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We present a series of numerical simulations that explore how the `X-factor',$X_{CO}$ -- the conversion factor between the observed integrated CO emissionand the column density of molecular hydrogen -- varies with the environmentalconditions in which a molecular cloud is placed. Our investigation is centredaround two environmental conditions in particular: the cosmic ray ionisationrate (CRIR) and the strength of the interstellar radiation field (ISRF). Sinceboth these properties of the interstellar medium have their origins in massivestars, we make the assumption in this paper that both the strength of the ISRFand the CRIR scale linearly with the local star formation rate (SFR). The cloudmodelling in this study first involves running numerical simulations thatcapture the cloud dynamics, as well as the time-dependent chemistry, and ISMheating and cooling. These simulations are then post-processed with a lineradiative transfer code to create synthetic 12CO (1-0) emission maps from which$X_{CO}$ can be calculated. We find that for 1e4 solar mass virialised cloudswith mean density 100 cm$^{-3}$, $X_{CO}$ is only weakly dependent on the localSFR, varying by a factor of a few over two orders of magnitude in SFR. Incontrast, we find that for similar clouds but with masses of 1e5 solar masses,the X-factor will vary by an order of magnitude over the same range in SFR,implying that extra-galactic star formation laws should be viewed with caution.However, for denser ($10^4$ cm$^{-3}$), super-virial clouds such as those foundat the centre of the Milky Way, the X-factor is once again independent of thelocal SFR.

Does the CO-to-H2 conversion factor depend on the star formation rate?