Further evidence for a variable fine-structure constant from Keck/HIRES QSO absorption spectra

We have previously presented evidence for a varying fine-structure constant alpha, in two independent samples of Keck/ HIRES quasi- stellar object (QSO) absorption spectra. Here we present a detailed many-multiplet analysis of a third Keck/ HIRES sample containing 78 absorption systems. We also re-analyse the previous samples, providing a total of 128 absorption systems over the redshift range 0.2 < z(abs) < 3.7. The results, with raw statistical errors, indicate a smaller weighted mean in the absorption clouds: Deltaalpha/alpha = ( 0.574 +/- 0.102) x 10(-5). All three samples separately yield consistent and significant values of Deltaalpha/alpha. The analyses of low-z (i.e. z(abs) < 1.8) and high-z systems rely on different ions and transitions with very different dependences on alpha, yet they also give consistent results. We identify an additional source of random error in 22 high-z systems characterized by transitions with a large dynamic range in apparent optical depth. Increasing the statistical errors on Delta alpha/alpha for these systems gives our fiducial result, a weighted mean Delta alpha/alpha = (-0.543 +/- 0.116) x 10(-5), representing 4.7 sigma evidence for a varying alpha. Assuming that Delta alpha/alpha = 0 at z(abs) = 0, the data marginally prefer a linear increase in with time rather than a constant offset from the laboratory value: (alpha) over dot/alpha = (6 40 +/- 1 35) x 10(-1)6 yr(-1). The two-point correlation function for alpha is consistent with zero over 0.2-13 Gpc comoving scales and the angular distribution of Delta alpha/alpha shows no significant dipolar anisotropy. We therefore have no evidence for spatial variations in Delta alpha/alpha. We extend our previous searches for possible systematic errors, giving detailed analyses of potential kinematic effects, line blending, wavelength miscalibration, spectrograph temperature variations, atmospheric dispersion and isotopic/hyperfine structure effects. The latter two are potentially the most significant. However, overall, known systematic errors do not explain the results. Future many-multiplet analyses of independent QSO spectra from different telescopes and spectrographs will provide a now crucial check on our Keck/ HIRES results.