Based on highly accurate laboratory measurements of Lyman bands of H2 and an updated representation of the structure of the ground X 1sigma(g)+ and excited B 1sigma(u)+ and C 1pi(u) states, a new set of sensitivity coefficients K(i) is derived for all lines in the H2 spectrum, representing the dependence of their transition wavelengths on a possible variation of the proton-electron mass ratio mu = m(p)/m(e). Included are local perturbation effects between B and C levels and adiabatic corrections. The new wavelengths and K(i) factors are used to compare with a recent set of highly accurate H2 spectral lines observed in the Q 0347-383 and Q 0405-443 quasars, yielding a fractional change in the mass ratio of deltamu/mu = (2.4 +/- 0.6) x 10(-5) for a weighted fit and deltamu/mu = (2.0 +/- 0.6) x 10(-5) for an unweighted fit. This result indicates, at a 3.5sigma confidence level, that mu could have decreased in the past 12 Gyr.

Molecular transitions recently discovered at redshift zabs= 2.059 towards the bright background quasar J2123−0050 are analysed to limit cosmological variation in the proton‐to‐electron mass ratio, μ≡mp/me. Observed with the Keck telescope, the optical echelle spectrum has the highest resolving power and largest number (86) of H2 transitions in such analyses so far. Also, (seven) HD transitions are used for the first time to constrain μ‐variation. These factors, and an analysis employing the fewest possible free parameters, strongly constrain μ's relative deviation from the current laboratory value: Δμ/μ= (+5.6 ± 5.5stat± 2.9sys) × 10−6, indicating an insignificantly larger μ in the absorber. This is the first Keck result to complement recent null constraints from three systems at zabs > 2.5 observed with the Very Large Telescope. The main possible systematic errors stem from wavelength calibration uncertainties. In particular, distortions in the wavelength solution on echelle order scales are estimated to contribute approximately half the total systematic error component, but our estimate is model dependent and may therefore under or overestimate the real effect, if present. To assist future μ‐variation analyses of this kind, and other astrophysical studies of H2 in general, we provide a compilation of the most precise laboratory wavelengths and calculated parameters important for absorption‐line work with H2 transitions redwards of the hydrogen Lyman limit.

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...

We report two detections of deuterated molecular hydrogen (HD) in QSO absorption-line systems at z > 2. Toward J2123-0500, we find N (HD) = 13.84 ± 0.2 for a sub-DLA with metallicity ≃ 0.5Z ⊙ and N (H 2 ) = 17.64 ± 0.15 at z = 2.0594. Toward FJ0812+32, we find N (HD) = 15.38 ± 0.3 for a solar-metallicity DLA with N (H 2 ) = 19.88 ± 0.2 at z = 2.6265. These systems have ratios of HD to H 2 above that observed in dense clouds within the Milky Way disk and apparently consistent with a simple conversion from the cosmological ratio of D/H. These ratios are not readily explained by any available model of HD chemistry and there are no obvious trends with metallicity or molecular content. Taken together, these two systems and the two published z > 2 HD-bearing DLAs indicate that HD is either less effectively dissociated or more efficiently produced in high-redshift interstellar gas, even at low molecular fraction and/or solar metallicity. It is puzzling that such diverse systems should show such consistent HD/H 2 ratios. Without clear knowledge of all the aspects of HD chemistry that may help determine the ratio HD/H 2 , we conclude that these systems are potentially more revealing of gas chemistry than of D/H itself and that it is premature to use such systems to constrain D/H at high-redshift.

Abstract. Molecular transitions recently discovered at redshift z ab s = 2.059 toward the bright background quasar J2123−0050 are analysed to limit cosmological variation in the proton-toelectron mass ratio, μ ≡ mp /me . Observed with the Keck telescope, the optical spectrum has the highest resolving power and largest number (86) of H2 transitions in such analyses so far. Also, (7) HD transitions are used for the first time to constrain μ-variation. These factors, and an analysis employing the fewest possible free parameters, strongly constrain μ's relative deviation from the current laboratory value: Δμ/μ = (+5.6 ± 5.5 stat ± 2.7sys ) × 10 −6 . This is the first Keck result to complement recent constraints from three systems at z ab s > 2.5 observed with the Very Large Telescope.