Gravitational Waveforms

The gravitational wavetrain from a compact binary system may be separated into three qualitatively different phases: the inspiral, the merger, and the ringdown. During the inspiral phase, which takes up most of the binary's lifetime, gravity wave emission gradually reduces the binary separation. When the black holes get close enough, they merge into one black hole. Finally, ringdown radiation is emitted as the distorted black hole settles down to Kerr-like equilibrium. The polarization mode hx is shown for the three cases.

Here we track two spinning black holes with different mass ratios inspiralling towards each other surrounded by a gaseous disk. The evolution is followed through inspiral, merger, and ringdown. The matter is now evolved by solving the relativistic MHD equations and the gravitational field is evolved by solving the Einstein field equations via the BSSN formalism.

Shown below are two types of plots:

(1) Full 3D rendering of the hx strain in the lower hemisphere viewed from a top-down view. In this plot, values of hx close to zero are made transparent. In case B and case C, the black hole horizons are overlayed on top of the plots.

(2) Surface plots of the h+ strain on the equatorial plane. The gray hole that is cut out in the surface plot is the wave near zone.

Case A: Q1 (1:1 mass ratio)

hx Polarization (top-down view of lower hemisphere)
In the q1 case, the two black holes have equal masses. They start with initial spins $\chi=0.26$ in the equatorial plane.
Fig. 3-1: hx at time t/M = 231
 Fig. 3-2: hx at time t/M = 2846
 Fig. 3-3: hx at time t/M = 3272
Fig. 3-4: hx at time t/M = 3343
 Fig. 3-5: hx at time t/M = 3391
 Fig. 3-6: hx at time t/M = 3429
PLAY MOVIE: hx Top-Down View of Lower Hemisphere

h+ Polarization (surface plot of equatorial plane)
Fig. 3-1: hx at time t/M = 231
 Fig. 3-2: hx at time t/M = 2846
 Fig. 3-3: hx at time t/M = 3272
PLAY MOVIE: h+ Surface Plot of Equatorial Plane

Case B: q2 hx Polarization (Top View)

In the q2 case, the two black holes have a 2:1 mass ratio. They start with initial spins $\chi=0.26$ which are $45^{\circ}$ above the equatorial plane.
Fig. 3-1: hx at time t/M = 231
 Fig. 3-2: hx at time t/M = 2846
 Fig. 3-3: hx at time t/M = 3272
Fig. 3-4: hx at time t/M = 3343
 Fig. 3-5: hx at time t/M = 3391
 Fig. 3-6: hx at time t/M = 3429
PLAY MOVIE: hx Top-Down View of Lower Hemisphere

h+ Polarization (surface plot of equatorial plane)
Fig. 3-1: hx at time t/M = 231
 Fig. 3-2: hx at time t/M = 2846
 Fig. 3-3: hx at time t/M = 3272
PLAY MOVIE: h+ Surface Plot of Equatorial Plane

Case C: q4 hx Polarization (Top View)

In the q4 case, the two black holes have a 4:1 mass ratio. They start with initial spins $\chi=0.26$ which are $45^{\circ}$ above the equatorial plane.
Fig. 3-1: hx at time t/M = 231
 Fig. 3-2: hx at time t/M = 2846
 Fig. 3-3: hx at time t/M = 3272
Fig. 3-4: hx at time t/M = 3343
 Fig. 3-5: hx at time t/M = 3391
 Fig. 3-6: hx at time t/M = 3429
PLAY MOVIE: hx Top-Down View of Lower Hemisphere

h+ Polarization (surface plot of equatorial plane)
Fig. 3-1: hx at time t/M = 231
 Fig. 3-2: hx at time t/M = 2846
 Fig. 3-3: hx at time t/M = 3272
PLAY MOVIE: h+ Surface Plot of Equatorial Plane

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CTA Center for Theoretical Astrophysics---University of Illinois at Urbana-Champaign

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last updated 13 Apr 23 by Eric