The basics of binary coalescence
M. Favata/SXS/K. Thorne
Many of the sounds on this site focus on the collisions of compact object binaries, so let's begin with an overview of these systems. Compact object binaries consist of pairs of neutron stars (NS) or black holes (BH). These are likely to be the "loudest" sources for LIGO (which is why we devote so much attention to them). For simplicity, let's consider two black holes orbiting each other. When the BHs are widely separated, they orbit relatively slowly and emit weak gravitational waves (GWs). These waves carry away energy from the system, "pushing" the binary into an orbit with a smaller radius (and a higher orbital frequency). [This is called radiation reaction, since the system reacts to the emission of radiation.] As this process continues, the binary moves to smaller and smaller orbital frequencies. The BHs orbit faster and faster, and the waves they emit release more and more energy (which in turn causes the system to shrink even faster). This phase of the coalescence is called the inspiral. In the figure above you see a plot of the GW signal vs. time. During the inspiral this looks like an oscillating function, but the amplitude is increasing with time along with the frequency of the oscillation. This phase proceeds the same for binaries with two neutron stars or a BH/NS binary.
During the phase labeled merger above, the two black holes get close enough to collide together and form a single black hole. The strongest GWs are emitted during this process (which is highly nonlinear and requires supercomputer simulations to model). What remains is a BH with large distortions in its shape. Like a struck bell, these distortions are quickly radiated away as more GWs during the ringdown phase, leaving behind an undistorted (but rotating) BH. The GW signal during the ringdown looks like an oscillating function with an exponentially damped amplitude. The merger is a very short part of the signal that joins the inspiral and ringdown.
Here you can see a numerical relativity simulation of this process from the SXS Collaboration:
During the phase labeled merger above, the two black holes get close enough to collide together and form a single black hole. The strongest GWs are emitted during this process (which is highly nonlinear and requires supercomputer simulations to model). What remains is a BH with large distortions in its shape. Like a struck bell, these distortions are quickly radiated away as more GWs during the ringdown phase, leaving behind an undistorted (but rotating) BH. The GW signal during the ringdown looks like an oscillating function with an exponentially damped amplitude. The merger is a very short part of the signal that joins the inspiral and ringdown.
Here you can see a numerical relativity simulation of this process from the SXS Collaboration:
Because the merger and ringdown are very short (just a few cycles), while the inspiral consists of many cycles, it is easy to hear the inspiral but very difficult to hear the merger+ringdown.
As an example of this we took a numerical simulation from the SXS Gravitational Waveform Database (Sim#0090) and produced a sound with and without the merger. Here you see a plot of the signal (with a zoom-in of the merger region below), followed by two sound clips.
As an example of this we took a numerical simulation from the SXS Gravitational Waveform Database (Sim#0090) and produced a sound with and without the merger. Here you see a plot of the signal (with a zoom-in of the merger region below), followed by two sound clips.
Gravitational wave signal from coalescence of two 3.5 solar-mass black holes. The complete signal is shown in blue; in red the merger/ringdown is removed. [For this and the remaining plots on this page, the y-axis is arbitrarily scaled; only the real-part of the h_22 mode is shown.]
Zoom-in near the merger.
The two sounds are almost indistinguishable. (You can hear a short extra high-frequency "blip" at the end of the sound that includes the merger.) Notice that in the plot above the merger/ringdown lasts only 0.003 sec (3 milliseconds).
If we use the same simulation data but adjust the total mass to be larger (two 50 solar mass black holes), then each cycle of the wave lasts longer and likewise the overall signal lasts longer (since the number of cycles is fixed by our choice of this particular simulation); unfortunately most of the signal is shifted below what you can hear. However, the merger part is still in the audible range (if you use headphones or non-laptop speakers with a subwoofer or good bass). This plot shows the same simulation with the timescale appropriate for a 100-solar mass binary, followed by the sounds.
If we use the same simulation data but adjust the total mass to be larger (two 50 solar mass black holes), then each cycle of the wave lasts longer and likewise the overall signal lasts longer (since the number of cycles is fixed by our choice of this particular simulation); unfortunately most of the signal is shifted below what you can hear. However, the merger part is still in the audible range (if you use headphones or non-laptop speakers with a subwoofer or good bass). This plot shows the same simulation with the timescale appropriate for a 100-solar mass binary, followed by the sounds.
Merger of two 50 solar mass black holes, zoomed-in near merger.
In this case you notice that the sound is much shorter than the 7 solar mass case. In the merger case, you can hear that the sound is slightly louder and ends in a slightly higher frequency. In this case, the merger/ringdown is closer to 0.05 sec in length. To make it last longer without shifting the sound below the range of human hearing, we will have to come up with a non-physical model.
To learn more about coalescing binaries, continue on to the section on circular binaries.
To learn more about coalescing binaries, continue on to the section on circular binaries.
