Conformally curved binary black hole initial data including tidal deformations and outgoing radiation

By asymptotically matching a post-Newtonian (PN) metric to two perturbed Schwarzschild metrics, we generate approximate initial data (in the form of an approximate 4-metric) for a nonspinning black hole binary in a circular orbit. We carry out this matching through O(v4) in the binary's orbital velocity v, and thus the resulting data, like the O(v4) PN metric, are conformally curved. The matching procedure also fixes the quadrupole and octupole tidal deformations of the holes, including the 1PN corrections to the quadrupole fields. Far from the holes, we use the appropriate PN metric that accounts for retardation, which we construct using the highest-order PN expressions available to compute the binary's past history. The data set's uncontrolled remainders are thus O(v5) throughout the time slice; we also generate an extension to the data set that has uncontrolled remainders of O(v6) in the purely PN portion of the time slice (i.e., not too close to the holes). This extension also includes various other readily available higher-order terms. The addition of these terms decreases the constraint violations in certain regions, even though it does not increase the data's formal accuracy. The resulting data are smooth, since we join all the metrics together by smoothly interpolating between them. We perform this interpolation using transition functions constructed to avoid introducing excessive additional constraint violations. Because of their inclusion of tidal deformations and outgoing radiation, these data should substantially reduce both the high- and low-frequency components of the initial spurious ('junk') radiation observed in current simulations that use conformally flat initial data. Such reductions in the nonphysical components of the initial data will be necessary for simulations to achieve the accuracy required to supply Advanced LIGO and LISA with the templates necessary for parameter estimation.