WIYN Open Cluster Study. I. Deep Photometry of NGC 188

We have employed precise V and I photometry of NGC 188 at WIYN to explore thecluster luminosity function (LF) and study the cluster white dwarfs (WDs). Ourphotometry is offset by V = 0.052 (fainter) from Sandage (1962) and Eggen &Sandage (1969). All published photometry for the past three decades have beenbased on these two calibrations, which are in error by 0.05 +- 0.01. We employthe Pinsonneault etal (1998) fiducial main sequence to derive a clusterdistance modulus of 11.43 +- 0.08. We report observations that are >= 50%complete to V = 24.6 and find that the cluster central-field LF peaks at M_I ~3 to 4. This is unlike the solar neighborhood LF and unlike the LFs ofdynamically unevolved portions of open and globular clusters, which risecontinuously until M_I ~ 9.5. Although we find that >= 50% of the unresolvedcluster objects are multiple systems, their presence cannot account for theshape of the NGC 188 LF. For theoretical reasons (Terlevich 1987; Vesperini &Heggie 1997) having to do with the survivability of NGC 188 we believe thecluster is highly dynamically evolved and that the missing low luminosity starsare either in the cluster outskirts or have left the cluster altogether. Weidentify nine candidate WDs, of which we expect three to six are bona fidecluster WDs. The luminosities of the faintest likely WD indicates an age(Bergeron, Wesemael, & Beauchamp 1995) of 1.14 +- 0.09 Gyrs. This is a lowerlimit to the cluster age and observations probing to V = 27 or 28 will benecessary to find the faintest cluster WDs and independently determine thecluster age. While our age limit is not surprising for this ~6 Gyr old cluster,our result demonstrates the value of the WD age technique with its very lowinternal errors. (abridged)Comment: 26 pages, uuencoded gunzip'ed latex + 16 postscrip figures, to be published in A