A 3D radiative transfer framework: III. periodic boundary conditions

We present a general method to solve radiative transfer problems including scattering in the continuum as well as in lines in 3D configurations with periodic boundary conditions. he scattering problem for line transfer is solved via means of an operator splitting (OS) technique. The formal solution is based on a full characteristics method. The approximate $\Lambda$ operator is constructed considering nearest neighbors exactly. The code is parallelized over both wavelength and solid angle using the MPI library. We present the results of several test cases with different values of the thermalization parameter and two choices for the temperature structure. The results are directly compared to 1D plane parallel tests. The 3D results agree very well with the well-tested 1D calculations.Comment: A&A, in press, visualization figure omitted due to size, available at ftp://phoenix.hs.uni-hamburg.de/preprints/3DRT_paper3.pd

A 3D radiative transfer framework: XI. multi-level NLTE

Multi-level non-local thermodynamic equilibrium (NLTE) radiation transfer calculations have become standard throughout the stellar atmospheres community and are applied to all types of stars as well as dynamical systems such as novae and supernovae. Even today spherically symmetric 1D calculations with full physics are computationally intensive. We show that full NLTE calculations can be done with fully 3 dimensional (3D) radiative transfer. With modern computational techniques and current massive parallel computational resources, full detailed solution of the multi-level NLTE problem coupled to the solution of the radiative transfer scattering problem can be solved without sacrificing the micro physics description. We extend the use of a rate operator developed to solve the coupled NLTE problem in spherically symmetric 1D systems. In order to spread memory among processors we have implemented the NLTE/3D module with a hierarchical domain decomposition method that distributes the NLTE levels, radiative rates, and rate operator data over a group of processes so that each process only holds the data for a fraction of the voxels. Each process in a group holds all the relevant data to participate in the solution of the 3DRT problem so that the 3DRT solution is parallelized within a domain decomposition group. We solve a spherically symmetric system in 3D spherical coordinates in order to directly compare our well-tested 1D code to the 3D case. We compare three levels of tests: a) a simple H+He test calculation, b) H+He+CNO+Mg, c) H+He+Fe. The last test is computationally large and shows that realistic astrophysical problems are solvable now, but they do require significant computational resources. With presently available computational resources it is possible to solve the full 3D multi-level problem with the same detailed micro-physics as included in 1D modeling.Comment: 20 pages, 14 figures, A&A, in pres

A 3D radiative transfer framework: X. Arbitrary Velocity Fields in the Co-moving Frame

3-D astrophysical atmospheres will have random velocity fields. We seek to combine the methods we have developed for solving the 1-D problem with arbitrary flows to those that we have developed for solving the fully 3-D relativistic radiative transfer problem in the case of monotonic flows. The methods developed in the case of 3-D atmospheres with monotonic flows, solving the fully relativistic problem along curves defined by an affine parameter, are very flexible and can be extended to the case of arbitrary velocity fields in 3-D. Simultaneously, the techniques we developed for treating the 1-D problem with arbitrary velocity fields are easily adapted to the 3-D problem. The algorithm we present allows the solution of 3-D radiative transfer problems that include arbitrary wavelength couplings. We use a quasi-analytic formal solution of the radiative transfer equation that significantly improves the overall computation speed. We show that the approximate lambda operator developed in previous work gives good convergence, even neglecting wavelength coupling. Ng acceleration also gives good results. We present tests that are of similar resolution to what has been presented using Monte-Carlo techniques, thus our methods will be applicable to problems outside of our test setup. Additional domain decomposition parallelization strategies will be explored in future work.Comment: 9 pages, 9 figures, A&A, in press, new version matches copy edited version, definition restore