Extremely precise age and metallicity of the open cluster NGC 2506 using
  detached eclipsing binaries
  Accurate stellar parameters of stars in open clusters can help constrain
models of stellar structure and evolution. Here we wish to determine the age
and metallicity content of the open cluster NGC 2506. To this end we
investigated three detached eclipsing binaries (DEBs; V2032, V4, and V5) for
which we determined their masses and radii, as well as four red giant branch
stars for which we determined their effective temperatures, surface gravities,
and metallicities. Three of the stars in the DEBs have masses close to the
cluster turn-off mass, allowing for extremely precise age determination.
Comparing the values for the masses and radii of the binaries to BaSTI
isochrones we estimated a cluster age of $2.01 \pm 0.10$ Gyr. This does depend
on the models used in the comparison, where we have found that the inclusion of
convective core-overshooting is necessary to properly model the cluster. From
red giant branch stars we determined values for the effective temperatures, the
surface gravities, and the metallicities. From these we find a cluster
metallicity of $-0.36 \pm 0.10$ dex. Using this value and the values for the
effective temperatures we determine the reddening to be E$(b - y) = 0.057 \pm
0.004$ mag. Furthermore, we derived the distance to the cluster from Gaia
parallaxes and found $3.101 \pm 0.017$ kpc, and we have performed a radial
velocity membership determination for stars in the field of the cluster.
Finally, we report on the detection of oscillation signals in $\gamma$ Dor and
$\delta$ Scuti members in data from the TESS mission, including the possible
detection of solar-like oscillations in two of the red giants.
