On a possible variation of the proton-to-electron mass ratio: H2 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 l = 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 theWerner band systems at an accuracy of (4-11) · 10 À8, 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 0405À443 and Q 0347À383) resulted in 76 reliably determined transition wavelengths of H 2 lines at accuracies in the range 2 · 10 À7 to 1 · 10 À6 . 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 l. 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 R þ g ground electronic state and the presently determined level energies in the B 1 R þ u and C 1 P 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 Dl/l = (2.45 ± 0.59) · 10 À5 for a weighted fit and Dl/l = (1.99 ± 0.58) · 10 À5 for an unweighted fit. This result, indicating the decrease of l, has a statistical significance of 3.5r. 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 0405À443 and Q 0347À383. The statistical analysis is further documented and possible systematic shifts underlying the data, with the possibility of mimicking a non-zero Dl/l value, are discussed. The observed decrease in l corresponds to a rate of change of d lnl/dt = À2 · 10 À15 per year, if a linear variation with time is assumed. Expe...

Perspective: Tipping the scales: Search for drifting constants from molecular spectra

“…This definition of K μ yields opposite signs to that used in Refs. [25][26][27]. Although electronic transitions in atoms are sensitive to α, they are relatively immune to a variation of μ.…”

“…While Thompson proposed using high-redshift H 2 lines as a search ground for a varying proton-electron mass ratio, 44 Varshalovich and Levshakov 45 first calculated K μ sensitivity coefficients for the H 2 molecule. Later updated values for sensitivity coefficients of H 2 were obtained in a semi-empirical (SE) fashion, based on newly established spectroscopic data, 25,26 and via ab initio (AI) calculations. 46 In the semi-empirical approach, rovibrational level energies of the relevant electronic states are fitted to a Dunham expansion 47…”

Robust limit on a varying proton-to-electron mass ratio from a single H2system

“…Figure 5 plots the results of this paper, Ubachs et al (2007) and Thompson et al (2009a), who published the individual fit parameters. The redshifts derived are of 3.0248969 (56), 3.0248988(29) and 3.0248987(61) for this paper, Ubachs et al (2007) and Thompson (2009a) respectively, which is not surprising being based at least partially on the same data. All three analysis are based on the same source for sensitivity coefficients.…”

“…Subsequent measures of the quasar absorption systems of QSO 0347-382 and QSO 1232+082 provided hints for a variation (2.4 ± 0.6) × 10 −5 , i.e. at 3.5σ (Reinhold et al 2006;Ivanchik et al 2005;Ubachs et al 2007). The new analysis used additional high-resolution spectra and updated laboratory data of the energy levels and of the rest frame wavelengths of the H 2 molecule.…”

Extreme ultraviolet laser calibration of D_2Lyman and Werner transitions

“…Since a similar procedure was also used by Dabrowski and Herzberg [2] for calibration of their D 2 spectrum, a systematic shift of their data with respect to the present laser-based results may have the same origin. A second comparison is made between the observed transition frequencies and calculations based on the theoretical framework as presented in [7,8] [2], and will be used, together with the highly accurate XUV measurements on H 2 [19], as calibration lines for VUV emission studies, in particular for the D 2 and HD molecules. …”