Gravitational Waves: The First Swell!

A Big Discovery

On 14 September 2015 at 4:50:45 AM Eastern standard time, the LIGO experiment detected for the first time the passage of gravitational waves. Scientists saw a very specific pattern of stretching and compression of space-time called a “chirp”. The detection was done independently at the two locations of the experiment, one in Hanford (Washington) and the other one in Livingstone (Louisiana). This amazing discovery has occurred almost exactly 100 years after Albert Einstein published his General Theory of Relativy (Einstein, 1916), and represents the last verification of this beautiful theory of gravity.

How did the waves look like? Glassy and double-overhead!

Left: Al ’Surfer’ Einstein excited about gravitational waves (adapted from a Mark Summers artwork). Right: The first gravitational waves signal detected by humankind. Data from the Washington (Top) and Hanford (middle) detectors are compared to the expected theoretical signal from two merging black holes. The two detected signals are compared after being shifted by about 7 ms in the bottom panel (the small delay between the two signals is due to the finite speed of the gravitational waves, which move at the speed of light).

What Made the Gravitational Waves?

The cosmic storm that produced the gravitational waves was quite gnarly: Two black holes with a combined mass larger than 60 times the mass of our Sun and separated by just a few hundred kilometers spiraling towards each other at half the speed of light and then merging. The gravitational waves detected by LIGO were produced during the very last part of the in-spiraling process (last half second), when the two black holes were almost touching each other and the amount of energy deposited in gravitational waves was the largest. Looking at the received signal, scientist were able to determine how much energy was produced during the merger event. The initial masses of the two black holes were 36 and 29 times the mass of the Sun, but after the merger the mass of the newly formed black hole was only 62 solar masses. Where did the extra 3 solar masses go? The mass was converted into energy and used to produce the gravitational waves. Which means that the power emitted by the source for the very short duration of the event was larger than the integrated power emitted by all stars in the Universe! Isn’t that awesome? This represents the most powerful event ever observed by humankind (after the Big Bang). The gravitational waves allowed the LIGO team to determine the distance of the merger, which turned out to have occurred 1.2 billion light years away. Why so far? The answer is that this kind of events is expected to be quite rare, and it’s statistically very unlikely to have one nearby. We need to look at a large chunk of the Universe to catch one. This also explains why the LIGO experiment was so challenging: Initially the waves are pretty big and they distort space-time by a large amount, but by the time the waves reach Earth their amplitude has decreased by a factor \(1/d\), where \(d\) is the source’s distance. For the event detected last September, the gravitational waves had to travel a distance 10000 times larger than the diameter of our Galaxy. So that when they arrived on Earth, LIGO had to measure a change in distance as small as 1/1000 the diameter of a proton to detect them. The other reason why gravitational waves are so hard to detect (compared to electromagnetic waves, aka light) is that gravity is a very weak force compared to the other forces of nature. This translates to spacetime being quite stiff. To continue the surfing analogy, is like if the ocean was made of solid metal instead of water. A hurricane would still create perturbations that propagate as waves (although of a different kind), but their amplitude would be very, very small compared to the water waves, due to the increased stiffness. To perturb specetime a lot of energy is required, and in general only tiny waves are produced, except in the proximity of cataclysmic events like black holes mergers.

The “Chirp” Signal Explained

Gravitational waves are produced when mass is accelerated, but their amplitude is generally super tiny. However when two massive, compact objects rotate very close to each other (for example two neutron stars or two black holes) then we have both very large masses and huge accelerations, the key ingredients for producing high amplitude gravitational waves. A very specific gravitational wave signal called a “chirp” is expected when two such compact objects merge. Let’s look at the case of two black holes, as for the LIGO signal. First the two black holes orbit each other and go through an inspiral phase in which the orbit shrinks due to increasing energy loss into gravitational waves. Smaller orbits correspond to higher orbital speeds, with the black holes moving faster and faster (up to about 50% the speed of light in the case of the system observed by LIGO, see figure below) and the frequency of the generated gravitational waves increasing accordingly. The amplitude of the gravitational waves increases too, until the two black holes coalesce and the gravitational waves emission reaches a peak. After that the newly formed, more massive black hole goes through a sort of adjustment phase called ring-down. The event emits large amounts of gravitational waves only during the very last second before the coalescence occurs. Most importantly, the mass of the black holes, their distance and other important parameters can be reconstructed by looking at the particular properties of this very distinctive chirp signal. Sweet!

Chirp: A gravitational waves signal called a “chirp” is expected when two black holes merge. It’s a signal that follows a very specific expectation of evolution of frequency and amplitude as function of time, both increasing rapidly before coalescence of the two black holes. Figure adapted from Abbott et al. (2016)

Previous: “The Surfer’s Guide to Gravitational Waves”


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