Spectroscopic Binaries in Globular Clusters. I. A Search for Ultra-Hard Binaries on the Main Sequence in M4

A search for spectroscopic binaries on the main sequence of the nearby globular cluster M4 has been undertaken with Argus, the multi-object spectrograph on the CTIO 4.0m telescope. A pair of radial velocities (median precision $\simeq$ 2 km/s) separated by 11 months have been obtained for 33 turnoff dwarfs in the magnitude range 16.9 $\le$ V $\le$ 17.4. Monte-Carlo simulations have been used to derive a binary fraction, X, for systems with periods in the range 2 days $\lae {\rm P} \lae$ 3 years and mass ratios between 0.2 and 1.0. This short-period cutoff is more than an order of magnitude smaller than those of existing radial velocity surveys and is comparable to the shortest periods possible for main-sequence turnoff stars. Our survey therefore provides a first glimpse into the abundance of ``ultra-hard" spectroscopic binaries in globular clusters. Although no star shows a velocity variation larger than 14 km/s, two objects are observed to have chi-square probabilities below 0.1\%. No such stars are expected in a sample of 33. We find a best-fit binary fraction of X $\simeq$ 0.15, a value which is consistent with recent estimates based on deep HST color-magnitude diagrams, as well as with the binary fraction of X $\simeq$ 0.1 for nearby solar-type stars having similar periods and mass ratios. Our derived binary fraction suggests that exchange interactions with pre-existing binaries are a plausible means of explaining the origin of the hierarchical triple system containing the pulsar PSR 1620-26.