Warm gas in the cold diffuse interstellar medium:: Spectral signatures in the H2 pure rotational lines

We present ISO-SWS observations of five pure rotational lines of H-2 along a line of sight through the Galaxy which avoids regions of massive star formation. It samples 30 mag of gas, half of it (i.e. 15 mag) being diffuse gas running from the solar neighbourhood to the molecular ring, up to the far side of the Galaxy. The intensities of the S(1) and S(2) lines are too large relative to S( 0) to be produced by UV excitation in the known radiation field of the Galaxy. The excitation of these transitions has to tap a more powerful source of energy. We investigate the possibility that it takes place in a large number of magneto-hydrodynamic (MHD) shocks or coherent small-scale vortices, two processes responsible for the intermittent dissipation of MHD turbulence. These dissipation bursts locally and temporarily heat the diffuse gas to temperatures (T-k similar to 10(3) K) well above that of the ambient diffuse gas. We compute the spectroscopic signatures of these processes in the H-2 lines. Not only are the computed relative line intensities in good agreement with the observations, but the few percent of warm gas involved is consistent with other independent determinations. We find that the fraction of warm H-2 in the diffuse gas (i.e. H-2 molecules in J(u) >= 3 levels) on that line of sight, N(H-2*)/A(v) approximate to 4 x 10(17) cm(-2) mag(-1), is the same as that found from far UV spectroscopy in the direction of nearby stars. It is also the same as that estimated in the solar neighbourhood to reproduce the large observed abundances of molecules like CH+. These results suggest that the existence, within the cold neutral medium (CNM), of a few percent of warm gas, for which UV photons cannot be the sole heating source, is ubiquitous and presumably traces the intermittent dissipation of MHD turbulence in the cold diffuse gas.