Numerically generated quasiequilibrium orbits of black holes: Circular or eccentric?

We make a comparison between results from numerically generated, quasiequilibrium configurations of compact binary systems of black holes in close orbits, and results from the post-Newtonian (PN) approximation. The post-Newtonian results are accurate through third PN order [O(v/c)⁶ beyond Newtonian gravity], and include rotational and spin-orbit effects, but are generalized to permit orbits of nonzero eccentricity. Both treatments ignore gravitational radiation reaction. The energy E and angular momentum J of a given configuration are compared between the two methods as a function of the orbital angular frequency Ω. For small Ω, corresponding to orbital separations a factor of two larger than that of the innermost stable orbit, we find that, if the orbit is permitted to be slightly eccentric, with e ranging from ≈0.03 to ≈0.05, and with the two objects initially located at the orbital apocenter (maximum separation), our PN formulas give much better fits to the numerically generated data than do any circular-orbit PN methods, including various ``effective one-body'' resummation techniques. We speculate that the approximations made in solving the initial value equations of general relativity numerically may introduce a spurious eccentricity into the orbits.