Gravitational Waveforms
When the orbital angular momentum and the black hole spin are misaligned this will cause the precession of the orbit and perturbations in the disk. These effects will induce gravitational waves. In the left column of the figure below we plot the (2,2) mode (top panel) and the (2,1) mode (bottom panel) of h+ for the tilted case A2 (initial black hole spin θs=45°). The (2,1) mode has a larger initial amplitude than the (2,2) mode due to the large nonaxisymetry of the system at t=0. Disk perturbation in the aligned case A1 (initial black hole spin θs=0°) induces a much smaller peak strain even though the rest mass of the disk is larger. There is similar behavior in the right column, which plot the (2,2) and (2,0) modes for the tilted case A3 (initial black hole spin θs=90°). In contrast to the A2 case where the l=3 modes are negligible, the case A3 has significant amplitude l=3 modes.
In the plots rA is the areal extraction radius (rA/M≅1200 for A2, rA/M≅1080 for A3) and tret is retarded time.
 Fig. 1: Extraction radius multiplied by strain amplitude vs. retarded time |
Gravitational waves from black holes surrounded by massive accretion disks aren't as widely studied as those from compact binary coaleces. The following plots and movies will hopefuly help the reader gain some intuition about the nature of gravity waves from self-gravitating disk-black hole systems. For the two cases of interest, A2 and A3, three snapshots from the gravitational wave movie are matched with three snapshots from the movie of the black-hole disk source. Since gravitational waves are extracted at a radius rext far from the origin in numerical simulations, the time used in the gravitational wave movie is the retarded time tret = t - rext. By synchronizing the two movies in this way, an event that occurs in the black-hole disk source movie will be immediately reflected in the gravitational wave movie.
The gravitational wave movies are contour plots on the equatorial plane (z = 0) of the h+ polarization, summed over all the l = 2,3,4 modes. The gray hole that is cut out in the contour plot is the wave near zone.
For each case, two movies are linked. One plays the gravitational wave movie alongside the black-hole disk source movie by synchronizing them using the method described above. The other plays the gravitational wave movie with a one-dimensional plot of the strain h+ at some distant point on the equator (specifically at ɸ=π/4, θ=π/2). The contour plots of the different cases can be compared, as they were scaled by the same factor. However, the 1D plots are normalized for each case individually. For a more quantitative analysis, refer to the 1D plots at the beginning of the page.
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