The star cluster age function in the Galactic disc with Gaia DR2: Fewer
  old clusters and a low cluster formation efficiency
  We perform a systematic reanalysis of the age distribution of Galactic open
star clusters. Using a catalogue of homogeneously determined ages for 834 open
clusters contained in a 2 kpc cylinder around the Sun and characterised with
astrometric and photometric data from the Gaia satellite, we find that it is
necessary to revise earlier works that relied on data from the Milky Way Star
Cluster survey. After establishing age-dependent completeness limits for our
sample, we find that the cluster age function in the range $6.5 < \log t<10$ is
compatible with a Schechter-type or broken power-law function, whose parameters
we determine by MCMC fitting. Our best-fit values indicate an earlier drop of
the age function (by a factor of $2-3$) with respect to the results obtained in
the last five years, and are instead more compatible with results obtained in
the early 2000s and radio observations of inner-disc clusters. Furthermore, we
find a typical destruction time-scale of $\sim1.5$ Gyr for a $10^4\, {\rm
M}_{\odot}$ cluster and a present-day cluster-formation rate of
$0.55_{-0.15}^{+0.19}$ Myr$^{-1}$kpc$^{-2}$, suggesting that only
$16_{-8}^{+11}$ \% of all stars born in the solar neighbourhood form in bound
clusters. Accurate cluster-mass measurements are now needed to place more
precise constraints on open-cluster formation and evolution models.
