Probing variations in fundamental constants with radio and optical quasar absorption-line observations

Nine quasar absorption spectra at 21-cm and UV rest-wavelengths are used to estimate possible variations in x=alpha^2 g_p mu, (alpha is the fine structure constant, g_p the proton g-factor and mu=me/mp the electron-to-proton mass ratio). We find <Delta x/x>^weighted_total(=Dxxwt)=(0.63+-0.99) 10^-5 over 0.23~<z_abs~<2.35 (2.7 to 10.5 Gyr, look-back time, t_lb). A linear best fit against t_lb, tied to Delta x/x=0 at z=0, gives (dot x)/x=(-0.6+-1.2) 10^-15 /yr. Our large sample demonstrates that intrinsic line-of-sight velocity differences between the 21-cm and UV absorption redshifts, (on average Delta_vlos~6km/s), with random sign and magnitude in each absorption system, limit our precision. Combining our Delta x/x measurement with absorption-line constraints on alpha-variation yields strong limits on the variation of mu. Our most conservative estimate, obtained by assuming no variations in alpha or g_p is Delta mu/mu(=Dmm)=Dxxwt. If we use only the four high-redshift absorbers in our sample, we obtain Dmm=(0.58+-1.95) 10^-5, which agrees (2sigma) with recent, more direct estimates from two absorption systems containing molecular hydrogen, also at high redshift, and which have hinted at a possible mu-variation, Dmm=(-2.0+-0.6) 10^-5. Our method of constraining Dmm is completely independent from the molecular hydrogen observations. If we include the low-redshift systems, our Dmm result differs significantly from the high-redshift molecular hydrogen results. We detect a dipole variation in mu across the sky, but this model is required by the data at only the 88 per cent confidence level. Clearly, much larger samples of 21-cm and molecular hydrogen absorbers are required to adequately resolve the issue of the variation of mu and x.(Abridged)