HELIOS-K: An Ultrafast, Open-source Opacity Calculator for Radiative Transfer

We present an ultrafast opacity calculator that we name HELIOS-K. It takes a line list as an input, computes the shape of each spectral line and provides an option for grouping an enormous number of lines into a manageable number of bins. We implement a combination of Algorithm 916 and Gauss-Hermite quadrature to compute the Voigt profile, write the code in CUDA and optimise the computation for graphics processing units (GPUs). We restate the theory of the k-distribution method and use it to reduce $\sim 10^5$ to $10^8$ lines to $\sim 10$ to $10^4$ wavenumber bins, which may then be used for radiative transfer, atmospheric retrieval and general circulation models. The choice of line-wing cutoff for the Voigt profile is a significant source of error and affects the value of the computed flux by $\sim 10\%$. This is an outstanding physical (rather than computational) problem, due to our incomplete knowledge of pressure broadening of spectral lines in the far line wings. We emphasize that this problem remains regardless of whether one performs line-by-line calculations or uses the k-distribution method and affects all calculations of exoplanetary atmospheres requiring the use of wavelength-dependent opacities. We elucidate the correlated-k approximation and demonstrate that it applies equally to inhomogeneous atmospheres with a single atomic/molecular species or homogeneous atmospheres with multiple species. Using a NVIDIA K20 GPU, HELIOS-K is capable of computing an opacity function with $\sim 10^5$ spectral lines in $\sim 1$ second and is publicly available as part of the Exoclimes Simulation Platform (ESP; www.exoclime.org).Comment: Accepted by ApJ. 8 pages, 5 figure

General relativistic neutrino transport using spectral methods

We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, theta, phi, epsilon, Theta, Phi)$, and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (theta, phi, Theta, Phi), and is fully energy-dependent. This approach is implemented in a spherical shell, using either Chebyshev polynomials or Fourier series as decomposition bases. It is here restricted to simplified collision terms (isoenergetic scattering) and to the case of a static fluid. We finish this paper by presenting test results using basic configurations, including general relativistic ones in the Schwarzschild metric, in order to demonstrate the convergence properties, the conservation of particle number and correct treatment of some general-relativistic effects of our code. The use of spectral methods enables to run our test cases in a six-dimensional setting on a single processor.Comment: match published versio

Thermal Analysis of Convective-Radiative Fin with Temperature-Dependent Thermal Conductivity Using Chebychev Spectral Collocation Method

yesIn this paper, the Chebychev spectral collocation method is applied for the thermal analysis of convective-radiative straight fins with the temperature-dependent thermal conductivity. The developed heat transfer model was used to analyse the thermal performance, establish the optimum thermal design parameters, and also, investigate the effects of thermo-geometric parameters and thermal conductivity (nonlinear) parameters on the thermal performance of the fin. The results of this study reveal that the rate of heat transfer from the fin increases as the convective, radioactive, and magnetic parameters increase. This study establishes good agreement between the obtained results using Chebychev spectral collocation method and the results obtained using Runge-Kutta method along with shooting, homotopy perturbation, and adomian decomposition methods

Molecfit: A general tool for telluric absorption correction II. Quantitative evaluation on ESO-VLT X-Shooter spectra

Context: Absorption by molecules in the Earth's atmosphere strongly affects ground-based astronomical observations. The resulting absorption line strength and shape depend on the highly variable physical state of the atmosphere, i.e. pressure, temperature, and mixing ratio of the different molecules involved. Usually, supplementary observations of so-called telluric standard stars (TSS) are needed to correct for this effect, which is expensive in terms of telescope time. We have developed the software package molecfit to provide synthetic transmission spectra based on parameters obtained by fitting narrow ranges of the observed spectra of scientific objects. These spectra are calculated by means of the radiative transfer code LBLRTM and an atmospheric model. In this way, the telluric absorption correction for suitable objects can be performed without any additional calibration observations of TSS. Aims: We evaluate the quality of the telluric absorption correction using molecfit with a set of archival ESO-VLT X-Shooter visible and near-infrared spectra. Methods: Thanks to the wavelength coverage from the U to the K band, X-Shooter is well suited to investigate the quality of the telluric absorption correction with respect to the observing conditions, the instrumental set-up, input parameters of the code, the signal-to-noise of the input spectrum, and the atmospheric profiles. These investigations are based on two figures of merit, I_off and I_res, that describe the systematic offsets and the remaining small-scale residuals of the corrections. We also compare the quality of the telluric absorption correction achieved with moelcfit to the classical method based on a telluric standard star. (Abridged)Comment: Acc. by A&A; Software available via ESO: http://www.eso.org/sci/software/pipelines/skytools

An algorithm for computing the 2D structure of fast rotating stars

Stars may be understood as self-gravitating masses of a compressible fluid whose radiative cooling is compensated by nuclear reactions or gravitational contraction. The understanding of their time evolution requires the use of detailed models that account for a complex microphysics including that of opacities, equation of state and nuclear reactions. The present stellar models are essentially one-dimensional, namely spherically symmetric. However, the interpretation of recent data like the surface abundances of elements or the distribution of internal rotation have reached the limits of validity of one-dimensional models because of their very simplified representation of large-scale fluid flows. In this article, we describe the ESTER code, which is the first code able to compute in a consistent way a two-dimensional model of a fast rotating star including its large-scale flows. Compared to classical 1D stellar evolution codes, many numerical innovations have been introduced to deal with this complex problem. First, the spectral discretization based on spherical harmonics and Chebyshev polynomials is used to represent the 2D axisymmetric fields. A nonlinear mapping maps the spheroidal star and allows a smooth spectral representation of the fields. The properties of Picard and Newton iterations for solving the nonlinear partial differential equations of the problem are discussed. It turns out that the Picard scheme is efficient on the computation of the simple polytropic stars, but Newton algorithm is unsurpassed when stellar models include complex microphysics. Finally, we discuss the numerical efficiency of our solver of Newton iterations. This linear solver combines the iterative Conjugate Gradient Squared algorithm together with an LU-factorization serving as a preconditionner of the Jacobian matrix.Comment: 40 pages, 12 figures, accepted in J. Comput. Physic