I'd think binary systems made up of similarly sized objects where the orbits are in some sense "close" are almost by definition not eccentric. To get to that p

I'd think binary systems made up of similarly sized objects where the orbits are in some sense "close" are almost by definition not eccentric. To get to that point from a previously eccentric orbit they convert the eccentricity to spin. Check out this out for an example with neutron stars: https://www.youtube.com/watch?v=-JZBmgOEfdo https://www.youtube.com/watch?v=-JZBmgOEfdo As to the second part, I'd think it becomes axially symmetric in very minimal time. I don't have a good answer as to why, except that my intuition says the GW signature of blackhole mergers at the point of the merger has a frequency that appears to get infinitely fast as it radiates away the axial asymmetry.