A study of the Czernik 2 and NGC 7654 open clusters using CCD UBV
  photometric and Gaia EDR3 data
  We analysed the open clusters Czernik 2 and NGC 7654 using CCD UBV
photometric and Gaia Early Data Release 3 (EDR3) photometric and astrometric
data. Structural parameters of the two clusters were derived, including the
physical sizes of Czernik 2 being r=5 and NGC 7654 as 8 min. We calculated
membership probabilities of stars based on their proper motion components as
released in the Gaia EDR3. To identify member stars of the clusters, we used
these membership probabilities taking into account location and the impact of
binarity on main-sequence stars. We used membership probabilities higher than
$P=0.5$ to identify 28 member stars for Czernik 2 and 369 for NGC 7654. We
estimated colour-excesses and metallicities separately using two-colour
diagrams to derive homogeneously determined parameters. The derived $E(B-V)$
colour excess is 0.46(0.02) mag for Czernik 2 and 0.57(0.04) mag for NGC 7654.
Metallicities were obtained for the first time for both clusters, -0.08(0.02)
dex for Czernik 2 and -0.05(0.01) dex for NGC 7654. Keeping the reddening and
metallicity as constant quantities, we fitted PARSEC models using
colour-magnitude diagrams, resulting in estimated distance moduli and ages of
the two clusters. We obtained the distance modulus for Czernik 2 as 12.80(0.07)
mag and for NGC 7654 as 13.20(0.16) mag, which coincide with ages of 1.2(0.2)
Gyr and 120(20) Myr, respectively. The distances to the clusters were
calculated using the Gaia EDR3 trigonometric parallaxes and compared with the
literature. We found good agreement between the distances obtained in this
study and the literature. Present day mass function slopes for both clusters
are comparable with the value of Salpeter (1955), being X=-1.37(0.24) for
Czernik 2 and X=-1.39(0.19) for NGC 7654.
