Wolfgang Tichy
Conformally curved binary black hole initial data including tidal
deformations and outgoing radiation
Nathan K. Johnson-McDaniel,
Nicolas Yunes,
Wolfgang Tichy,
Benjamin J. Owen,
arXiv:0907.0891 [gr-qc]
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(v^4) in the binary's orbital
velocity v, and thus the resulting data, like the O(v^4) 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(v^5) throughout the timeslice; we also
generate an extension to the data set that has uncontrolled remainders of
O(v^6) in the purely PN portion of the timeslice (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. Due to 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.
We have already coded this data set
into Maple scripts, which were then converted to C code. Both the
scripts and codes are freely available to anyone who is interested
in evolving or otherwise studying the data.
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Documentation: README
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Order v^4 (O4):
C-files,
Maple 12 Scripts,
Backward Compatible Maple Scripts,
Maple Scripts in text format
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Order v^4 without high-order corrections to octopole moments (O4_NoOct):
C-files,
Maple 12 Scripts,
Backward Compatible Maple Scripts,
Maple Scripts in text format
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Order v^5 (O5):
C-files,
Maple 12 Scripts,
Backward Compatible Maple Scripts,
Maple Scripts in text format
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State of the Art (all):
C-files,
Maple 12 Scripts,
Backward Compatible Maple Scripts,
Maple Scripts in text format