Spinning compact binary inspiral: Independent variables and dynamically preserved spin configurations

We establish the set of independent variables suitable to monitor the complicated evolution of the spinning compact binary during the inspiral. Our approach is valid up to the second post-Newtonian order, including leading order spin-orbit, spin-spin and mass quadrupol-mass monopole effects, for generic (noncircular, nonspherical) orbits. Then we analyze the conservative spin dynamics in terms of these variables. We prove that the only binary black hole configuration allowing for spin precessions with equal angular velocities about a common intantaneous axis roughly aligned to the normal of the osculating orbit, is the equal mass and parallel (aligned or antialigned) spin configuration. This analytic result puts limitations on what particular configurations can be selected in numerical investigations of compact binary evolutions, even in those including only the last orbits of the inspiral.