Keck telescope constraint on cosmological variation of the proton-to-electron mass ratio

Molecular transitions recently discovered at redshift z_abs=2.059 toward the bright background quasar J2123-0050 are analysed to limit cosmological variation in the proton-to-electron mass ratio, mu=m_p/m_e. Observed with the Keck telescope, the optical echelle spectrum has the highest resolving power and largest number (86) of H_2 transitions in such analyses so far. Also, (seven) HD transitions are used for the first time to constrain mu-variation. These factors, and an analysis employing the fewest possible free parameters, strongly constrain mu's relative deviation from the current laboratory value: dmu/mu =(+5.6+/-5.5_stat+/-2.9_sys)x10^{-6}, indicating an insignificantly larger mu in the absorber. This is the first Keck result to complement recent null constraints from three systems at z_abs>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 mu-variation analyses of this kind, and other astrophysical studies of H_2 in general, we provide a compilation of the most precise laboratory wavelengths and calculated parameters important for absorption-line work with H_2 transitions redwards of the hydrogen Lyman limit.