# Binary Black Hole Mergers in Gaseous Disks: Simulations in General Relativity

- Brian D. Farris
- Yuk Tung Liu
- Stuart L. Shapiro

*University of Illinois at Urbana-Champaign*
## Abstract

Simultaneous gravitational and electromagnetic wave observations of merging black hole binaries (BHBHs) can
provide unique opportunities to study gravitation physics, accretion and cosmology. Here we perform fully general
relativistic, hydrodynamic simulations of equal-mass, nonspinning BHBHs coalescing in a circumbinary disk. We
evolve the metric using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of Einstein's field equations
with standard moving puncture gauge conditions. We handle the hydrodynamics via a high-resolution shock-capturing
(HRSC) scheme. We track the inspiral starting from a binary separation of 10M, where M is the total binary mass.
We take the disks to have an inner radius at R_{in}≈ 15M to account for the hollow created by the binary torques. Our
disks extend to R ≈ 65M and have an initial scale height of H/R ≈ 0.03-0.11. The gas is governed by a Γ-law EOS,
with Γ equal to 5/3, 4/3, and 1.1. Disks are allowed to relax in the "early inspiral" epoch to provide
quasistationary realistic initial data. We then evolve the metric and matter during the "late inspiral and merger"
epoch. The later simulations are designed to track BHBH inspiral following disk-binary decoupling, through merger
and ringdown, terminating before viscosity has time to fill the hollow about the remnant. We compute the gas flow
and accretion rate and estimate the electromagnetic luminosity due to bremsstrahlung and synchrotron emission as
a perturbation for optically thin disks. The synchrotron component of the luminosity peaks in the infrared band
and should be detectable by WFIRST and possibly the LSST for a 10^{8} M_{ʘ} binary embedded in a disk with a density
n ~ 10^{12}/cm^{3} at z = 1, beginning with a maximum value of L ~ 10^{46} n_{12}^{2} M_{8}^{ 3} erg/s at decoupling, and decreasing
steadily over a timescale of ~100 M_{8} hours to a value of L ~ 10^{45} n_{12}^{2} M_{8}^{ 3} erg/s at merger.

arXiv:1105.2821v1

## Rendering

For this simulation we use both 2D and 3D rendering to illustrate our data. When comparing the two, there are two important things to consider: 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 3D rendering, we integrate rays from the observer through 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.