BEER analysis of Kepler and CoRoT light curves. III. Spectroscopic confirmation of seventy new beaming binaries discovered in CoRoT light curves

(abridged for arXiv) The BEER algorithm searches stellar light curves for the BEaming, Ellipsoidal, and Reflection photometric modulations that are caused by a short-period companion. Applying the search to the first five long-run center CoRoT fields, we identified $481$ non-eclipsing candidates with periodic flux amplitudes of $0.5-87$ mmag. Optimizing the Anglo-Australian-Telescope pointing coordinates and the AAOmega fiber-allocations with dedicated softwares, we acquired six spectra for $231$ candidates and seven spectra for another $50$ candidates in a seven-night campaign. Analysis of the red-arm AAOmega spectra, which covered the range of $8342-8842\AA{}$, yielded a radial-velocity precision of $\sim1$ km/s. Spectra containing lines of more than one star were analyzed with the two-dimensional correlation algorithm TODCOR. The measured radial velocities confirmed the binarity of seventy of the BEER candidates$-45$ single-line binaries, $18$ double-line binaries, and $7$ diluted binaries. We show that red giants introduce a major source of false candidates and demonstrate a way to improve BEER's performance in extracting higher fidelity samples from future searches of CoRoT light curves. The periods of the confirmed binaries span a range of $0.3-10$ days and show a rise in the number of binaries per $\Delta$log$P$ toward longer periods. The estimated mass ratios of the double-line binaries and the mass ratios assigned to the single-line binaries, assuming an isotropic inclination distribution, span a range of $0.03-1$. On the low-mass end, we have detected two brown-dwarf candidates on a $\sim1$ day period orbit. This is the first time non-eclipsing beaming binaries are detected in CoRoT data, and we estimate that $\sim300$ such binaries can be detected in the CoRoT long-run light curves.