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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 (Be 20), and   BVI   CCD imaging of Berkeley 66 (Be 66) and Tombaugh 2 (To 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 the 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  τ  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,  τ= 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  τ  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.

Old open clusters and the Galactic metallicity gradient: Berkeley 20, Berkeley 66 and Tombaugh 2 ★