Star formation rates and efficiencies in the Galactic Centre
  The inner few hundred parsecs of the Milky Way harbours gas densities,
pressures, velocity dispersions, an interstellar radiation field and a cosmic
ray ionisation rate orders of magnitude higher than the disc; akin to the
environment found in star-forming galaxies at high-redshift. Previous studies
have shown that this region is forming stars at a rate per unit mass of dense
gas which is at least an order of magnitude lower than in the disc, potentially
violating theoretical predictions. We show that all observational star
formation rate diagnostics - both direct counting of young stellar objects and
integrated light measurements - are in agreement within a factor two, hence the
low star formation rate is not the result of the systematic uncertainties that
affect any one method. As these methods trace the star formation over different
timescales, from $0.1 - 5$ Myr, we conclude that the star formation rate has
been constant to within a factor of a few within this time period. We
investigate the progression of star formation within gravitationally bound
clouds on $\sim$ parsec scales and find $1 - 4$ per cent of the cloud masses
are converted into stars per free-fall time, consistent with a subset of the
considered "volumetric" star formation models. However, discriminating between
these models is obstructed by the current uncertainties on the input
observables and, most importantly and urgently, by their dependence on
ill-constrained free parameters. The lack of empirical constraints on these
parameters therefore represents a key challenge in the further verification or
falsification of current star formation theories.
