Spectral Line Identification and Modelling (SLIM) in the MAdrid Data CUBe Analysis (MADCUBA) package

Context. The increase in bandwidth and sensitivity of state-of-the-art radio observatories is providing a wealth of molecular data from nearby star-forming regions up to high-z galaxies. Analysing large data sets of spectral cubes requires efficient and user-friendly tools optimised for astronomers with a wide range of backgrounds. Aims. In this paper we present the detailed formalism at the core of Spectral Line Identification and Modelling (SLIM) within the MAdrid Data CUBe Analysis (MADCUBA) package and their main data-handling functionalities. These tools have been developed to visualise, analyse, and model large spectroscopic data cubes. Methods. We present the highly interactive on-the-fly visualisation and modelling tools of MADCUBA and SLIM, which includes a stand-alone spectroscopic database. The parameters stored therein are used to solve the full radiative transfer equation under local thermodynamic equilibrium (LTE). The SLIM package provides tools to generate synthetic LTE model spectra based on input physical parameters of column density, excitation temperature, velocity, line width, and source size. It also provides an automatic fitting algorithm to obtain the physical parameters (with their associated errors) better fitting the observations. Synthetic spectra can be overlayed in the data cubes/spectra to ease the task of multi-molecular line identification and modelling. Results. We present the Java-based MADCUBA and its internal module SLIM packages which provide all the necessary tools for manipulation and analysis of spectroscopic data cubes. We describe in detail the spectroscopic fitting equations and make use of this tool to explore the breaking conditions and implicit errors of commonly used approximations in the literature. Conclusions. Easy-to-use tools like MADCUBA allow users to derive physical information from spectroscopic data without the need for simple approximations. The SLIM tool allows the full radiative transfer equation to be used, and to interactively explore the space of physical parameters and associated uncertainties from observational data.

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Discontinuities in numerical radiative transfer

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833984 ◽

2019 ◽

Vol 622 ◽

pp. A162 ◽

Cited By ~ 1

Author(s):

Gioele Janett

Keyword(s):

Radiative Transfer ◽

Transfer Equation ◽

Radiative Transfer Equation ◽

Transfer Problem ◽

Stellar Atmospheres ◽

Physical Parameters ◽

Radiative Transfer Problem ◽

Intermittent Behavior ◽

High Order Convergence ◽

Magnetohydrodynamic Simulations

Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of the stationary radiative transfer equation is particularly challenging in such situations, because standard numerical methods may perform very inefficiently in the absence of local smoothness. However, a rigorous investigation of the numerical treatment of the radiative transfer equation in discontinuous media is still lacking. The aim of this work is to expose the limitations of standard convergence analyses for this problem and to identify the relevant issues. Moreover, specific numerical tests are performed. These show that discontinuities in the atmospheric physical parameters effectively induce first-order discontinuities in the radiative transfer equation, reducing the accuracy of the solution and thwarting high-order convergence. In addition, a survey of the existing numerical schemes for discontinuous ordinary differential systems and interpolation techniques for discontinuous discrete data is given, evaluating their applicability to the radiative transfer problem.

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FIRTEZ-dz

Astronomy and Astrophysics ◽

10.1051/0004-6361/201935692 ◽

2019 ◽

Vol 629 ◽

pp. A24 ◽

Cited By ~ 3

Author(s):

A. Pastor Yabar ◽

J. M. Borrero ◽

B. Ruiz Cobo

Keyword(s):

Radiative Transfer ◽

Transfer Equation ◽

Radiative Transfer Equation ◽

Three Dimensional ◽

Direct Calculation ◽

Momentum Equation ◽

Gas Pressure ◽

Numerical Code ◽

Physical Parameters ◽

Geometrical Scale

We present a numerical code that solves the forward and inverse problem of the polarized radiative transfer equation in geometrical scale under the Zeeman regime. The code is fully parallelized, making it able to easily handle large observational and simulated datasets. We checked the reliability of the forward and inverse modules through different examples. In particular, we show that even when properly inferring various physical parameters (temperature, magnetic field components, and line-of-sight velocity) in optical depth, their reliability in height-scale depends on the accuracy with which the gas-pressure or density are known. The code is made publicly available as a tool to solve the radiative transfer equation and perform the inverse solution treating each pixel independently. An important feature of this code, that will be exploited in the future, is that working in geometrical-scale allows for the direct calculation of spatial derivatives, which are usually required in order to estimate the gas pressure and/or density via the momentum equation in a three-dimensional volume, in particular the three-dimensional Lorenz force.

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Completely Spectral Collocation Solution of Radiative Heat Transfer in an Anisotropic Scattering Slab With a Graded Index Medium

Journal of Heat Transfer ◽

10.1115/1.4024990 ◽

2013 ◽

Vol 136 (1) ◽

Cited By ~ 7

Author(s):

Jing Ma ◽

Ya-Song Sun ◽

Ben-Wen Li

Keyword(s):

Radiative Transfer ◽

Transfer Equation ◽

Radiative Transfer Equation ◽

Anisotropic Scattering ◽

Discrete Ordinates ◽

Spectral Collocation ◽

Graded Index ◽

Wide Range ◽

Derivative Term ◽

Scattering Phase Function

A completely spectral collocation method (CSCM) is developed to solve radiative transfer equation in anisotropic scattering medium with graded index. Different from the Chebyshev collocation spectral method based on the discrete ordinates method (SP-DOM), the CSCM is used to discretize both the angular domain and the spatial domain of radiative transfer equation. In this approach, the angular derivative term and the integral term are approximated by the high order spectral collocation scheme instead of the low order finite difference approximations. Compared with those available data in literature, the CSCM has a good accuracy for a wide range of the extinction coefficient, the scattering albedo, the scattering phase function, the gradient of refractive index and the boundary emissivity. The CSCM can provide exponential convergence for the present problem. Meanwhile, the CSCM is much more economical than the SP-DOM. Moreover, for nonlinear anisotropic scattering and graded index medium with space-dependent albedo, the CSCM can provide smoother results and mitigate the ray effect.

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Influence of turbulence on the shape of a spectral line: the analytical approach

Proceedings of the International Astronomical Union ◽

10.1017/s1743921307012525 ◽

2007 ◽

Vol 3 (S242) ◽

pp. 32-33

Author(s):

N. A. Silant'ev ◽

E. E. Lekht ◽

J. E. Mendoza-Torres ◽

G. M. Rudnitskij

Keyword(s):

Radiative Transfer ◽

Spectral Line ◽

Transfer Equation ◽

Radiative Transfer Equation ◽

Simple Analytical Expression ◽

Line Radiation ◽

Explicit Analytical Solution ◽

Point Correlation ◽

Point Correlation Function ◽

Factor Α

AbstractWe consider the propagation of spectral-line radiation in a correlated turbulent atmosphere. The ensembles of turbulent velocities u(r,t) and optical depths, τν, are assumed to be Gaussian. We investigate the explicit analytical solution of the stochastic radiative transfer equation for the intensity Iν of radiation. The scattering term is not taken into account. It is shown that, in addition to the usual Doppler broadening of the spectral line, correlated turbulent motions of atoms and molecules give rise to considerable changes in the shape of a spectral line. We find that the mean intensity I(0)ν (Iν=I(0)ν+I′ν, I′ν = 0) obeys the usual radiative transfer equation with renormalized extinction factor αeffν if the correlation length R0 of the turbulence is small as compared to a photon free path. A simple analytical expression for αeffν is given. This expression integrally depends on the two-point correlation function of the turbulent velocity field.

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A numerical light curve model for interaction-powered supernovae

Publications of the Astronomical Society of Japan ◽

10.1093/pasj/psaa050 ◽

2020 ◽

Vol 72 (4) ◽

Cited By ~ 1

Author(s):

Yuki Takei ◽

Toshikazu Shigeyama

Keyword(s):

Radiative Transfer ◽

Light Curve ◽

Transfer Equation ◽

Energy Equation ◽

Radiative Transfer Equation ◽

Circumstellar Matter ◽

Physical Parameters ◽

Time Step ◽

Curve Model ◽

Forward Shock

Abstract We construct a numerical light curve model for interaction-powered supernovae that arise from an interaction between the ejecta and the circumstellar matter (CSM). In order to resolve the shocked region of an interaction-powered supernova, we solve the fluid equations and radiative transfer equation assuming steady states in the rest frames of the reverse and forward shocks at each time step. Then we numerically solve the radiative transfer equation and the energy equation in the CSM with the radiative flux obtained from the forward shock as a radiation source. We also compare the results of our models with observational data of two supernovae, 2005kj and 2005ip, classified as type IIn, and discuss the validity of our assumptions. We conclude that our model can predict the physical parameters associated with supernova ejecta and the CSM from the observed features of the light curve as long as the CSM is sufficiently dense. Furthermore, we found that the absorption of radiation in the CSM is an important factor in calculating the luminosity.

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