Old open clusters and the Galactic metallicity gradient: Berkeley 20,
  Berkeley 66, and Tombaugh 2
  To study the crucial range of Galactocentric distances between 12 and 16 kpc,
where little information is available, we have obtained VI CCD imaging of
Berkeley 20 and BVI CCD imaging of Berkeley 66 and Tombaugh 2, three distant,
old open clusters. Using the synthetic colour magnitude diagram (CMD) technique
with three types of evolutionary tracks of different metallicities, we have
determined age, distance, reddening and indicative metallicity of these
systems. The CMD of Be 20 is best reproduced by stellar models with a
metallicity about half of solar (Z=0.008 or 0.01), in perfect agreement with
high resolution spectroscopic estimates. Its age is between 5 and 6 Gyr from
stellar models with overshooting and between 4.3 and 4.5 Gyr from models
without it. The distance modulus from the best fitting models is always
(m-M)0=14.7 (corresponding to a Galactocentric radius of about 16 kpc), and the
reddening E(B-V) ranges between 0.13 and 0.16. A slightly lower metallicity (Z
~ 0.006) appears to be more appropriate for Be 66. This cluster is younger,
(age of 3 Gyr), and closer, (m-M)0=13.3 (i.e., at 12 kpc from the Galactic
centre), than Be 20, and suffers from high extinction, 1.2 < E(B-V) < 1.3,
variable at the 2-3 per cent level. Finally, the results for To 2 indicate that
it is an intermediate age cluster, with an age of about 1.4 Gyr or 1.6-1.8 Gyr
for models without and with overshooting, respectively. The metallicity is
about half of solar (Z=0.006 to 0.01), in agreement with spectroscopic
determinations. The distance modulus is (m-M)0=14.5, implying a distance of
about 14 kpc from the Galactic centre; the reddening E(B-V) is 0.31-0.4,
depending on the model and metallicity, with a preferred value around 0.34.
