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Register a new userRio: A new computational framework for accurate initial data of binary black holes
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We present a computational framework (Rio) in the ADM 3+1 approach for numerical relativity. This work enables us to carry out high resolution calculations for initial data of two arbitrary black holes. We use the transverse conformal treatment, the Bowen-York and the puncture methods. For the numerical solution of the Hamiltonian constraint we use the domain decomposition and the spectral decomposition of Galerkin-Collocation. The nonlinear numerical code solves the set of equations for the spectral modes using the standard Newton-Raphson method, LU decomposition and Gaussian quadratures. We show the convergence of the Rio code. This code allows for easy deployment of large calculations. We show how the spin of one of the black holes is manifest in the conformal factor.
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We obtain an explicit solution of the momentum constraint for conformally flat, maximal slicing, initial data which gives an alternative to the purely longitudinal extrinsic curvature of Bowen and York. The new solution is related, in a precise form, with the extrinsic curvature of a Kerr slice. We study these new initial data representing spinning black holes by numerically solving the Hamiltonian constraint. They have the following features: i) Contain less radiation, for all allowed values of the rotation parameter, than the corresponding single spinning Bowen-York black hole. ii) The maximum rotation parameter $J/m^2$ reached by this solution is higher than that of the purely longitudinal solution allowing thus to describe holes closer to a maximally rotating Kerr one. We discuss the physical interpretation of these properties and their relation with the weak cosmic censorship conjecture. Finally, we generalize the data for multiple black holes using the ``puncture and isometric formulations.
We present improvements to construction of binary black hole initial data used in SpEC (the Spectral Einstein Code). We introduce new boundary conditions for the extended conformal thin sandwich elliptic equations that enforce the excision surfaces to be slightly inside rather than on the apparent horizons, thus avoiding extrapolation into the black holes at the last stage of initial data construction. We find that this improves initial data constraint violations near and inside the apparent horizons by about 3 orders of magnitude. We construct several initial data sets that are intended to be astrophysically equivalent but use different free data, boundary conditions, and initial gauge conditions. These include free data chosen as a superposition of two black holes in time-independent horizon-penetrating harmonic and damped harmonic coordinates. We also implement initial data for which the initial gauge satisfies the harmonic and damped harmonic gauge conditions; this can be done independently of the free data, since this amounts to a choice of the time derivatives of the lapse and shift. We compare these initial data sets by evolving them. We show that the gravitational waveforms extracted during the evolution of these different initial data sets agree very well after excluding initial transients. However, we do find small differences between these waveforms, which we attribute to small differences in initial orbital eccentricity, and in initial BH masses and spins, resulting from the different choices of free data. Among the cases considered, we find that superposed harmonic initial data leads to significantly smaller transients, smaller variation in BH spins and masses during these transients, smaller constraint violations, and more computationally efficient evolutions. Finally, we study the impact of initial data choices on the construction of zero-eccentricity initial data.
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 binarys 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 $3leq lleq8$ 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.
The production of numerical relativity waveforms that describe quasicircular binary black hole mergers requires high-quality initial data, and an algorithm to iteratively reduce residual eccentricity. To date, these tools remain closed source, or in commercial software that prevents their use in high performance computing platforms. To address these limitations, and to ensure that the broader numerical relativity community has access to these tools, herein we provide all the required elements to produce high-quality numerical relativity simulations in supercomputer platforms, namely: open source parameter files to numerical simulate spinning black hole binaries with asymmetric mass-ratios; open source $texttt{Python}$ tools to produce high-quality initial data for numerical relativity simulations of spinning black hole binaries on quasi-circular orbits; open source $texttt{Python}$ tools for eccentricity reduction, both as stand-alone software and deployed in the $texttt{Einstein Toolkit}$s software infrastructure. This open source toolkit fills in a critical void in the literature at a time when numerical relativity has an ever increasing role in the study and interpretation of gravitational wave sources. As part of our community building efforts, and to streamline and accelerate the use of these resources, we provide tutorials that describe, step by step, how to obtain and use these open source numerical relativity tools.
Black hole (BH) shadows in dynamical binary BHs (BBHs) have been produced via ray-tracing techniques on top of expensive fully non-linear numerical relativity simulations. We show that the main features of these shadows are captured by a simple quasi-static resolution of the photon orbits on top of the static double-Schwarzschild family of solutions. Whilst the latter contains a conical singularity between the line separating the two BHs, this produces no major observable effect on the shadows, by virtue of the underlying cylindrical symmetry of the problem. This symmetry is also present in the stationary BBH solution comprising two Kerr BHs separated by a massless strut. We produce images of the shadows of the exact stationary co-rotating (even) and counter-rotating (odd) stationary BBH configurations. This allow us to assess the impact on the binary shadows of the intrinsic spin of the BHs, contrasting it with the effect of the orbital angular momentum.
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