On a possible variation of the proton-to-electron mass ratio: H 2 spectra in the line of sight of high-redshift quasars and in the laboratory

Abstract

Recently the finding of an indication for a decrease of the proton-to-electron mass ratio μ = m p/ m e by 0.002% in the past 12 billion years was reported in the form of a Letter [E. Reinhold, R. Buning, U. Hollenstein, P. Petitjean, A. Ivanchik, W. Ubachs, Phys. Rev. Lett. 96 (2006) 151101]. Here we will further detail the methods that led to that result and put it in perspective. Laser spectroscopy on molecular hydrogen, using a narrow-band and tunable extreme ultraviolet laser system at the Laser Centre Vrije Universiteit Amsterdam, results in transition wavelengths of spectral lines in the B 1 Σ u + - X 1 Σ g + Lyman and C 1 Π u - X 1 Σ g + Werner band systems at an accuracy of (4–11) × 10 −8, depending on the wavelength region. This corresponds to an absolute accuracy of 0.000004–0.000010 nm. A database of 233 accurately calibrated H 2 lines is presented here for future reference and comparison with astronomical observations. Recent observations of the same spectroscopic features in cold hydrogen clouds at redshifts z = 2.5947325 and z = 3.0248970 in the line of sight of two quasar light sources (Q 0405−443 and Q 0347−383) resulted in 76 reliably determined transition wavelengths of H 2 lines at accuracies in the range 2 × 10 −7 to 1 × 10 −6. Those observations were performed with the Ultraviolet and Visible Echelle Spectrograph at the Very Large Telescope of the European Southern Observatory at Paranal, Chile. A third ingredient in the analysis is the calculation of an improved set of sensitivity coefficients K i , a parameter associated with each spectral line, representing the dependence of the transition wavelength on a possible variation of the proton-to-electron mass ratio μ. The new model for calculation of the K i sensitivity coefficients is based on a Dunham representation of ground state and excited state level energies, derived from the most accurate data available in literature for the X 1 Σ g + ground electronic state and the presently determined level energies in the B 1 Σ u + and C 1Π u states. Moreover, the model includes adiabatic corrections to electronic energies as well as local perturbation effects between B and C levels. The full analysis and a tabulation of the resulting K i coefficients is given in this paper. A statistical analysis of the data yields an indication for a variation of the proton-to-electron mass ratio of Δ μ/ μ = (2.45 ± 0.59) × 10 −5 for a weighted fit and Δ μ/ μ = (1.99 ± 0.58) × 10 −5 for an unweighted fit. This result, indicating the decrease of μ, has a statistical significance of 3.5 σ. Mass-variations as discussed relate to inertial or kinematic masses, rather than gravitational masses. Separate treatment of the data gives a similar positive result for each of the quasars Q 0405−443 and Q 0347−383. The statistical analysis is further documented and possible systematic shifts underlying the data, with the possibility of mimicking a non-zero Δ μ/ μ value, are discussed. The observed decrease in μ corresponds to a rate of change of d ln μ/d t = −2 × 10 −15 per year, if a linear variation with time is assumed. Experiments for detecting a possible variation of μ in the modern epoch via ultra-precision experiments on H 2 quadrupole transitions are proposed.