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 Omega. For small Omega, 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 approximate to0.03 to approximate to0.05, 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.