ZeeTurbo: Stellar Magnetism Modeling

• ZeeTurbo is a suite of astrophysical modeling tools that couples Zeeman effect computations with synthetic spectra generation for detailed analysis of M dwarf atmospheres.
• It leverages high-resolution near-infrared spectro-polarimetric observations from SPIRou and refined radiative transfer techniques to derive precise atmospheric parameters and magnetic fluxes.
• The framework uses grid-based fitting of magnetically sensitive and insensitive spectral lines, achieving typical magnetic flux precisions around 0.05 kG and validating its methods on active cool stars.

ZeeTurbo refers to a suite of astrophysical modeling codes and methodologies developed for the characterization of atmospheric parameters and surface magnetic fields in cool stars, specifically M dwarfs, based on high-resolution near-infrared (nIR) spectro-polarimetric observations. This system is principally used with SPIRou, the nIR spectro-polarimeter at the Canada-France-Hawaii Telescope, and relies on the physical modeling of the Zeeman effect and polarised radiative transfer within the framework of synthetic spectra generation. ZeeTurbo builds upon the well-established Turbospectrum radiative transfer code by incorporating magnetic field effects and MARCS model atmospheres, enabling simultaneous fitting of stellar parameters and magnetic field strengths through detailed analysis of both magnetically sensitive and insensitive spectral lines.

1. Development and Architecture of ZeeTurbo

ZeeTurbo is designed by augmenting Turbospectrum, a classical code for the computation of synthetic spectra in stellar atmospheres, with two major capabilities: explicit computation of the Zeeman effect and handling polarised radiative transfer. These expansions enable simulation of magnetic field-split spectral line profiles as observed in highly magnetic stars. The theoretical underpinnings draw from the Zeeman Hamiltonian and radiative transfer theory in magnetized plasmas, allowing the modeling of Stokes I profiles (intensity), with planned extensions to full Stokes vector computation.

The core inputs to ZeeTurbo are MARCS model atmospheres, which deliver parameterized physical properties ($T_{\mathrm{eff}}$, $\log{g}$, [M/H], [$\alpha$/Fe]), and atomic/molecular line lists containing Landé $g$-factors and splitting patterns required for magnetic sensitivity. The code computes a dense grid of synthetic spectra by varying atmospheric parameters and average surface magnetic flux $|\mathbf{B}|_{\mathrm{surf}}$ over physically plausible ranges.

2. Physical Modeling of Zeeman Effect and Radiative Transfer

Spectroscopic measurement of magnetic fields in cool stars hinges on the Zeeman splitting of spectral lines. ZeeTurbo explicitly models this effect by calculating wavelength shifts and relative line strengths for each Zeeman component, given the line's Landé $g$-factor and the local field strength. For each atomic transition, the magnetic splitting is given by

$$\Delta \lambda = 4.67 \times 10^{-13} ~ g_{\mathrm{eff}} ~ \lambda^2 ~ B$$

where $\Delta \lambda$ is the splitting in Ångström, $g_{\mathrm{eff}}$ is the effective Landé factor, $\lambda$ is the line's central wavelength, and $B$ is the magnetic field strength in Gauss. The radiative transfer solver accounts for the line formation in strong fields and includes magnetically broadened profiles for polarized radiative transfer in the context of selective absorption and emission.

This modeling is crucial for distinguishing magnetic and non-magnetic contributions to observed spectra, especially in wavelength regions where molecular Zeeman components overlap significantly (e.g., FeH, Ti I lines).

3. Parameter Fitting and Grid-Based Inference Framework

The parameter inference in ZeeTurbo is based on direct $\chi^2$ minimization or Bayesian sampling across the synthetic grid. The key stellar atmospheric parameters constrained are:

• Effective temperature: $T_{\mathrm{eff}}$
• Surface gravity: $\log{g}$
• Metallicity: [M/H]
• Alpha element enhancement: [$\alpha$/Fe]
• Average surface magnetic field: $\langle B \rangle$, or surface magnetic flux $|\mathbf{B}|_{\mathrm{surf}}$

Fitting involves simultaneous comparison of observed and synthetic spectra, targeting both magnetically sensitive (Zeeman-split) and insensitive lines. The method is devised to minimize parameter degeneracies, e.g., those between $T_{\mathrm{eff}}$ and Zeeman broadening, by careful line selection and joint fitting. Grid resolution is chosen to balance accuracy and computational feasibility, with typical field strengths scanned between 0.0 and $\sim$5 kG in increments of 0.05–0.1 kG.

For each observed spectrum, the best-fit parameters are found by minimizing

$$\chi^2(\mathbf{p}, B) = \sum_{i} \left[ F_{\text{obs}}(\lambda_i) - F_{\text{syn}}(\lambda_i; \mathbf{p}, B) \right]^2 / \sigma^2(\lambda_i)$$

where $F_{\text{obs}}$ and $F_{\text{syn}}$ are the observed and model fluxes, $\mathbf{p}$ is the vector of atmospheric parameters, $B$ is the average magnetic field, and $\sigma$ is the flux uncertainty.

4. Performance Validation and Precision Assessment

Simulation studies using ZeeTurbo grid spectra demonstrate the ability to recover input atmospheric and magnetic parameters with high fidelity under realistic synthetic noise levels. Reported precisions for the surface magnetic flux are typically $\sim0.05$ kG, commensurate with the scale and contrast of Zeeman splitting in observed spectral features.

Application to empirical SPIRou spectra of six active M dwarfs (AU Mic, EV Lac, AD Leo, CN Leo, PM J18482+0741, DS Leo) yielded atmospheric parameters in agreement with literature spectroscopic and interferometric determinations. Simultaneously derived surface magnetic fluxes were in the range $2$–$4$ kG, consistent with the saturated dynamo regime observed in fast-rotating late-type stars. These results validate the method's reliability for high-resolution nIR data, independent of detailed assumptions about field geometry or spot coverage.

5. Extensions and Limitations

ZeeTurbo's approach is generalized for both weakly and strongly magnetic stars, but its current grid-based methodology can become computationally demanding for very large parameter spaces or for modeling temporal/spatial field variability. The typical precision and accuracy depend on line selection, SNR, and systematics in model atmospheres and line lists (e.g., completeness of Landé $g$-data).

Sensitivity analyses show that fitted magnetic field strengths are robust to the treatment of magnetically insensitive lines. However, assumptions regarding surface gravity ($\log{g}$) can bias estimates of $\langle B \rangle$, necessitating careful prior constraints (e.g., from independent photometric or dynamical measurements).

6. Impact on Stellar Magnetic Field Studies

Deployments of ZeeTurbo across SPIRou Legacy Survey data have elucidated the prevalence of strong small-scale magnetic fields in M dwarfs, with inferred fields accounting for more than 70% of the total average field in most cases with existing large-scale field measurements. These findings challenge standard dynamo models, particularly the relationship between Rossby number and magnetic field saturation; notably, there are cases (e.g., GJ 1289, GJ 1286) of unusually strong small-scale fields at long rotation periods, pointing toward non-traditional dynamo modes or magnetic topologies that decouple small and large-scale field generation mechanisms.

7. Prospects and Future Directions

Continued development of ZeeTurbo aims to integrate full Stokes vector calculations, expanded molecular Zeeman modeling, and machine learning–accelerated parameter inference. Prospective work seeks to characterize time-dependent and spot-modulated field signatures, investigate boundary conditions for dynamo saturation, and systematically survey M dwarfs and other cool stars for empirical magnetic field population studies.

ZeeTurbo establishes a precision, physically motivated methodology for the simultaneous atmospheric and surface field inference in cool stars, offering insights into magnetic activity, dynamo operation, and the reliability of nIR spectro-polarimetric diagnostics in the context of high-resolution stellar spectroscopy.