Binary Properties from Cepheid Radial Velocities (CRaV)

We have examined high accuracy radial velocities of Cepheids to determine the binary frequency. The data are largely from the CORAVEL spectrophotometer and the Moscow version, with a typical uncertainty of $\leq1$~km~s$^{-1}$, and a time span from 1 to 20 years. A systemic velocity was obtained by removing the pulsation component using a high order Fourier series. From this data we have developed a list of stars showing no orbital velocity larger than $\pm1$~km~s$^{-1}$. The binary fraction was analyzed as a function of magnitude, and yields an apparent decrease in this fraction for fainter stars. We interpret this as incompleteness at fainter magnitudes, and derive the preferred binary fraction of $29\pm8$\% ( $20\pm6$\% per decade of orbital period) from the brightest 40 stars. Comparison of this fraction in this period range (1-20 years) implies a large fraction for the full period range. This is reasonable in that the high accuracy velocities are sensitive to the longer periods and smaller orbital velocity amplitudes in the period range sampled here. Thus the Cepheid velocity sample provides a sensitive detection in the period range between short period spectroscopic binaries and resolved companions. The recent identification of $\delta$ Cep as a binary with very low amplitude and high eccentricity underscores the fact that the binary fractions we derive are lower limits, to which other low amplitude systems will probably be added. The mass ratio (q) distribution derived from ultraviolet observations of the secondary is consistent with a flat distribution for the applicable period range (1 to 20 years).