The distribution of open clusters in the Galaxy
  In this work we explore the new catalog of galactic open clusters that became
available recently, containing 1750 clusters that have been re-analysed using
the Gaia DR2 catalog to determine the stellar memberships. We used the young
open clusters as tracers of spiral arms and determined the spiral pattern
rotation speed of the Galaxy and the corotation radius, the strongest Galactic
resonance. The sample of open clusters used here increases the last one from
Dias et al. (2019) used in the previous determination of the pattern speed by
dozens objects. In addition, the distances and ages values are better
determined, using improvements to isochrone fitting and including an updated
extinction polynomial for the Gaia DR2 photometric band-passes, and the
Galactic abundance gradient as a prior for metallicity. In addition to the
better age determinations, the catalog contains better positions in the
Galactic plane and better proper motions. This allow us to discuss not only the
present space distribution of the clusters, but also the space distribution of
the clusters's birthplaces, obtained by integration of the orbits for a time
equal to their age. The value of the rotation velocity of the arms ($28.5 \pm
1.0$ km s$^{-1}$ kpc$^{-1}$) implies that the corotation radius ($R_c$) is
close to the solar Galactic orbit ($R_c/R_0 = 1.01\pm0.08$), which is supported
by other observational evidence discussed in this text. A simulation is
presented, illustrating the motion of the clusters in the reference frame of
corotation. We also present general statistics of the catalog of clusters, like
spatial distribution, distribution relative to height from the Galactic plane,
and distribution of ages and metallicity. An important feature of the space
distribution, the corotation gap in the gas distribution and its consequences
for the young clusters, is discussed.
