Molecular gas in low-metallicity starburst galaxies: Scaling relations
  and the CO-to-H$_2$ conversion factor
  We study the molecular content and the star formation efficiency of 21 Blue
Compact Dwarfs (BCDs). We present CO(1-0) and (2-1) observations, further
supplemented with additional CO measurements and multiwavelength ancillary data
from the literature. We find the CO luminosity to be correlated with the
stellar and HI masses, SFR tracers, the size of the starburst and its
metallicity. BCDs appear offset from the Schmidt-Kennicutt (SK) law, showing
extremely low ($\lesssim$0.1 Gyr) H2 and H2+HI depletion timescales. The
departure from the SK law is smaller when considering H2+HI rather than H2
only, and is larger for BCDs with lower metallicity and higher specific SFR.
Thus, the molecular fraction and H2 depletion timescale of BCDs is found to be
strongly correlated with metallicity. Using this and assuming that the
empirical correlation found between the specific SFR and galaxy-averaged H2
depletion timescale of more metal-rich galaxies extends to lower masses, we
derive a metallicity-dependent CO-to-H2 conversion factor $\alpha_{CO, Z}
\propto (Z/Z_{\odot})^{-y}$, with $y=1.5(\pm 0.3)$ in qualitative agreement
with previous determinations, dust-based measurements, and recent model
predictions. Our results suggest that in vigorously star-forming dwarfs the
fraction of H2 traced by CO decreases by a factor of about 40 from $Z \sim
Z_{\odot}$ to $Z \sim 0.1 Z_{\odot}$, leading to a strong underestimation of
the H2 mass in metal-poor systems when a Galactic $\alpha_{CO, MW}$ is
considered. Adopting $\alpha_{CO, Z}$ we find that departures from the SK law
are partially resolved. Our results suggest that starbursting dwarfs have
shorter depletion gas timescales and lower molecular fractions compared to
normal late-type disc galaxies even accounting for the molecular gas not traced
by CO emission in metal-poor environments, raising additional constraints to
model predictions (Abridged).
