Numerical black hole initial data with low eccentricity based on post-Newtonian orbital parameters

Black hole binaries on noneccentric orbits form an important subclass of gravitational wave sources, but it is a nontrivial issue to construct numerical initial data with minimal initial eccentricity for numerical simulations. We compute post-Newtonian orbital parameters for quasispherical orbits using the method of Buonanno, Chen and Damour, (2006) and examine the resulting eccentricity in numerical simulations. Four different methods are studied resulting from the choice of Taylor-expanded or effective-one-body Hamiltonians, and from two choices for the energy flux. For equal-mass, nonspinning binaries the approach succeeds in obtaining low-eccentricity numerical initial data with an eccentricity of about e = 0.002 for rather small initial separations of D >= 10M. The eccentricity increases for unequal masses and for spinning black holes, but remains smaller than that obtained from previous post-Newtonian approaches. The effective-one-body Hamiltonian offers advantages for decreasing initial separation as expected, but in the context of this study also performs significantly better than the Taylor-expanded Hamiltonian for binaries with spin. For mass ratio 4: 1 and vanishing spin, the eccentricity reaches e = 0.004. For mass ratio 1:1 and aligned spins of size 0.85M(2) the eccentricity is about e = 0.07 for the Taylor method and e = 0.014 for the effective-one-body method.