Deep Wide-Field Spectrophotometry of the Open Cluster M67

We present nine color CCD intermediate-band spectrophotometry of a two square degree field centered on the old open cluster M67, from 3890$\rm \AA$ to nearly 1$\mu$. These observations are taken as a part of the BATC (Beijing-Arizona-Taipei-Connecticut) Color Survey of the Sky, for both scientific and calibration reasons. With these data we show that the BATC survey can reach its goal of obtaining spectrophotometry to a zero point accuracy of 0.01 mag, and down to V = 21 with 0.3 mag random error. We fit the color-magnitude diagrams (CMDs) with Worthey's theoretical models. The net result is the excellent fit of the 4.0 Gyr, [Fe/H] = $-0.10$ model to our data, including a good fit to the main sequence (MS) turn-off. Our data are consistent with a toy model with 50\% of the stars in M67 being binaries and a random distribution of binary mass-ratios, although other models with different mass-ratio distributions cannot be ruled out. The spatial distribution and mass function (MF) of stars in M67 show marked effects of dynamical evolution and evaporation of stars from the cluster. Blue stragglers and binary stars are the most condensed within the cluster, with degree of condensation depending on mass.We find M67 to have an elongated shape, oriented at an angle of $15^{\circ}$ relative to the galactic plane. Within its tidal radius, the observed MF of M67 between 1.2 $\rm M_\odot$ and $\rm 0.8 M_\odot$ has a Salpeter slope $\rm \eta = -1.93 \pm 0.66$. For stars of mass below 0.8 $\rm M_\odot$, $\rm \eta \sim 0$. It is plausible that the leveling-off of the MF at lower masses is a result of evaporation of lower mass stars in this mass range at a rate of one every $\sim 10^7$ years. If so, it is plausible that the IMF of M67 has the canonical field value of $\rm \eta = -2.0$.