We report the detection of H2 in a zabs= 0.0963 Damped Lyman-{alpha} (DLA) system towards zem = 0.4716 QSO J1619+3342. This DLA has log N(H I) = 20.55 (0.10), 18.13 < log N(H2) < 18.40, [S/H] = -0.62 (0.13), [Fe/S] = -1.00 (0.17) and the molecular fraction -2.11 < log f(H2) < -1.85. The inferred gas kinetic temperature using the rotational level population is in the range 95 - 132 K. We do not detect C I or C II* absorption from this system. Using R- and V-band deep images we identify a sub-L* galaxy at an impact parameter of 14 kpc from the line of sight, having consistent photometric redshift, as a possible host for the absorber. We use the photoionization code CLOUDY to get the physical conditions in the H2 component using the observational constrains from H2, C I, C II* and Mg I. All the observations can be consistently explained if one or more of the following is true: (i) Carbon is underabundant by more than 0.6 dex as seen in halo stars with Z ~ 0.1 Z_sun, (ii) H I associated with H2 component is less than 50% of the H I measured along the line of sight and (iii) the H2 formation rate on the dust grains is at least a factor two higher than what is typically used in analytic calculations for Milky Way interstellar medium. Even when these are satisfied, the gas kinetic temperature in the models are much lower than what is inferred from the ortho-to-para ratio of the molecular hydrogen. Alternatively the high kinetic temperature could be a consequence of contribution to the gas heating from non-radiative heating processes seen in hydrodynamical simulations.
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