WIYN Open Cluster Study LXXX: HDI CCD $UBVRI$ Photometry of the Old Open
  Cluster NGC 7142 and Comparison to M67
  We present $UBVRI$ photometry of 8702 stars in a $0.5 ^\circ\times0.5 ^\circ$
field in the direction of NGC 7142, taken with the Half Degree Imager (HDI) at
the WIYN 0.9-meter telescope, to improve knowledge of this cluster's basic
parameters. Our photometry spans the ranges 10.6 - 20.4 mag in $U$, 10.6 - 22.0
mag in $B$, 10.0 - 21.8 mag in $V$, 9.2 - 20.7 mag in $R$, and 8.5 - 19.9 mag
in $I$. Using color-color diagrams that employ all four color combinations that
include $U$, versus $B-V$, we derive a reddening-metallicity relation for the
cluster, with preferred values $E(B-V$) = 0.338 $\pm$ 0.031 mag for the
left-edge fiducial of the main sequence and [Fe/H] = 0.0 $\pm$ 0.1 dex, where
the Hyades cluster has been used as an unreddened reference cluster, the
extinction relations of Cardelli have been employed, and the metallicity
dependence of the Yonsei-Yale ($Y^2$) isochrones has been assumed. Comparison
of our data to the $Y^2$ isochrones in multiple color-magnitude diagrams (CMDs)
yields distance-metallicity and age-metallicity relations, with preferred
values of $m-M\ =\ 12.65\ \pm\ 0.23$ mag and age = $4.0 ^{-0.7}_{+1.3}$ Gyr.
Re-evaluation of the parameters of M67 using Stetson's $UBVI$ photometry yields
[Fe/H] = -0.02 $\pm$ 0.05 dex, $E(B-V$) = 0.04 $\pm$ 0.01 mag, $m-M$ = 9.75
$\pm$ 0.03 mag, and age = 3.85 $\pm$ 0.17 Gyr; we thus find the metallicity and
age of the two clusters to be indistinguishable. A semi-independent analysis
adopting the parameters of M67 and shifting the fiducials of the two clusters
in six CMDs until they match strongly corroborates the values listed above. The
differences between our inferred parallaxes and the Gaia DR2 values are $87\
\pm\ 60$ $\mu$as for NGC 7142 and 48 $\pm$ 15 $\mu$as for M67, consistent with
previous studies.
