Limits on a gravitational field dependence of the proton-electron mass ratio from H2 in white dwarf stars

Spectra of molecular hydrogen (H2) are employed to search for a possible proton-to-electron mass ratio (μ) dependence on gravity. The Lyman transitions of H2, observed with the Hubble Space Telescope towards white dwarf stars that underwent a gravitational collapse, are compared to accurate laboratory spectra taking into account the high temperature conditions (T∼13000K) of their photospheres. We derive sensitivity coefficients Ki which define how the individual H2 transitions shift due to μ dependence. The spectrum of white dwarf star GD133 yields a Δμ/μ constraint of (-2.7±4.7stat±0.2syst)×10-5 for a local environment of a gravitational potential φ∼104 φEarth, while that of G29-38 yields Δμ/μ=(-5.8±3.8stat±0.3syst)×10-5 for a potential of 2×104 φEarth.