New Cepheid variables in the young open clusters Berkeley 51 and
  Berkeley 55
  As part of a wider investigation of evolved massive stars in Galactic open
clusters, we have spectroscopically identified three candidate classical
Cepheids in the little-studied clusters Berkeley 51, Berkeley 55 and NGC 6603.
Using new multi-epoch photometry, we confirm that Be 51 #162 and Be 55 #107 are
bona fide Cepheids, with pulsation periods of 9.83+/-0.01 d and 5.850+/-0.005 d
respectively, while NGC 6603 star W2249 does not show significant photometric
variability. Using the period-luminosity relationship for Cepheid variables, we
determine a distance to Be 51 of 5.3(+1.0,-0.8) kpc and an age of 44(+9,-8)
Myr, placing it in a sparsely-attested region of the Perseus arm. For Be 55, we
find a distance of 2.2+/-0.3 kpc and age of 63(+12,-11) Myr, locating the
cluster in the Local arm. Taken together with our recent discovery of a
long-period Cepheid in the starburst cluster VdBH222, these represent an
important increase in the number of young, massive Cepheids known in Galactic
open clusters. We also consider new Gaia (data release 2) parallaxes and proper
motions for members of Be 51 and Be 55; the uncertainties on the parallaxes do
not allow us to refine our distance estimates to these clusters, but the
well-constrained proper motion measurements furnish further confirmation of
cluster membership. However, future final Gaia parallaxes for such objects
should provide valuable independent distance measurements, improving the
calibration of the period-luminosity relationship, with implications for the
distance ladder out to cosmological scales.
