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[Black Hole] A black hole is one of the simplest objects in th
[Black Hole] A black hole is one of the simplest objects in the Universe. It has only two characteristics: its mass (which determines its size), and its spin (how much spacetime swirls around). When you have two black holes in a binary system, things get more complicated. We now have the masses and spins of both black holes, the spins stay the same size during the orbit, but their directions wobble around in a process called precession. The gravitational waves reaching Earth from the binary also depend on where the binary is and which way it is orientated.
[Stages] One of the reasons we divide up the gravitational wav
[Stages] One of the reasons we divide up the gravitational wave signal is because different techniques can be used to calculate the waves at different points. The early inspiral can be calculated using post-Newtonian theory (this starts with Newton’s theory of gravity and adds little extra bits to account for how things change in general relativity). The ringdown can be calculated using black hole perturbation theory (this starts with the final shape of the black hole, and sees how it reacts to small changes). The merger can only be calculated using numerical relativity (simulations of the full equations of general relativity which take lots of computing power); this has only been possible in the last 10 years, so the merger was the last part of the puzzle. If we had a binary containing neutron stars instead of black holes, the inspiral would be much the same, but there would not be the same merger and ringdown. The signal would be much messier, possibly featuring neutron stars being ripped apart, before colliding and collapsing to a final black hole.
[Chirp mass] The way the signal changes during the inspiral is
[Chirp mass] The way the signal changes during the inspiral is primarily fixed by a combination of the black hole masses we call the chirp mass. If we see lots of cycles of inspiral, we can measure the chirp mass really well (better than a fraction of a percent). When thinking about what we can learn from gravitational waves, people often first think about the chirp mass.
[Ringdown] The ringdown part of the signal comes from the fina
[Ringdown] The ringdown part of the signal comes from the final black hole, so it depends upon its mass and spin. The final mass is almost the same as the total mass of the two initial black holes (some energy is lost, carried away by the gravitational waves). The final spin depends upon the spin of the initial black holes and how they were orbiting around each other when they merged.
[Sky] With multiple detectors, we can work out which direction
[Sky] With multiple detectors, we can work out which direction the gravitational waves came from by looking at the times when the signals arrived at each detector. This is similar to how you can locate the source of a sound using your ears. We can get some extra information about the direction from how loud each signal is (since each of the detectors has its best sensitivity in a different direction), and where the wave is in its cycle.
[Spin] As the black holes orbit each other, their spins change
[Spin] As the black holes orbit each other, their spins change direction. This also causes the orientation of the orbit to topple backwards and forwards a little. This precession leaves an imprint on the gravitational waves: they become louder and quieter as the spins wobble around. The precession depends on directions of the two spins, compared to each other and compared to that of the orbit. The spin of the more massive black hole has a larger effect than that of the smaller one. We don't see much sign of precession in GW150914. This may be because spins are small, its inclination means the wobbles aren't visible, or a combination of both. Since the inspiral is short, we would not expect to see a large effect in any case.
[Total mass] The total mass of the system determines how long
[Total mass] The total mass of the system determines how long it takes for things to happen. Heavy systems are bigger, and so change more slowly. The gravitational waves are at lower frequencies, which means that LIGO can only see the final parts. Lighter systems produce gravitational waves at higher frequencies, so we can measure more of the inspiral. The total mass of the system sets which parameters are most easily measured. For really massive systems we measure the total mass best (as we only see the merger and ringdown), but for light systems, like binary neutron stars, we measure the chirp mass best (as we only see the inspiral). GW150914 is somewhere in the middle.
[Inclination] The way the binary is facing the Earth determine
[Inclination] The way the binary is facing the Earth determines the gravitational waves we see. If it is edge on, the signal is quieter, but it is easier to spot small changes caused by the black holes’ spins. If it is facing us, the signal is louder, but it’s harder to tell if the orbit wobbles because of precession. We have a greater chance of detecting a face-on binary because they can be detected from further away.
[Amplitude] The size of the signal, its amplitude, depends on
[Amplitude] The size of the signal, its amplitude, depends on how far away the binary is. If the distance were twice as big, the amplitude would be half. The quieter a signal is, the harder it is to detect, and the less we can learn about its properties. Heavier systems produce louder gravitational waves as there is more mass moving around to create the waves. The signal amplitude depends upon the way the binary is facing (its inclination), and its position in the sky: the detectors are not equally sensitive to gravitational waves from all directions (the signal is loudest when the source is directly above or below a detector.
[Redshift] The expansion of the Universe affects gravitational
[Redshift] The expansion of the Universe affects gravitational waves in a couple of ways. As the Universe expands, it stretches the waves travelling through it. This is well known in astronomy and is called redshift, as it makes visible light more red. To have a large effect, the waves must have travelled a long way. The first effect is that the frequency of the wave changes. This has the same impact as changing the masses: things further away appear more massive. The second effect is to change the amplitude, which is the same as changing the distance: we often talk about the luminosity distance, which absorbs this effect, but isn’t the same as if we measured the distance to the source using a tape measure. If we get enough measurements of how gravitational waves are redshifted, we could possibly learn something about how the Universe is expanding.
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