Binary galaxy orbit statistics. I - Fixed mass and major axis

Averages for the projected separation, squared radial velocity difference, and the product of these, are presented for a binary galaxy system of fixed mass and major axis, but any orbital eccentricity. The average of the product varies by a factor about 3 for eccentricities from 0 to 1.0. For circular orbits, the results agree with those of Page (1952, 1960, 1961), but for linear orbits his mass estimate is too small by a factor 6. The mutual regressions of the velocity and separation on each other are calculated, and are presented in such a way as to exhibit the relative likelihood of occupation of the different parts of the regression curves. 'Isopleths' for the probability distribution are presented for a few values of the eccentricity to illustrate the underlying cause of pileup at certain parts of the regression curves. It is concluded that previous analyses were inadequate for failing to take into account that the regression curves represent in many cases a distribution that is almost wholly depopulated through most of the range. It is evident that the data are insufficient to draw a firm conclusion about the distribution of eccentricities.