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(Abridged) H2 is the most abundant molecule in the Universe. Thanks to itswidely spaced energy levels, it predominantly lights up in warm gas, T > 100 K,such as shocked regions, and it is one of the key targets of JWST observations.These include shocks from protostellar outflows, all the way up to starburstgalaxies and AGN. Shock models are able to simulate H2 emission. We aim toexplore H2 excitation using such models, and to test over which parameter spacedistinct signatures are produced in H2 emission. We present simulated H2emission using the Paris-Durham shock code over an extensive grid of 14,000plane-parallel stationary shock models, a large subset of which are exposed toan external UV radiation field. The grid samples 6 input parameters: preshockdensity, shock velocity, transverse magnetic field strength, UV radiation fieldstrength, cosmic-ray-ionization rate, and PAH abundance. Physical quantities,such as temperature, density, and width, have been extracted along with H2integrated line intensities. The strength of the transverse magnetic field, setby the scaling factor, b, plays a key role in the excitation of H2. At lowvalues of b (<~ 0.3, J-type shocks), H2 excitation is dominated byvibrationally excited lines; at higher values (b >~ 1, C-type shocks),rotational lines dominate the spectrum for shocks with an external radiationfield comparable to (or lower than) the solar neighborhood. Shocks with b >= 1can be spatially resolved with JWST for nearby objects. When the input kineticenergy flux increases, the excitation and integrated intensity of H2 increasessimilarly. An external UV field mainly serves to increase the excitation,particularly for shocks where the input radiation energy is comparable to theinput kinetic energy flux. These results provide an overview of the energeticreprocessing of input kinetic energy flux and the resulting H2 line emission.

Shock excitation of H$_2$ in the James Webb Space Telescope era