Theories of binary fluid mixtures: from phase-separation kinetics to active emulsions
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The currently operating space missions, as well as those that will be launched in the near future, will deliver high-quality data for millions of stellar objects. Since the majority of stellar astrophysical applications still at least partly rely on spectroscopic data, an efficient tool for the analysis of medium- to high-resolution spectroscopy is needed.
We aim at developing an efficient software package for the analysis of medium- to high-resolution spectroscopy of single stars and those in binary systems. The major requirements are that the code should have a high performance, represent the state-of-the-art analysis tool, and provide accurate determinations of atmospheric parameters and chemical compositions for different types of stars. We use the method of atmosphere models and spectrum synthesis, which is one of the most commonly used approaches for the analysis of stellar spectra.
The method is first tested on the simulated data and is then applied to the spectra of real stellar objects. The majority of test runs on the simulated data were successful in that we were able to recover the initially assumed sets of atmospheric parameters.
We experimentally find the limits in signal-to-noise ratios of the input spectra, below which the final set of parameters is significantly affected by the noise. We found an overall agreement of the final sets of the fundamental parameters with the original studies. The gssp software package is a compilation of three individual program modules suitable for spectrum analysis of single stars and individual binary components.
The code is highly effective and can be used for spectrum analysis of large samples of stars. The gssp software package can be downloaded from https: Nowadays, spectrum analysis is the main source of precise atmospheric parameters and chemical compositions of stars. The problem of chemical composition determination in different classes of stars is directly linked to the problems of production and down and out binary call options b less than kindle of chemical elements, stellar and galactic evolution, etc.
Interpretation of the observed atmospheric chemical composition in down and out binary call options b less than kindle star gives a general impression of its evolutionary status. For example, it is well known that a star initially has the chemical composition of the molecular cloud it has formed from.
Shortly after the start of nuclear fusion in the star, the chemical composition in its central parts undergoes certain changes. At this stage, the atmospheric composition remains quite stable. On the main-sequence, certain processes may occur in the star that will cause the exchange of matter between the stellar interior and the atmosphere. Some of the processes that can cause the above-mentioned mixing of the material are convection or turbulent diffusion.
At the early stages of giant evolution, the stars generally go through the phase of deep convective mixing which has a certain impact on the atmospheric down and out binary call options b less than kindle of light chemical elements and later on heavier ones.
Detailed studies of atmospheric chemical composition can also reveal signatures of mass loss in massive stars e. Chemically peculiar stars are another example of how detailed studies of atmospheric chemical composition allow for a better understanding of different physical processes occurring in stars e. High-quality photometric data obtained from space have revealed countless numbers of interesting physical effects in different types of stellar objects and have led to very interesting discoveries.
Needless to say, however, that both fields still heavily depend on high-quality, high-resolution spectroscopic data, and a significant fraction of the analyses rely on the interpretation of combined space-based photometric and ground-based spectroscopic data.
The recently launched Gaia mission Perryman et al. Efficient and fast tools are particularly needed for the analysis of ground-based spectroscopic data of single and multiple stellar objects. Nowadays, the method of atmosphere models and spectrum synthesis is a dominant approach in the analysis of high-resolution spectra of single stars and those in binary systems. One of the advantages of the spectrum synthesis over the traditional methods that rely on the calculation of equivalent widths is that the effects of line blending can be accurately taken into account.
This in turn minimizes the uncertainties in the determination of fundamental stellar parameters and chemical abundances. In this paper, we present a new Grid Search in Stellar Parameters gssp software package for spectrum analysis of high-resolution spectra of single stars and those in binary systems. In the following sections, we describe the implemented methodology and test the code both on simulated and real stellar down and out binary call options b less than kindle. In this section we discuss in all necessary detail the methodology implemented in the gssp software package.
This includes the description of each of the three program modules and the results of the test runs. Although there are small differences in the realization of the individual algorithms, the general methodology is the same for all three modules. The software package is based on a grid search in the fundamental atmospheric parameters and optionally individual chemical abundances of the star or binary stellar components in question. We use the method of atmosphere models and spectrum synthesis, which assumes a comparison of the observations with each theoretical spectrum from the grid.
For calculation of synthetic spectra, we use the S ynth V LTE-based radiative transfer code Tsymbal and a grid of atmosphere models precomputed down and out binary call options b less than kindle the LL models code Shulyak et al. Our grid of models covers wide ranges in all fundamental atmospheric parameters and is freely distributed together with the software package itself. The summary of the available models is given in Table 1.
In fact, the gssp package is compatible with any kind of atmosphere model grid as long as the models are provided in the Kurucz format. The authors also possess a grid of Kurucz models 1 Kurucz which have been interpolated in all fundamental parameters to match the resolution of our LL models grid. The interpolated grid of Kurucz models is available upon request.
We allow for optimization of five stellar parameters at a time: The synthetic spectra can be computed in any number of wavelength ranges, and each considered spectral interval can be from a few angstroems up to a few thousand angstroems wide. The individual abundances have to be iterated element by element, thus there is no option to optimize abundances of more than one element at the same time.
From our experience, any reasonable deviations of the individual abundances from the global atmospheric metallicity within about 0. An exception needs to be made however for the elements showing a large amount of lines in their spectrum: For this reason, the process should be started with chemical elements having the largest number of lines in the spectrum when determining the detailed chemical composition of the star in down and out binary call options b less than kindle. The grid of theoretical spectra is built from all possible combinations of the above mentioned parameters.
We also account for possible global-scale imperfection in the normalization of the observed spectrum by means of a scaling factor that is computed from the least-squares fit of the synthetic spectrum to the observations and is applied to the latter.
For the analysis of binary stars, whether the disentangled spectra or the observed composite spectra are used for the characterization of the system, the percentage contribution of a stellar component to the total light of the system becomes one of the most important parameters.
This light contribution is often referred to as a light dilution factor designated as f i throughout this paper and effects the depths of lines in the spectra of both binary components.
This correction factor for the line depths has to be taken into account down and out binary call options b less than kindle the analysis, and is ideally determined along with the other atmospheric parameters of the star. There are two basic ways of accounting for the light dilution factor in the spectroscopic analysis: Which of the two methods to use depends on the analysis approach, on whether the individual binary components are characterized independent of each other or simultaneously by means of fitting their disentangled spectra.
More details on both methods are given in Sects. The grid search method is generally more CPU time demanding than any of the optimization algorithms but has a big advantage that it guarantees that the global minimum solution will be found as long as the considered parameter range is large enough.
We use the O pen MPI 2 distribution to parallelize our code, which solves the CPU time-related problem and makes the code fast and very effective. At least for one of the software modules, there seems to be a linear relation between the number of used CPUs and the calculation time. However, there still exists an upper limit for the number of CPUs to be used.
The limit strongly depends on the configuration of the system and is likely to occur when the system load becomes large enough to start effecting the performance of the code. We will down and out binary call options b less than kindle rough estimates of down and out binary call options b less than kindle calculation times below, when discussing each of the gssp package modules individually.
In this particular module we treat the observed spectrum as the one of a single star. The module is thus applicable to spectra of single stellar objects as well as to the disentangled spectra of multiple stellar systems. In practice, each synthetic spectrum from the computed grid is represented in the form of Eq. The two identical branches showed in the diagram indicate multiprocessing.
See text for more details. In the first step, the code reads in all necessary information provided by the user in the configuration file. We provide an example of the input file with detailed description of each entry in the Appendix.
In the next step, the code sets up the grid and checks whether the required grid of atmosphere models is available. Should any of the models not exist, the user will be notified about the need to revise the input set up, and the detailed report is saved in one of the log-files. At this point, the observed spectrum can be optionally cross-correlated with the first synthetic spectrum from the grid, and the radial velocity RV is computed as the first order moment of the cross-correlation function.
This way, the code accounts for a possible RV shift of the observed spectrum with respect to the laboratory wavelength, should the user request that. As soon as the grid has been set up depending on the grid size, this might take up to half a minute of timethe code enters a multiprocessing mode and performs the actual calculations.
The S ynth V code is executed on each of the available CPUs and provides a synthetic spectrum for a given set of atmospheric parameters and in the requested wavelength range. The code computes specific line and continuum intensities for different positions of the stellar disk, thus providing an accurate treatment of the limb darkening effect. As soon as the spectrum is computed, a convolution program is executed to perform the disk integration and a convolution of the spectrum with projected rotational and macroturbulent velocities, and the resolving power of the instrument.
The convolution code outputs the normalized synthetic spectrum as well as the line and continuum fluxes. The above described calculations may take from a few seconds up to a few minutes, depending on the spectral type and considered wavelength range. Once the convolved synthetic spectrum is released, there are two options for the code to contiue with see Fig.
The light dilution factor is 0. The simulated observed spectrum is shown with light grey lines, the black solid line refers to the best fit synthetic spectrum. The spectrum of the secondary was vertically shifted by a constant value for better visualization. The calculations may take a bit longer when fitting disentangled spectra, as there is an additional parameter light dilution factor to account for.
The module was tested on simulated data of single stars; in addition, we refer the reader to the papers of Down and out binary call options b less than kindle et al. The quality of the fit to one pair of spectra is illustrated in Fig. The only set up where we have encountered certain difficulties in recovering the assumed fundamental parameters refers to the case of peculiar stars see Table A.
Since in the unconstrained fitting the spectra of individual components are considered separately, there is no way the results obtained for one of the components will influence the parameters of the companion. In our case, both factors were set as free parameters and optimized along with other fundamental parameters for each of the components. As an example, in Fig. As it has been mentioned by Debosscher et al.
Thus, following the procedure adopted in down and out binary call options b less than kindle original study of Debosscher et al. This module has been specifically designed for fitting disentangled spectra of both binary components simultaneously. Instead of assuming wavelength-independent light dilution for each of the components, we optimize the ratio of the radii of the binary components which is obviously the same for both stars.
Starting from the definition of disentangled spectra of individual binary components given in Eq. By optimizing the ratio of the radii, we take into account the wavelength-dependence of the light dilution factor through the ratio of continuum intensities of the two stars.
Obviously, any change in the atmospheric parameters of one of the binary components will influence its continuum intensity, which will in turn affect the light dilution factor for the companion star. In practice, disentangled spectra of two binary components are analyzed simultaneously by scaling synthetic spectra from the corresponding grids and comparing them to the observations on the scale of the latter.