Molecular hydrogen in the z = 2.66 damped Lyman-alpha absorber toward Q J0643-5041

We use high signal-to-noise ratio, high-resolution VLT-UVES data of Q J0643-5041 amounting to a total of more than 23 hours exposure time and fit the neutral hydrogen, metals and H2 absorption features with multiple-component Voigt profiles. We study the relative populations of H2 rotational levels and the fine-structure excitation of neutral carbon to determine the physical conditions in the H2-bearing cloud. We find some evidence for part of the quasar broad line emission region not being fully covered by the H2-bearing cloud. We measure a total neutral hydrogen column density of log N(H) = 21.03 +/- 0.08. Molecular hydrogen is detected in several rotational levels, possibly up to J = 7, in a single component. The corresponding molecular fraction is log f = -2.19+0.07-0.08, where f = 2N(H2)/(2N(H2)+N(H)). The H2 Doppler parameter is of the order of 1.5 km/s for J = 0, 1 and 2 and larger for J>2. The molecular component has a kinetic temperature of T = 80 K, which yields a mean thermal velocity of about 1 km/s, consistent with the Doppler broadening of the lines. The UV ambient flux is of the order of the mean ISM Galactic flux. We discuss the possible detection of HD and derive an upper limit of log N(HD) < 13.65 +/- 0.07 leading to log HD/(2 H2) < -5.19 +/- 0.07 which is consistently lower than the primordial D/H ratio. Metals span about 210 km/s with [Zn/H] = -0.91 +/- 0.09 relative to solar, with iron depleted relative to zinc [Zn/Fe] = 0.45 +/- 0.06, and with the rare detection of copper. We follow the procedures used in our previous works to derive a constraint on the cosmological variation of the proton-to-electron mass ratio of (7.4 +/- 4.3 (stat) +/- 5.1 (syst)) ppm.