Spectral line fluorescence in moving envelopes of stars

I. Theoretical background, numerical code, and proof of concept

Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
e-mail: cb.work@snoqualm.org

Received: 29 February 2024
Accepted: 28 May 2024

Abstract

Context. Fluorescence of the optical FeI lines is observed in active T Tauri stars, and is considered a defining characteristic of this class of young stellar objects.

Aims. The formation of optical fluorescent lines in moving media has not yet been studied in detail. This work represents a first step in investigating the fluorescence process in different types of macroscopic velocity fields: (a) accelerated outflows, (b) accelerated infalls, and (c) non-monotonic velocity fields (such as an accelerating outflow followed by a deceleration region or an accretion shock front). We aim to develop a general computer code for studying the fluorescent emission in any 2D macroscopic velocity field. As an illustration, we investigate FeI T Tauri-like fluorescent emission in these moving stellar envelopes.

Methods. We solved the radiative transfer equations for the lines involved in the fluorescent process, assuming spherical symmetry and a simplified atomic model. We used the framework of the generalized Sobolev theory to compute the interacting, nonlocal source functions. The emergent line fluxes were then integrated exactly.

Results. Because of Doppler shifts in the moving gaseous envelope, photons of the three lines involved in T Tauri star FeI fluorescence (CaII H, FeIλ3969, and H_ϵ) interact with each other in a complex way, such that fluorescent amplification of the line flux occurs not only for FeIλ3969, but also for the other two lines, in all velocity fields that we investigated. With the assumption of local thermodynamic equilibrium populations, the line source functions of moderately optically thick lines are not strongly affected by line interactions, while they are depressed in the inner envelope for optically thick lines because of stellar photon absorption in the interaction regions. Fluorescent amplification takes place mainly in the observer’s reference frame during the flux integration. We define a measure of fluorescence based on the line equivalent widths and perform a parameter study for an accretion flow with a broad range of envelope temperatures and densities while including approximate collisional de-excitation rates in the source function computations. Significant fluorescence occurs over the entire temperature range of the investigated flow, but only in the higher density range, suggesting that relatively high mass accretion rates are needed to trigger the fluorescence process.

Conclusions. Further comparison with observations will require solving the rate equations for the atomic populations involved, along with the radiation field computed with the method presented here. The main product of this research is the open-source computer code SLIM2 (Spectral Line Interactions in Moving Media), written in Python/NumPy, which numerically solves the fluorescence problem for arbitrary 2D velocities.