previously calculated MARCS model grids. Altogether 1980 chemical compositions were used for the ATLAS9 grid, and 175 for the MARCS grid. Over 808 thousand ATLAS9 models were computed spanning temperatures from 3500K to 30000K and log g from 0 to 5, where larger temperatures only have high gravities. The MARCS models span from 3500K to 5500K, and log g from 0 to 5. All model atmospheres are publically available online.

The non-local thermodynamic equilibrium barium abundance in dwarf stars in the metallicity range of

We present the results of determination of the barium abundance considering the non-LTE (NLTE) effects in 172 dwarf stars in the metallicity range of -1< [Fe/H] <+0.3, assigned to different Galactic substructures by kinematic criteria. We used a model of the Ba atom with 31 levels of Ba I and 101 levels of Ba II. The atmosphere models for the investigated stars were computed using the ATLAS9 code modified by new opacity distribution functions. The NLTE profiles of the unblended Ba II (4554 A, 5853 A, 6496 A) were computed and then compared to those observed. The line 6141 A was also used, but with an allowance for its correlation with the iron line. The average barium abundances in the thin and thick discs are 0.01 +/- 0.08 and -0.03 +/- 0.07, respectively. The comparison to the calculations of the Galactic chemical evolution by Serminato et al. (2009) was conducted. The trend obtained for the Ba abundance versus [Fe/H] suggests a complex barium production process in the thin and thick discs.

NLTE model calculations for the solar atmosphere with an iterative treatment of opacity distribution functions

Context. Modeling the variability of the solar spectral irradiance is a key factor in understanding the Sun’s influence on the climate of the Earth. Aims. As a first step toward calculating the solar spectral irradiance variations, we reproduce the solar spectrum for the quiet Sun over a broad wavelength range with an emphasis on the UV. Methods. We introduce the radiative transfer code COSI, which calculates solar synthetic spectra under conditions of non-local thermodynamic equilibrium (NLTE). A self-consistent simultaneous solution of the radiative transfer and the statistical equation for the level populations guarantees that the correct physics is considered for wavelength regions where the assumption of local thermodynamic equilibrium (LTE) breaks down. The new concept of iterated opacity distribution functions (NLTE-ODFs) is presented, through which all line opacities are included in the NLTE radiative transfer calculation. Results. We show that it is essential to include the line opacities in the radiative transfer to reproduce the solar spectrum in the UV. Conclusions. Through the implemented scheme of NLTE-ODFs, the COSI code is successful in reproducing the spectral energy distribution of the quiet Sun.

Computation of Radiation in the Apollo AS-501 Reentry Using Opacity Distribution Functions

F ORcalculating radiation in reentry problems, the variation of the radiation with frequency must be addressed. Complex frequency dependence appears in both the source function and the opacity (or absorption coefficient, cm ) field of the radiative transfer equation (RTE). This complexity is due to a very large number of bound–bound and bound–free transitions happening in very hot, partially ionized, nonequilibrium air. Full resolution of the problem is possible but requires treatment of the radiation transport at 10 frequencies. Such computations are commonly done at NASA Ames Research Center using theNEQAIR96 code [1] to postprocess flowfield data. This fully resolved approach is infeasible in a timedependent computation due to extreme computational cost. There are many methods to reduce the cost of the solution, and we can divide these into two families [2]. One can divide the frequency spectrum into ng contiguous groups, average, and solve the transport for each group; these are the multigroup methods. Or one can reorganize the frequency spectra into nb opacity bins or pickets, according to the value of the opacity [2]. This creates disjointed sets of frequencies , the bins or pickets, with similar mean opacities. The second method is usually referenced as the opacity distribution function (ODF) method and as been in use formany years [2–6]. It is based on the key recognition that transport depends on the value of the opacity, not the value of the frequency, as stated in [7]. In its usual and sophisticated form, theODFmethod, also called themultibandmethod [8], merges both approaches by reorganizing the opacity into nb bins inside each of the ng groups. In our case, we compare the results of 1) the multiband technique in which ng n groups are defined but with a single bin nb 1 inside each group (this is simply the multigroup approach), versus 2) the multiband technique in which a single group is defined for the whole spectrum (ng 1) but which is divided into nb n bins. For simplicity and clarity, we designate this as the multibin method. The multibin method has notably been used by astrophysicists for solar computations [5,9]. The goal of this paper is to compare the multigroup andmultibinmethods for theApolloAS-501 reentry.We demonstrate that it allows solution of this reentry radiation problem with high accuracy for a very low number of bins (10 bins), an accuracy that is attained by the multigroup approach for only a very large number of groups.

Photonic superdiffusive motion in resonance line radiation trapping Partial frequency redistribution effects

The relation between the jump length probability distribution function and the spectral line profile in resonance atomic radiation trapping is considered for partial frequency redistribution (PFR) between absorbed and reemitted radiation. The single line opacity distribution function [M. N. Berberan-Santos et al., J. Chem. Phys. 125, 174308 (2006)] is generalized for PFR and used to discuss several possible redistribution mechanisms (pure Doppler broadening; combined natural and Doppler broadening; and combined Doppler, natural, and collisional broadening). It is shown that there are two coexisting scales with a different behavior: the small scale is controlled by the intricate PFR details while the large scale is essentially given by the atom rest frame redistribution asymptotic. The pure Doppler and combined natural, Doppler, and collisional broadening are characterized by both small- and large-scale superdiffusive Levy flight behaviors while the combined natural and Doppler case has an anomalous small-scale behavior but a diffusive large-scale asymptotic. The common practice of assuming complete redistribution in core radiation and frequency coherence in the wings of the spectral distribution is incompatible with the breakdown of superdiffusion in combined natural and Doppler broadening conditions.

ATLAS 9 and ATLAS 12 under GNU-Linux

AbstractWe successfully ported the suite of codes developed by R. L. Kurucz for stellar atmosphere modelling, abundance determination and synthetic spectra calculation, to run under GNU-Linux. The ported codes include ATLAS 9 and ATLAS 12 for 1-D plane-parallel atmosphere model calculation, DFSYNTHE, which calculates the Opacity Distribution Functions (ODF) to be used with ATLAS 9, WIDTH to derive chemical abundances from measured line Equivalent Widths (EW) and SYNTHE to calculate synthetic spectra. The codes input and output files remain fully compatible with the VMS versions, while the computation speed has been greatly increased due to the high efficiency of modern PC CPUs. As an example, ATLAS 9 model calculations and the computation of large (e.g. 10 nm) synthetic spectra can be executed in a matter of minutes on any mainstream laptop computer. Arbitrary chemical compositions can be used in calculations (by using ATLAS 12 through opacity sampling or by calculating ad-hoc ODFs for ATLAS 9). The large set of scripting languages existing under Linux (shell, perl, python. . .) and the availability of low-cost multiprocessor Linux architectures (such as Beowulf) makes the port highly effective to build model farms to produce large quantities of atmosphere models or synthetic spectra (e.g. for the production of integrated light synthetic spectra). The port is hosted on a dedicated website including a download section for source codes, precompiled binaries, needed data (opacities, line lists and so on), sample launch scripts and documentation.

LTE model atmospheres with new opacities

We describe an opacity sampled version of the LTE model atmosphere code STERNE with revised continuous opacities. In particular, we examine the results of replacing the existing treatment of the continuous opacities which followed the method of Kurucz (1970, SAOSR, No. 309) and Peach (1970, MNRAS, 73, 1), with photoionization cross-sections from the Opacity Project and the IRON Project, and the effects of substituting an opacity distribution function method for treating the line opacities with an opacity sampling method. In studying the application of these new models to atmospheres with hydrogen-rich and extreme chemical compositions, we find the new opacity treatment increases the temperature in the line forming region by up to 3000 K for extremely hydrogen-poor stars and up to 1250 K for hydrogen-rich stars with T eff = 30 000 K and log g = 3.00. This translates into systematically cooler effective temperature measurements for these types of stars. © ESO 2006.

Approximations for non-grey radiative transfer in numerical simulations of the solar photosphere

Realistic simulations of solar (magneto-)convection require an accurate treatment of the non-grey character of the radiative energy transport. Owing to the large number of spectral lines in the solar atmosphere, statistical representations of the line opacities have to be used in order to keep the problem numerically tractable. We consider two statistical approaches, the opacity distribution function (ODF) concept and the multigroup (or opacity binning) method and provide a quantitative assessment of the errors that arise from the application of these methods in the context of 2D/3D simulations. In a first step, the ODF- and multigroup methods are applied to a 1D model-atmosphere and the resulting radiative heating rates are compared. A number of 4−6 frequency bins is found to warrant a satisfactory modeling of the radiative energy exchange. Further tests in 2D model-atmospheres show the applicability of the multigroup method in realistic situations and underline the importance of a non-grey treatment. Furthermore, we address the question of an appropriate opacity average in multigroup calculations and discuss the significance of velocity gradients for the radiative heating rates.