Does the CO-to-H2 conversion factor depend on the star formation rate?
  We present a series of numerical simulations that explore how the `X-factor',
$X_{CO}$ -- the conversion factor between the observed integrated CO emission
and the column density of molecular hydrogen -- varies with the environmental
conditions in which a molecular cloud is placed. Our investigation is centred
around two environmental conditions in particular: the cosmic ray ionisation
rate (CRIR) and the strength of the interstellar radiation field (ISRF). Since
both these properties of the interstellar medium have their origins in massive
stars, we make the assumption in this paper that both the strength of the ISRF
and the CRIR scale linearly with the local star formation rate (SFR). The cloud
modelling in this study first involves running numerical simulations that
capture the cloud dynamics, as well as the time-dependent chemistry, and ISM
heating and cooling. These simulations are then post-processed with a line
radiative 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 clouds
with mean density 100 cm$^{-3}$, $X_{CO}$ is only weakly dependent on the local
SFR, varying by a factor of a few over two orders of magnitude in SFR. In
contrast, 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 found
at the centre of the Milky Way, the X-factor is once again independent of the
local SFR.
