Relativistic Simulations of Compact Binary Mergers: 3D Renderings

University of Illinois at Urbana-Champaign


The calculation of a binary black hole inspiral and coalescence is one of the great triumphs of numerical relativity. The successful solution to this problem has required contributions from many people working over many years. The chief ingredients include a stable algorithm to solve Einstein's field equations in 3+1 dimensions, valid initial data for two black holes in quasiequilibrium circular orbit, a means of avoiding the black hole spacetime singularity on the computational grid, a good gauge choice for performing the evolution, and adaptivity to achieve high resolution both in the strong-field region near the black holes and in the far zone where the gravitational waves are measured. By now, solving binary black hole coalescence on computers has become almost routine.

By simulating the gravitational radiation waveforms from black hole-black hole (BHBH) mergers, we hope to test strong-field general relativity by comparing theoretical waveform templates with measurements made by ground-based laser interferometers like LIGO (Laser Inteferometer Gravitational Wave Observatory), VIRGO, GEO, and TAMA, and space-based interferometers like LISA (Laser Interferometer Space Antenna). These numerical calculations are especially important because BHBH binaries are expected to be among the most promising sources of gravitational waves. Also, BHBH merger calculations serve as a warm-up for the calculations of binary black hole-neutron star (BHNS) mergers. BHNS merger calculations are more challenging because of the presence of hydrodynamic matter.

The representative BHBH calculations summarized here were performed with the Illinois relativistic hydrodynamics code with the hydrodynamics turned "off" to solve the pure vacuum problem. The code utilizes the BSSN scheme for evolving the Einstein equations and employs AMR (adaptive mesh refinement). The initial data is "puncture" data for a BHBH binary in a quasicircular orbit and the evolution is performed with "moving puncture" gauge conditions.

Black hole-neutron star (BHNS) binary mergers are candidate engines for generating both short-hard gamma-ray bursts (SGRBs) and detectable gravitational waves. Using our most recent conformal thin-sandwich BHNS initial data and our fully general relativistic hydrodynamics code, which is now AMR-capable, we are able to efficiently and accurately simulate these binaries from large separations through inspiral, merger, and ringdown. We evolve the metric using the BSSN formulation with the standard moving puncture gauge conditions and handle the hydrodynamics with a high-resolution shock-capturing scheme. We explore the effects of BH spin (aligned and anti-aligned with the orbital angular momentum) by evolving three sets of initial data with BH:NS mass ratio q=3: the data sets are nearly identical, except the BH spin is varied between SBH/MBH2 = -0.5 (anti-aligned), 0.0, and 0.75. The number of orbits before merger increases with SBH/MBH2, as expected. We also study the nonspinning BH case in more detail, varying q between 1, 3, and 5. We calculate gravitational waveforms for the cases we simulate and compare them to binary black-hole waveforms. Only a small disk (< 0.01 Msun) forms for the anti-aligned spin case (SBH/MBH2 = -0.5) and for the most extreme mass ratio case (q=5). By contrast, a massive (Mdisk is about 0.2 Msun), hot disk forms in the rapidly spinning (SBH/MBH2 = 0.75) aligned BH case. Such a disk could drive a SGRB, possibly by, e.g., producing a copious flux of neutrino-antineutino pairs. Here we show the case with q=3 and SBH/MBH2 = 0.

Phys.Rev.D79:044024 (2009), arXiv:0812.2245v2

3D Rendering

There are two things to consider when comparing our previous 2D view in the orbital plane to volumetric rendering: spacial mappings and color mappings. In the 2D view, each point on the screen maps directly to a point in the orbital plane. The value of the mass per volume at that point corresponds to a specific color of our choice. In volumetric rendering, we integrate rays from the observer thru a viewing plane. Each point on that viewing plane corresponds to a point on the screen, but this time we consider all points along the ray. Each ray gives a mass per area which corresponds to a specific color of our choice. The result reveals the structure of a density distribution in 3D. Note the difference between this and the way we perceive clouds is in the way light scatters in each volume element, giving bright and shadowy areas in real life. The software we used to achieve this is ZIBAmira from Zuse Institute Berlin, to which we give our thanks.

University of Illinois at Urbana-Champaign

BHBH without spin
SBH / MBH2 = 0.00, mass ratio q = 1.00
BHBH with spin
SBH / MBH2 = 0.85, mass ratio q = 1.00
SBH / MBH2 = 0.00, mass ratio q = 3.00