Star-forming dwarf galaxies in the Virgo cluster: the link between
  molecular gas, atomic gas, and dust
  We present $^{12}$CO(1-0) and $^{12}$CO(2-1) observations of a sample of 20
star-forming dwarfs selected from the Herschel Virgo Cluster Survey, with
oxygen abundances ranging from 12 + log(O/H) ~ 8.1 to 8.8. CO emission is
observed in ten galaxies and marginally detected in another one. CO fluxes
correlate with the FIR 250 $\mu$m emission, and the dwarfs follow the same
linear relation that holds for more massive spiral galaxies extended to a wider
dynamical range. We compare different methods to estimate H2 molecular masses,
namely a metallicity-dependent CO-to-H2 conversion factor and one dependent on
H-band luminosity. The molecular-to-stellar mass ratio remains nearly constant
at stellar masses <~ 10$^9$ M$_{\odot}$, contrary to the atomic hydrogen
fraction, M$_{HI}$/M$_*$, which increases inversely with M$_*$. The flattening
of the M$_{H_2}$/M$_*$ ratio at low stellar masses does not seem to be related
to the effects of the cluster environment because it occurs for both
HI-deficient and HI-normal dwarfs. The molecular-to-atomic ratio is more
tightly correlated with stellar surface density than metallicity, confirming
that the interstellar gas pressure plays a key role in determining the balance
between the two gaseous components of the interstellar medium. Virgo dwarfs
follow the same linear trend between molecular gas mass and star formation rate
as more massive spirals, but gas depletion timescales, $\tau_{dep}$, are not
constant and range between 100 Myr and 6 Gyr. The interaction with the Virgo
cluster environment is removing the atomic gas and dust components of the
dwarfs, but the molecular gas appears to be less affected at the current stage
of evolution within the cluster. However, the correlation between HI deficiency
and the molecular gas depletion time suggests that the lack of gas
replenishment from the outer regions of the disc is lowering the star formation
activity.
