Is the molecular KS relationship universal down to low metallicities?

In recent years, it has been speculated that in extreme low-metallicity galactic environments, stars form in regions that lack H-2. In this paper, we investigate how changing the metallicity and ultraviolet (UV) field strength of a galaxy affects the star formation within, and the molecular gas Kennicutt-Schmidt (KS) relation. Using extremely high-resolution AREPO simulations of isolated dwarf galaxies, we independently vary the metallicity and UV field to between 1 per cent and 10 per cent solar neighbourhood values. We include a non-equilibrium, time-dependent chemical network to model the molecular composition of the interstellar medium and include the effects of gas shielding from an ambient UV field. Crucially, our simulations directly model the gravitational collapse of gas into star-forming clumps and cores and their subsequent accretion using sink particles. In this first publication, we find that reducing the metallicity and UV field by a factor of 10 has no effect on star formation and minimal effect on the cold, dense star-forming gas. The cold gas depletion times are almost an order of magnitude longer than the molecular gas depletion time due to the presence of star formation in HI dominated cold gas. We study the H-2 KS relationship that arises naturally within the simulations and find a near-linear power-law index of N = 1.09 +/- 0.014 in our fiducial 10 per cent solar metallicity model. As the metallicity and UV field are reduced, this becomes moderately steeper, with a slope of N = 1.24 +/- 0.022 for our 1 per cent solar metallicity and 1 per cent solar UV field model.