Progress towards a 3D Monte Carlo radiative transfer code for outflow wind modelling: II. 3-D applications

TL;DR

This work extends Andy Antares to robust 3-D Monte Carlo radiative transfer in arbitrarily velocity-structured winds, addressing the limitations of traditional 1-D analyses. It introduces a two-grid framework (modGrid for the hydrodynamic model and propGrid for RT) with a trilinear velocity interpolation that enables accurate Doppler shifting and Sobolev-like line interactions in non-monotonic flows. The authors validate the velocity interpolation against analytic fields for homologous and β-law winds, test optical depths in lines with generalized expressions, and demonstrate emergent spectra consistent with expectations, including noise-sensitive line features. They further showcase a 2-D hydrodynamic input from MPI-AMRVAC integrated into Andy Antares, highlighting substantial inhomogeneities and the resulting spectra that differ from angle-averaged 1-D models, underscoring the practical impact for mass-loss diagnostics in hot-star winds.

Abstract

The massive hot stars play crucial role in the dynamics of galaxies. These stars influence their surroundings through strong winds which are highly structured processes. The theoretical study of the non-symmetric phenomena of the stellar winds are becoming important these days, mainly because 1-D models are not sufficient enough. We present a new version of our Monte Carlo radiative transfer code Andy Antares with improved treatment of the velocity field for arbitrary geometries. Our aim is to develop a numerical scheme that can incorporate a general velocity field defined at discrete points. Our main objective is to calculate radiative transfer in a general input hydrodynamic model. The Andy Antares code currently calculates pure radiative transfer. The input model is pre-calculated by another hydrodynamical code. The whole radiative transfer calculation is then processed in a Cartesian grid. Radiative transfer is solved using the Monte Carlo approach in 3-D regardless of the input hydrodynamical model's dimension. The velocity field at any given point is interpolated using the trilinear interpolation. The optical depth is then integrated numerically along the photon's path. We verified the accuracy of the numerical velocity interpolation by comparison with results obtained for analytical velocity fields, achieving successful outcomes. We also tested the radiative transfer solution on a 3-D model generated from a 2-D hydrodynamic model, and obtained emergent radiation. The code is suitable for the numerical solution of radiative transfer in 3-D with arbitrary velocity fields.

Figures (8)

• Figure 1: An illustrative example of an adaptive propGrid with propGrid cells belonging to different modGrid cells. Each propGrid cell belongs to any modGrid cell, which is distinguished by different colours (the same colour of non-neigbouring cells does not mean the same associated modGrid cell, we did not want to use many colours). Above: An algorithm for choosing interpolation points based on the current propGrid cell. The current propGrid cell is the cell containing a dark star, which locates the place where we calculate the interpolated velocity vector. There are four such examples in the figure. The blue hexagons represent the central points of the current propGrid cells (where the dark stars are located), the red hexagons represent the derived points used for the trilinear interpolation. If more than one propGrid cell belongs to the same modGrid cell, the boundary between them is drawn with a dotted line. Below: The red arrows represent the velocity vectors defined in the input. The other arrows represent the velocity vectors used for trilinear interpolation at any particular point (in this picture represented by little red hexagons).
• Figure 2: The derivative $\mathrm{d}s/\mathrm{d}\nu^\leadsto$ is calculated using Eq. \ref{['Eq:tauline']}. A packet is located in the beginning of the dashed line, the arrow points to its current direction. The resonance point is denoted by $s_0$ and the packet's CMF frequency is exactly equal to the line frequency. $s_-$ and $s_+$ denote positions of points with a distance $\Delta s$ from the resonance point.
• Figure 3: A comparison of the numerical and analytical treatments of velocity, to assess the accuracy of the calculated velocity as a function of radius. The left panels are calculated using the homologous approximation \ref{['Eq:velhomol']} and the right panels are calculated using the $\beta$-velocity law \ref{['Eq:beta3D']}. The upper panels show the absolute magnitude of the velocity, and the lower panels show the relative difference in velocity magnitudes between the interpolated and analytical values.
• Figure 4: A comparison of the calculated spectra for two models. In the first model the velocity (and line optical depth) was interpolated from the 3-D velocity points. In the second model the velocity (and line optical depth) was calculated using an analytical formula. Left panels: homologous approximation, Right panels: $\beta$ velocity law
• Figure 5: The input model (density, temperature, and the radial and lateral velocities) calculated using the MPI-AMRVAC hydrodynamic code.