Turbospectrum Radiative Transfer Code

• Turbospectrum Radiative Transfer Code is a computational framework that models stellar spectra by solving the radiative transfer equation in both LTE and NLTE regimes.
• It employs detailed opacity treatments, including molecular and H⁻ absorptions, to improve chemical abundance analyses and accurate line profile computations.
• The tool offers flexibility with various atmospheric models and interpolation of NLTE departure coefficients, making it a benchmark for precision spectroscopic studies.

The Turbospectrum Radiative Transfer Code is a widely used tool for modeling stellar spectra through detailed spectrum synthesis, with applications spanning fundamental stellar parameter determination, chemical abundance analysis, and supporting large-scale stellar surveys. It is built as a flexible, efficient computational framework for solving the radiative transfer equation under both Local Thermodynamic Equilibrium (LTE) and, in recent versions, Non-Local Thermodynamic Equilibrium (NLTE) for a wide variety of atomic species. While its design centers on the modeling of cool stellar atmospheres, particularly evolved stars, its computational strategies, input flexibility, and emphasis on background opacity treatments position it as a reference code in comparative benchmarking studies and precision spectroscopic analyses.

1. Theoretical Foundations and Code Architecture

Turbospectrum implements classical spectrum synthesis by solving the unpolarized radiative transfer equation in 1D, supporting both LTE and, in its most recent updates, NLTE formulations (Gerber et al., 2022). In LTE mode, the code computes intensities via:

$$\frac{dI(\nu, \mathbf{n})}{ds} = -\chi(\nu,\mathbf{n}) I(\nu,\mathbf{n}) + \eta(\nu,\mathbf{n}),$$

where $\chi(\nu,\mathbf{n})$ and $\eta(\nu,\mathbf{n})$ denote the frequency- and direction-dependent opacity and emissivity. For NLTE treatments, Turbospectrum leverages precomputed departure coefficients $b_i$ for each atomic level $i$, modifying level populations relative to their LTE values: $b_i = n_i^{NLTE}/n_i^{LTE}$. These coefficients correct line opacities and source functions:

$$\alpha(\nu) = \alpha^*(\nu) \cdot b_l \Big[1 - \frac{b_u}{b_l}\exp\left(-\frac{h\nu}{kT}\right)\Big],$$

$$S(\nu) = \frac{b_u}{b_l} B_\nu / \Big[1 - \frac{b_u}{b_l} \exp\left(-\frac{h\nu}{kT}\right)\Big],$$

where $l$ and $u$ refer to the lower and upper levels, $B_\nu$ is the Planck function, and $h$, $k$, $T$ have their usual physical meanings.

The code’s logic is modular, with key components for radiative transfer, opacity computations, atmospheric interface, atomic and molecular data management, and interpolation tools to reconcile physical and computational grids.

2. Opacity Treatment and Background Physics

Turbospectrum calculates total opacity as a sum of line ($\chi_{\text{lines}}$) and continuous (background; $\chi_c$) contributions. For most regimes, background opacities are critically important: they include processes such as H$^-$ bound-free and free-free absorption, Thomson scattering, neutral hydrogen and molecular absorption. The code self-consistently solves for H$^-$ density via chemical equilibrium including molecules, ensuring robustness for cool stellar atmospheres commonly affected by molecular and negative hydrogen opacity (Tessore et al., 2021).

The treatment of background opacities in Turbospectrum can differ subtly but significantly from other radiative transfer codes, most notably in the handling of H$^-$ opacity near the Balmer jump and the continuum minimum. For example, discrepancies up to 10% in continuum flux (cool giant models) and up to 40% (Balmer jump in early-type models) arise between Turbospectrum and MCFOST-art, attributed to the specifics of H$^-$ density treatment (Tessore et al., 2021).

3. NLTE Capabilities and NLTE Implementation

The principal extension in recent Turbospectrum versions is the capability to synthesize spectra with NLTE line formation for multiple elements simultaneously (Gerber et al., 2022). This is realized by reading grids of precomputed NLTE departure coefficients—generated via statistical equilibrium solvers such as MULTI—for chemical elements including H, O, Na, Mg, Si, Ca, Ti, Mn, Fe, Co, Ni, Sr, and Ba.

These coefficients are interpolated across effective temperature, gravity, and metallicity sub-grids, mapping to the chosen stellar atmospheric model. Blends involving both NLTE and LTE-treated lines are supported, providing both flexibility and consistency for crowded spectral regions.

The NLTE implementation allows for improved accuracy in abundance determinations and line profile calculations, addressing systematic biases known to arise from LTE assumptions in FGK-type and M stars. The design achieves these with computational efficiency comparable to traditional LTE modeling—high-resolution synthetic spectra over wide wavelength intervals can be produced in minutes, facilitating large-sample analyses without prohibitive computational overhead.

4. Atmospheric Models and Input Flexibility

Turbospectrum supports a variety of input atmospheric models. The classical use case involves 1D, line-blanketed MARCS models, which assume hydrostatic equilibrium and LTE for opacities. Additionally, support exists for so-called $\langle 3\mathrm{D} \rangle$ models: temporally and spatially averaged 3D radiation-hydrodynamics simulations that inherently capture convective inhomogeneities and avoid parameterizations of micro- and macroturbulence (Gerber et al., 2022).

A dedicated interpolation module aligns the respective grids of model atmospheres and NLTE coefficients, enabling users to synthesize spectra at any parameter point within the grid boundaries. This approach ensures physical self-consistency and supports advanced analyses such as comparisons across evolutionary sequences or modeling observed line asymmetries.

5. Benchmarks, Comparisons, and Code Validation

The code has been rigorously benchmarked against alternative radiative transfer frameworks such as MCFOST-art and RH, both under LTE and out-of-equilibrium regimes (Tessore et al., 2021). Typical agreement is within a few percent across most wavelength ranges. Distinct differences become apparent near critical opacities, such as the H$^-$ minimum and Balmer jump, where the interplay between opacity prescriptions and chemical equilibrium solutions is acute.

Table 1 summarizes the main points of comparison between Turbospectrum and MCFOST-art:

Aspect	Turbospectrum	MCFOST-art
Equilibrium regime	LTE (NLTE new versions)	Non-LTE (MALI)
Geometry support	1D	3D
H$^-$ opacity treatment	Chemical equilibrium	Fixed between iterations
Main application regime	Cool stars, LTE-friendly	Non-LTE, multidimensional

These comparisons underscore the critical importance of detailed opacity modeling for high-precision spectroscopic diagnostics and the necessity to match code assumptions carefully to the target stellar regime.

6. Practical Applications and Community Impact

Turbospectrum’s public availability, coupled with its extensive atomic and molecular libraries, NLTE coefficient archives, and flexible input handling, has made it a standard for precision stellar spectroscopic analysis. It underpins studies that range from Galactic chemical evolution surveys to detailed investigations of benchmark stars and exoplanet host metallicities (Gerber et al., 2022). The efficient implementation of simultaneous NLTE corrections for multiple elements addresses previous limitations in the field, particularly in the context of large, inhomogeneous stellar samples and high-resolution spectroscopic surveys.

These capabilities have led to more accurate and physically robust determinations of stellar parameters (e.g., temperature, gravity, metallicity) and element abundances. The code’s approach to NLTE correction, blend treatment, and multi-atmosphere support allows users to simulate and interpret subtle spectroscopic features with improved fidelity, greatly benefitting studies that require population-wide homogeneity or detailed line-profile fitting.

7. Limitations and Regimes of Optimality

Despite its advanced features, Turbospectrum is less adapted to strongly non-LTE-dominated regimes requiring fully time-dependent, multidimensional radiative transfer, as found in dynamic stellar magnetospheres or far-from-equilibrium atmospheres. In such applications, frameworks like MCFOST-art—built on the MALI method with 3D geometry and statistical equilibrium solved iteratively—are more suitable (Tessore et al., 2021). For classical cool stars and LTE-dominated problems, Turbospectrum’s treatment of molecular and negative hydrogen opacities is particularly robust. Its modular design also enables continued extension and benchmarking as microphysics advances.

A plausible implication is that the primary constraint on Turbospectrum’s precision arises from the adopted background opacities and the completeness of atomic and molecular data rather than from the radiative transfer solver itself.

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In summary, Turbospectrum is a reference radiative transfer code for LTE and NLTE stellar spectrum synthesis in 1D geometry, offering detailed treatment of background opacities, flexible model input, and high computational efficiency. Its updates enable simultaneous NLTE treatment for multiple elements, integration with advanced atmosphere models, and extensive benchmarking against alternative codes. The choice of Turbospectrum for a given application depends critically on the equilibrium regime and required model complexity for background opacity and radiative transfer.