Spectroscopic characterization of the known O-star population in Cygnus
  OB2. Evidence of multiple star-forming bursts
  Cygnus OB2 provides a unique insight into the high-mass stellar content in
one of the largest groups of young massive stars in our Galaxy. Although
several studies of its massive population have been carried out over the last
decades, an extensive spectroscopic study of the whole known O-star population
in the association is still lacking. In this work, we created the most complete
spectroscopic census of O stars carried out so far in Cygnus OB2 using already
existing and new spectroscopy. We present the spectra for 78 O-type stars, from
which we identify new binary systems, obtain the distribution of rotational
velocities, and determine the main stellar parameters for all the stars in the
region that have not been detected as double-line spectroscopic binaries. We
also derive radii, luminosities, and masses for those stars with reliable Gaia
astrometry, in addition to creating the Hertzsprung-Russell Diagram to
interpret the evolutionary status of the association. This work has shown the
improvement reached when using accurate spectroscopic parameters and astrometry
for the interpretation of the evolutionary status of a population, revealing,
in the case of Cygnus OB2, at least two star-forming bursts at $\sim$3 and
$\sim$5 Myr. We find an apparent deficit of very fast rotators in the
distribution of rotational velocities. The inspection of the dynamical
distribution of the sample has allowed us to identify nine O stars with
peculiar proper motions and discuss a possible dynamical ejection scenario or
past supernova explosions in the region.
