Global survey of star clusters in the Milky Way VI. Age distribution and
  cluster formation history
  The all-sky Milky Way Star Clusters (MWSC) survey provides uniform and
precise ages and other parameters for a variety of clusters in the Solar
Neighbourhood. We construct the cluster age distribution, investigate its
spatial variations, and discuss constraints on cluster formation scenarios of
the Galactic disk during the last 5 Gyrs. Due to the spatial extent of the
MWSC, we consider spatial variations of the age distribution along
galactocentric radius $R_G$, and along $Z$-axis. For the analysis of the age
distribution we use 2242 clusters, which all lie within roughly 2.5 kpc of the
Sun. To connect the observed age distribution to the cluster formation history
we build an analytical model based on simple assumptions on the cluster initial
mass function and on the cluster mass-lifetime relation, fit it to the
observations, and determine the parameters of the cluster formation law.
Comparison with the literature shows that earlier results strongly
underestimated the number of evolved clusters with ages $t\gtrsim 100$ Myr.
Recent studies based on all-sky catalogues agree better with our data, but
still lack the oldest clusters with ages $t\gtrsim 1$ Gyr. We do not observe a
strong variation in the age distribution along $R_G$, though we find an
enhanced fraction of older clusters ($t>1$ Gyr) in the inner disk. In contrast,
the distribution strongly varies along $Z$. The high altitude distribution
practically does not contain clusters with $t<1$ Gyr. With simple assumptions
on the cluster formation history, cluster initial mass function and cluster
lifetime we can reproduce the observations. Cluster formation rate and cluster
lifetime are strongly degenerate, which does not allow us to disentangle
different formation scenarios. In all cases the cluster formation rate is
strongly declining with time, and the cluster initial mass function is very
shallow at the high mass end. (abridged)
