Observed Orbital Eccentricities

For binaries with periods of more than a few weeks, nearly all eccentricities from zero (circular) to nearly one (highly elliptical) are possible. What are the average characteristics and limiting values? I considered the 1169 spectroscopic and visual systems with known orbital elements and B0-M5 dwarf primaries. The average eccentricities as a function of orbital period show a very systematic behavior. For systems with periods greater than about 1000 days, all eccentricities are equally probable, showing that in the process of binary formation, no specific eccentricities are favored. It is well known that for periods of a few days, all systems have been circularized by tidal interactions. For periods between a few days and 1000 days, the mean eccentricities increase from zero to a mean asymptotic value of 0.5. The upper limiting eccentricities are 0.8 for periods of months, 0.7 for periods of weeks, and 0.3 for periods around one week. Double-lined binaries tend to have higher mean eccentricities than single-lined ones of the same periods in accord with Kepler's third law because they have greater total masses and hence larger separations. Systems with giant primaries have the same behavior except they are circularized for periods less than about 70 days.