Context. A statistically significant sampling of H2 rotational excitation in the diffuse interstellar medium (ISM) is essential to identifying its excitation mechanisms and assessing the importance of H2 in the cooling of the gas and the regulation of thermal pressure. Aims. To complement the statistics provided by ancillary telescopes, we conducted a search for pure rotational H2 emission lines in all publicly available background observations obtained with the Medium Resolution Spectrometer (MRS) aboard the JWST. Methods. The sample consists of 276 background observations acquired over the past three years. Departing from the standard pipeline, each uncalibrated MRS background file was reprocessed, enabling the analysis of H2 pure rotational emission. Lines of sight likely associated with star-forming complexes were excluded to focus on emission from the diffuse ISM. The results were compared with FUSE absorption data and were analyzed in relation to the column densities of H and H2 and to dust emission derived from HI4PI, Planck, and WISE data. Results. This analysis reveals widespread H2 emission throughout the Galaxy. We report the first detections of the pure rotational S(4), S(5), and S(7) lines in the diffuse ISM. The S(1) line is detected along 84 lines of sight, corresponding to a detection rate of 41%. Its integrated intensity decreases steeply with Galactic latitude, spanning nearly two orders of magnitude, in remarkable agreement with absorption measurements. The T_34 and T_35 excitation temperatures vary between 200 and 1000 K, are correlated with each other, and are anticorrelated with the column density of H2 , as expected from ancillary data. All lines of sight in the sample have undergone the H-H2 transition, at N_H ___ 10 +20 cm -2 , and are partly molecular, with f_H2 ___ 0.1. Under these conditions, the cooling rate associated with the S(1) line, expressed per hydrogen atom, is found to be remarkably constant, with a characteristic value of 4x10 -27 erg s-1 H-1. Conclusions. This study demonstrates that the high sensitivity of the JWST enables measurements that both strengthen and complement those from absorption studies. Observations collected over just a fraction of JWST’s lifetime have already yielded detections along dozens of lines of sight, significantly expanding the statistical sample of H2 rotational excitation in the diffuse ISM.

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