The eccentricity wall: why a circular pair does not capture a light body

The approximate absorptivity formula of note FR-TC-12 erred in the final eccentricity when two heavy stars meet a light one. We show that the cause is a threshold: in 225,000 planar scatterings with zero total angular momentum, a body with mass less than about 0.9 times the reduced mass of the pair is not captured when the eccentricity of the pair is below a value that ranges from about 0.2 to 0.9 as the body gets lighter. Below this wall, the absorptivity is below 1% with 95% confidence. The reduced mass of the pair unites an equal and an unequal pair better than the other normalizations tested. Including the wall raises the explained fraction of the absorptivity of the light channel outside the fit from 0.45 to 0.93, although the formula still does not reach the measured absorptivity in the free falls. In 48,000 free falls, 82% to 88% of the escapes come from a short last episode, whose final pair inherits the shape of the pair of the previous excursion, and with unequal masses the final eccentricity depends on the age of the system. With the same criterion of chaotic origin in absorption and in emission, the flux theory with the measured absorptivity passes 8 of 9 tests of the final eccentricity and all tests of the escape chances, which corrects the method of the previous notes.