Molecular hydrogen in a damped Lyα system at zabs=4.224

We present a direct detection of molecular hydrogen at the highest redshift known today (z(abs) = 4.224) in a damped Ly alpha (DLA) system toward the quasar PSS J1443+2724. This absorber is remarkable for having one of the highest metallicities among DLA systems at z(abs) > 3, with a measured iron abundance relative to solar of -1.12 +/- 0.10. We provide for the first time in this system accurate measurements of N I, Mg II, S II, and Ar I column densities. The sulfur and nitrogen abundances relative to solar, -0.63 +/- 0.10 and -1.38 +/- 0.10, respectively, correspond exactly to the primary nitrogen production plateau. H 2 absorption lines are detected in four different rotational levels (J = 0, 1, 2, and 3) of the vibrational ground state in three velocity components with total column densities log N(H-2) of 17.67, 17.97, 17.48, and 17.26, respectively. The J = 4 level is tentatively detected in the strongest component, with log N(H-2) similar to 14. The mean molecular fraction is log f = -2.38 +/- 0.13, with f p 2N(H-2)/[2N(H-2) + N(H I)]. We also measure log [N(HD)/N(H-2)] <- 4.2. The excitation temperatures T 01 for the two main components of the system are 96 K and 136 K, respectively. We argue that the absorbing galaxy, whose star formation activity must have started at least (2-5) x 10(8) yr before z = 4.224, is in a quiescent state at the time of observation. The density of the gas is low, n(H) <= 50 cm(-3), and the temperature is of the order of T similar to 90-180 K. The high excitation of neutral carbon in one of the components can be explained if the temperature of the cosmic microwave background radiation has the value expected at the absorber redshift, T = 14.2 K. These observations demonstrate the feasibility of studying H-2 at the highest redshifts, provided high enough spectral resolution and good signal-to-noise ratio are achieved.