[Paper Review] CO$_2$ collision-induced line parameters for the $ν_3$ band of $^{12}$CH$_4$ measured using a hard-collision speed-dependent line shape and the relaxation matrix formalism

Thibault Bertin, Jean Vander Auwera|arXiv (Cornell University)|Jan 15, 2026

Spectroscopy and Laser Applications0 citations

TL;DR

This study measures CO$_2$ broadening and shifting coefficients for the ν$_3$ band of $^{12}$CH$_4$ at near-room temperature, using hard-collision speed-dependent line shapes and relaxation matrix formalism, and compares with first-order line-mixing models.

ABSTRACT

Ten high resolution Fourier transform spectra of the pentad region near 3.3 μm of methane diluted in carbon dioxide at total pressures up to 800 hPa have been recorded at 296.5(5) K. Including a high resolution spectrum of pure methane at low pressure, these spectra have been analyzed using multi-spectrum fitting techniques. The methane lines were modeled using hard-collision speed-dependent line profiles and line mixing was included in the strongest absorption regions, considering the first order Rosenkranz approximation and the relaxation matrix formalism. CO$_2$ broadening and shift coefficients have been measured, together with the speed dependence of broadening. Results obtained using the two line mixing models are intercompared and compared with previous work.

Motivation & Objective

• Characterize CO$_2$ broadening and shifting effects on the ν$_3$ band of $^{12}$CH$_4$ in CH$_4$-CO$_2$ mixtures up to near-1 atm pressure.
• Assess speed dependence of line broadening and compare line-mixing models (first-order vs. relaxation matrix).
• Develop and apply a multispectrum fitting approach to extract line parameters from high-resolution spectra.
• Investigate the adequacy of CO$_2$ broadening parameters from HITRAN and determine methane self-broadening effects in this spectral region.

Proposed method

• Record 11 high-resolution Fourier transform spectra of CH$_4$ in CO$_2$ up to 800 hPa and one pure-CH$_4$ spectrum at 296.5 K.
• Model methane lines with hard-collision speed-dependent profiles; include line mixing in strongest absorption regions.
• Use first-order Rosenkranz line mixing and, alternatively, the relaxation matrix formalism to treat line coupling.
• Fit spectrum by convolving molecular transmittance with instrument line shape and optimize parameters via Trust Region Reflective least squares.
• Adopt a Maxwell-Boltzmann velocity distribution in the relaxation matrix framework and solve for a set of line-specific parameters including Γ(v), Δ, β, and off-diagonal W$_{mn}$ terms.

Experimental results

Research questions

• RQ1 What are the CO$_2$ broadening and shift coefficients for the ν$_3$ band of $^{12}$CH$_4$ at near-ambient temperatures?
• RQ2 How does speed-dependent broadening affect the ν$_3$ band shapes in CH$_4$–CO$_2$ mixtures across pressures approaching 1 atm?
• RQ3 What is the impact of including relaxation matrix line mixing versus first-order line mixing on retrieved line parameters?
• RQ4 Are HITRAN air-broadening parameters for CO$_2$-perturbed CH$_4$ lines adequate, or must CO$_2$-specific values be used?

Key findings

• CO$_2$ broadening and shift coefficients for multiple lines in the ν$_3$ band were extracted from high-resolution spectra.
• Speed dependence of broadening is significant and modeled with a parameter a$_W$, found to be around 0.110 in fits that include comprehensive line mixing.
• Relaxation matrix formalism (full line mixing) provides a more complete description at high pressures, with notable differences from first-order line-mixing results.
• Self-broadening and self-shift coefficients were compiled from literature and used to constrain the fits, with a fixed self-shift value derived from past measurements.
• The study identifies sensitivities to instrument line shape and calibration, and discusses limitations of various line-mixing models in the 3.3 μm region.