Adapted gauge to a quasilocal measure of the black holes recoil

We explore different gauge choices in the moving puncture formulation in order to improve the accuracy of a linear momentum measure evaluated on the horizon of the remnant black hole produced by the merger of a binary. In particular, motivated by the study of gauges in which m eta takes on a constant value, we design a gauge via a variable shift parameter m eta((r) over right arrow (t)). This new parameter takes a low value asymptotically, as well as at the locations of the orbiting punctures, and then takes on a value of approximately 2 at the final hole horizon. This choice then follows the remnant black hole as it moves due to its net recoil velocity. We find that this choice keeps the accuracy of the binary evolution. Furthermore, if the asymptotic value of the parameter m eta is chosen about or below 1.0, it produces more accurate results for the recoil velocity than the corresponding evaluation of the radiated linear momentum at infinity, for typical numerical resolutions. Detailed studies of an unequal mass q = m(1)/m(2) = 1/3 nonspinning binary are provided and then verified for other mass ratios (q = 1/2, 1/5) and spinning (q = 1) binary black hole mergers.