# H$_2$/HD molecular data for analysis of quasar spectra in search of varying constants

## TL;DR

This paper compiles highly accurate molecular data for H$_2$ and HD to improve the analysis of quasar spectra in the search for variations in the proton-to-electron mass ratio over cosmic time.

## Contribution

It provides a comprehensive, high-precision line list of H$_2$ and HD molecules, including wavelengths, oscillator strengths, damping parameters, and sensitivity coefficients, for use in astrophysical tests of fundamental constant variations.

## Key findings

- New molecular data list enables more accurate quasar spectrum analysis.
- Refit of quasar spectra yields constraints on proton-electron mass ratio variation.
- Results are consistent with no variation, supporting previous studies.

## Abstract

Absorption lines of H$_2$ and HD molecules observed at high redshift in the line of sight towards quasars are a test ground to search for variation of the proton-to-electron mass ratio $\mu$. For this purpose, results from astronomical observations are compared with a compilation of molecular data of the highest accuracy, obtained in laboratory studies as well as in first-principles calculations. Aims: A comprehensive line list is compiled for H$_2$ and HD absorption lines in the Lyman ($B^1\Sigma_u^+$ - $X^1\Sigma_g^+$) and Werner ($C^1\Pi_u$ - $X^1\Sigma_g^+$) band systems up to the Lyman cutoff at 912 Angstroms. Molecular parameters listed for each line $i$ are the transition wavelength $\lambda_i$, the line oscillator strength $f_i$, the radiative damping parameter of the excited state $\Gamma_i$, and the sensitivity coefficient $K_i$ for a variation of the proton-to-electron mass ratio. Methods: The transition wavelengths $\lambda_i$ for the H$_2$ and HD molecules are determined by a variety of advanced high-precision spectroscopic experiments involving narrowband vacuum ultraviolet lasers, Fourier-transform spectrometers, and synchrotron radiation sources. Results for the line oscillator strengths $f_i$, damping parameters $\Gamma_i$, and sensitivity coefficients $K_i$ are obtained in theoretical quantum chemical calculations. Results: A new list of molecular data is compiled for future analyses of cold clouds of hydrogen absorbers, specifically for studies of $\mu$-variation from quasar data. The list is applied in a refit of quasar absorption spectra of B0642$-$5038 and J1237$+$0647 yielding constraints on a variation of the proton-to-electron mass ratio $\Delta\mu/\mu$ consistent with previous analyses.