The little-studied cluster Berkeley 90. III. Cluster parameters
  The open cluster Berkeley 90 is the home to one of the most massive binary
systems in the Galaxy, LS III +46$^{\circ}$11, formed by two identical, very
massive stars (O3.5 If* + O3.5 If*), and a second early-O system (LS III
+46$^{\circ}$12 with an O4.5 IV((f)) component at least). Stars with spectral
types earlier than O4 are very scarce in the Milky Way, with no more than 20
examples. The formation of such massive stars is still an open question today,
and thus the study of the environments where the most massive stars are found
can shed some light on this topic. To this aim, we determine the properties and
characterize the population of Berkeley 90 using optical, near-infrared and
WISE photometry and optical spectroscopy. This is the first determination of
these parameters with accuracy. We find a distance of $3.5^{+0.5}_{-0.5}$ kpc
and a maximum age of 3 Ma. The cluster mass is around $1000$ $M_{\odot}$
(perhaps reaching $1500$ $M_{\odot}$ if the surrounding population is added),
and we do not detect candidate runaway stars in the area. There is a second
population of young stars to the Southeast of the cluster that may have formed
at the same time or slightly later, with some evidence for low-activity ongoing
star formation.
