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Recently an accurate analysis of absorption spectra of molecular hydrogen,observed with the Cosmic Origins Spectrograph aboard the Hubble SpaceTelescope, in the photosphere of white dwarf stars GD133 and GD29-38 waspublished in a Letter [Phys. Rev. Lett. 113, 123002 (2014)], yielding aconstraint on a possible dependence of the proton-electron mass ratio on agravitational field of strength 10,000 times that at the Earth's surface. Inthe present paper further details of that study are presented, in particular are-evaluation of the spectrum of the $B^1\Sigma_u^+ - X^1\Sigma_g^+ (v',v'')$Lyman bands relevant for the prevailing temperatures (12,000 - 14,000 K) of thephotospheres. An emphasis is on the calculation of so-called$K_i$-coefficients, that represent the sensitivity of each individual line to apossible change in the proton-electron mass ratio. Such calculations wereperformed by semi-empirical methods and by ab initio methods providing accurateand consistent values. A full listing is provided for the molecular physicsdata on the Lyman bands (wavelengths $\lambda_i$, line oscillator strengths$f_i$, radiative damping rates $\Gamma_i$, and sensitivity coefficients $K_i$)as required for the analyses of H$_2$-spectra in hot dwarf stars. A similarlisting of the molecular physics parameters for the $C^1\Pi_u - X^1\Sigma_g^+(v',v'')$ Werner bands is provided for future use in the analysis of whitedwarf spectra.

monthly notices of the royal astronomical society

H$_2$ Lyman and Werner band lines and their sensitivity for a variation  of the proton-electron mass ratio in the gravitational potential of white  dwarfs