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Stellar Radial Velocities in the Old Open Cluster M67 (NGC 2682) I. Memberships, Binaries, and Kinematics

(Abridged) We present results from 13776 radial-velocity (RV) measurements of 1278 candidate members of the old (4 Gyr) open cluster M67 (NGC 2682). The measurements are the results of a long-term survey that includes data from seven telescopes with observations for some stars spanning over 40 years. For narrow-lined stars, RVs are measured with precisions ranging from about 0.1 to 0.8 km/s. The combined stellar sample reaches from the brightest giants in the cluster down to about 4 magnitudes below the main-sequence turnoff (V = 16.5), covering a mass range of about 1.34 MSun to 0.76 MSun. Spatially, the sample extends to a radius of 30 arcmin (7.4 pc in projection at a distant of 850 pc or 6-7 core radii). We find M67 to have a mean RV of +33.64 km/s (with an internal precision of +/- 0.03 km/s). For stars with >=3 measurements, we derive RV membership probabilities and identify RV variables, finding 562 cluster members, 142 of which show significant RV variability. We use these cluster members to construct a color-magnitude diagram and identify a rich sample of stars that lie far from the standard single star isochrone, including the well-known blue stragglers, sub-subgiants and yellow giants. These exotic stars have a binary frequency of (at least) 80%, more than three times that detected for stars in the remainder of the sample. We confirm that the cluster is mass segregated, finding the binaries to be more centrally concentrated than the single stars in our sample at the 99.8% confidence level. The blue stragglers are centrally concentrated as compared to the solar-type main-sequence single stars in the cluster at the 99.7% confidence level. Accounting for both measurement precision and undetected binaries, we derive a RV dispersion in M67 of 0.59 +0.07 -0.06 km/s, which yields a virial mass for the cluster of 2100 +610 -550 MSun. WIYN Open Cluster Study. LXVII.