Limits on a Gravitational Field Dependence of the Proton--Electron Mass Ratio from H${}_2$ in White Dwarf Stars

Abstract

Spectra of molecular hydrogen (H${}_2$) are employed to search for a possible proton-to-electron mass ratio ($\mu$) dependence on gravity. The Lyman transitions of H${}_2$, 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 ($T\sim 13000$ K) of their photospheres. We derive sensitivity coefficients $K_i$ which define how the individual H${}_2$ transitions shift due to $\mu$-dependence. The spectrum of white dwarf star GD133 yields a $\Delta \mu /\mu$ constraint of $(-2.7\pm 4.7_{\mathrm{stat}}\pm 0.2_{\mathrm{sys}})\times 10^{-5}$ for a local environment of a gravitational potential $\varphi \sim 10^4{\varphi }_{\text{Earth}}$, while that of G29$-$38 yields $\Delta \mu /\mu =(-5.8\pm 3.8_{\mathrm{stat}}\pm 0.3_{\mathrm{sys}})\times 10^{-5}$ for a potential of $2\times 10^4$ ${\varphi }_{\text{Earth}}$.

5 pages, 3 figures. Accepted by PRL

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