Including realistic tidal deformations in binary black-hole initial data

Abstract

A shortcoming of current binary black-hole initial data is the generation of spurious gravitational radiation, so-called junk radiation, when they are evolved. This problem is a consequence of an oversimplified modeling of the binary's physics in the initial data. Since junk radiation is not astrophysically realistic, it contaminates the actual waveforms of interest and poses a numerical nuisance. The work here presents a further step towards mitigating and understanding the origin of this issue, by incorporating post-Newtonian results in the construction of constraint-satisfying binary black-hole initial data. Here we focus on including realistic tidal deformations of the black holes in the initial data, by building on the method of superposing suitably chosen black hole metrics to compute the conformal data. We describe the details of our initial data for an equal-mass and nonspinning binary, compute the subsequent relaxation of horizon quantities in evolutions, and quantify the amount of junk radiation that is generated. These results are contrasted with those obtained with the most common choice of conformally flat (CF) initial data, as well as superposed Kerr-Schild (SKS) initial data. We find that when realistic tidal deformations are included, the early transients in the horizon geometries are significantly reduced, along with smaller deviations in the relaxed black hole masses and spins from their starting values. Likewise, the junk radiation content in the $l=2$ modes is reduced by a factor of $\sim$1.7 relative to CF initial data, but only by a factor of $\sim$1.2 relative to SKS initial data. More prominently, the junk radiation content in the $3\le l\le 8$ modes is reduced by a factor of $\sim$5 relative to CF initial data, and by a factor of $\sim$2.4 relative to SKS initial data.

15 pages, 13 figures, 2 tables; minor typo fixes and text revisions

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• Toward computing gravitational initial data without elliptic solvers
• Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations
• Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations
• Construction of high precision numerical single and binary black hole initial data
• A simple method of constructing binary black hole initial data