Measurements and predictions of H2 pressure-broadening coefficients of CO2 absorption lines for exoplanet atmosphere studies

Technical Summary: Measurements and Predictions of H₂ Pressure-Broadening Coefficients of CO₂ Absorption Lines

Problem Statement
Accurate modeling of exoplanetary atmospheres, particularly those dominated by hydrogen (H₂), relies heavily on precise molecular spectroscopic data. Specifically, the retrieval of molecular abundances and atmospheric properties from observed spectra depends on the precision of molecular cross-sections, which require accurate knowledge of pressure-induced line broadening and shift coefficients. While Carbon Dioxide (CO₂) is a key molecule detected in exoplanet atmospheres (e.g., by the James Webb Space Telescope), reliable H₂ pressure-broadening data for CO₂ lines remain scarce. Existing datasets are often limited in scope, affected by large uncertainties, or derived by applying empirical scaling factors to air-broadened widths. Such approximations can lead to significant discrepancies in opacity modeling, potentially exceeding the 10% precision threshold required for JWST exoplanet studies. Furthermore, the wide temperature ranges encountered in exoplanet atmospheres (70 K to 3000 K) extend far beyond the conditions of existing experimental data.

Methodology
This work combines high-resolution laboratory measurements with first-principles theoretical simulations to generate a comprehensive dataset for the CO₂-H₂ system.

• Experimental Approach: High-resolution Fourier Transform Spectrometry (FTS) was employed at the LISA laboratory to record spectra of CO₂ highly diluted in H₂ at room temperature (~294 K). Measurements were conducted across the entire CO₂ ν₃ band (4.3 µm spectral region) with total pressures ranging from 150 mbar to 1060 mbar. A multi-fitting procedure was applied to the transmission spectra using three line-shape models: the standard Voigt profile, Voigt with line mixing (LM), and the hard-collision (HC) profile with LM. The analysis focused on 61 CO₂ lines (from P(62) to R(60)). A rigorous uncertainty analysis was performed, accounting for statistical errors, pressure and temperature measurement uncertainties, and instrument line shape (ILS) variations.
• Theoretical Approach: Requantized classical molecular dynamics simulations (rCMDS) were performed to predict broadening coefficients over a broad temperature range (200 K to 1000 K). These simulations utilized an accurate site-site intermolecular potential derived from ab initio calculations (Hellmann & Bich, 2025) without adjusting parameters to experimental data. The method involves simulating the time evolution of the system, calculating the dipole moment autocorrelation functions, and applying a requantization procedure to match classical rotational frequencies with quantum energy levels. The resulting spectral profiles were fitted to extract broadening coefficients.

Key Contributions

1. First Comprehensive Experimental Dataset: This study provides the first accurate measurement of H₂ pressure-broadening ($\gamma_{H2}$) and pressure-shift ($\delta_{H2}$) coefficients for the entire CO₂ ν₃ band at room temperature, covering rotational quantum numbers up to $J=62$.
2. Validation of rCMDS Method: The work demonstrates that rCMDS, when using accurate intermolecular potentials, can reproduce experimental line-shape parameters with high fidelity, serving as a reliable tool for extrapolating data to conditions inaccessible to current experiments.
3. Temperature Dependence Modeling: The study establishes the temperature dependence of H₂ broadening coefficients for CO₂ lines up to $J=120$ across the 200–1000 K range, utilizing both single and double power law fits to the simulation data.

Results

• Experimental Findings: The measured $\gamma_{H2}$ coefficients show a weak rotational dependence, varying from approximately 0.108 to 0.122 cm⁻¹/atm. The results agree very well with the measurements of Hanson & Whitty (2014) for the P(24) line (0.25% difference) but show significant deviations (up to 16.5%) from values currently in the HITRAN database, which are derived from scaled air-broadening coefficients. The measured pressure-shift coefficients ($\delta_{H2}$) have a mean value of -3.9 × 10⁻³ cm⁻¹/atm, which is significantly larger in magnitude than those for He-broadening.
• Theoretical Agreement: The rCMDS predictions at 296 K show excellent agreement with the new experimental data, with differences generally below 3% (well within the 2% experimental uncertainty). This agreement validates the simulation approach.
• Temperature Extrapolation: The rCMDS simulations successfully predicted broadening coefficients at temperatures up to 1000 K. The data reveals that discrepancies between rCMDS predictions and HITRAN values increase with temperature, reaching over 30% at 600 K and 1000 K. The double power law (DPL) was found to model the temperature dependence more accurately than the single power law (SPL), keeping deviations below 1% compared to direct simulation results.

Significance
The paper asserts that the generated dataset constitutes the first accurate and comprehensive resource of H₂ broadening coefficients for CO₂ lines suitable for modeling H₂-rich exoplanetary atmospheres. By providing data that satisfies the precision requirements (<10%) for JWST studies, this work addresses a critical gap in current opacity models. The authors conclude that relying on scaled air-broadening data or limited previous measurements may lead to substantial errors in the interpretation of exoplanet spectra. The validated rCMDS method offers a robust pathway to generate reliable spectroscopic parameters for a wide range of temperatures and rotational states, thereby improving the accuracy of atmospheric property retrievals for exoplanets.