Redshift factor and the small mass-ratio limit in binary black hole simulations

We present a calculation of the Detweiler redshift factor in binary black hole simulations based on its relation to the surface gravity. The redshift factor has far-reaching applications in analytic approximations, gravitational self-force calculations, and conservative two-body dynamics. By specializing to nonspinning, quasicircular binaries with mass ratios ranging from m(A)/m(B) = 1 to m(A)/m(B) = 9.5 we are able to recover the leading small-mass-ratio (SMR) prediction with relative differences of order 10(-5) from simulations alone. The next-to-leading order term that we extract agrees with the SMR prediction arising from selfforce calculations, with differences of a few percent. These deviations from the first-order conservative prediction are consistent with nonadiabatic effects that can be accommodated in an SMR expansion. This fact is also supported by a comparison to the conservative post-Newtonian prediction of the redshifts. For the individual redshifts, a reexpansion in terms of the symmetric mass ratio nu does not improve the convergence of the series. However we find that when looking at the sum of the redshift factors of both back holes, z(A) + z(B), which is symmetric under the exchange of the masses, a reexpansion in nu accelerates its convergence. Our work provides further evidence of the surprising effectiveness of SMR approximations in modeling even comparable mass binary black holes.