Gravitational Waves

A wave can generally be characterised as a wobbly motion carrying energy in a direction through some sort of medium (better known as stuff). When talking about gravitational waves, the stuff that is wobbling is spacetime. I have to say spacetime and not just space because these concepts are closely linked in the theory of general relativity where all of this mokey business is coming from.

Anyways, imagine this: when such a wave passes by, it stretches and shrinks space in a oscillating motion. This is how they are measured by a network of interferometers (two LIGO detectors in Hanford, Washington and Livingston, Louisiana, Virgo in Cascina, Italy which is being upgraded, GEO600 in Germany which is mostly used as a testing facility and KAGRA in Japan being build right now. There are also plans for a LIGO in India and the even bigger Einstein Telescope).  An L-shaped interferometer – such as used by Michelson and Morley in 1887 to measure the motion of the aether relative to earth (you have never heard of this because they found it actually did not exist) – has two long arms in which a laser beam travels to and fro, reflected by a mirror at the end. Because laser is simply light of a particular frequency, the two beams interfere as waves do. When in phase (meaning, the peaks of the waves arrive at the same time), they add up and light comes out. When out of phase, one is the opposite of the other and they cancel out; no light comes out. Changing the distance of one of the arms will change the phase of one of the beams and so changes the pattern of light coming out at the end. This is what a gravitational wave will do. However, gravity is such a weak force that the detector arm, some 3 (or 4) kilometers long, will only change by a fraction of the size of an atom. You can imagine this is a difficult task so I’m glad I don’t personally have to work on that.

 

MSc. thesis project (finished)

My masters project what to do now that we’ve actually measured gravitational waves. Needless to say, this is  super awesome and a huge deal for physics and astronomy. The detection on September 14, 2015 is a signal coming from the merger of two black holes, object that are otherwise invisible. Who knows what more we might find! It is also a first detection of things that are subject to very strong gravity, something that is in principle measurable with a “normal” telescope if two close-by neutron stars happen to merge, but you would have to wait roughly 80 billion years for this to happen in range. With gravitational waves, we can detect things much further away, and so there is a much bigger chance of such an event happening while the detector is on.
In any case, these strong fields specifically allow the theory of general relativity (GR), our working theory of gravity, to be tested in the strong field regime for the first time. It has long been shown that GR is needed for corrections on it predecessor, Newton’s theory of gravity, but always approximations where the gravity was assumed to be weak were enough. We therefore do not know yet for certain if the theory will hold with properly strong gravity.

The group I’ve worked in at NIKHEF (National Institute for subatomic physics, used to be nuclear (Kern) and High Energy  physics (Fysica) but nobody does that anymore) has developed some clever method to use gravitational waves coming from compact binary mergers to test GR. Such a merger happens when two compact object, neutron stars and black holes, spiral around each other in closer and closer orbits until they merge. For this test, you need to know what the gravitational wave will look like and compute this a bunch of times with slightly different parameters. For binaries with two neutron stars, this is quite doable because the messy part, where to two stars actually come together and merge, is not visible for the detectors anyway. However, for two black holes or a neutron star and a black hole, the frequencies are a bit different and the messy part is an important, or even the most important, part of the signal. Other than that, high spins complicate matters. It is still possible to neatly calculate the form of the signal, but this takes a long time. Approximations that are a lot faster to calculate have been made, but do not work equally well for all parameters.

My work was to compare these approximations and see for what parameters they work well and for which they don’t. First step was to set up a program that can calculate these waveforms. Therefore, zeroth step has been to install the code libraries used within the collaboration of people working on things with gravitational waves. Apparently, everyone has problems when they first do this on a computer, and the problems are always different, but I turned out to have an exceptional amount of problems. In the end, we made it (I’d say I made it but really I needed help from several people) and I programmed the waveforms. Then I set up a thingie that calculated the overlap between two waveforms (simply put, you give it two waveforms and it gives you a number between minus one and one, where zero meas ‘do not look alike at all’, one means ‘are the same’ and minus one meas ‘the same but opposite’). I used this to systematically study the overlap between waveform approximations for different parameters in the waveforms (masses of the merging blackholes, how much and in what directions the black holes are spinning, …). This helped us learn for what parameters the waveform approximations were less accurate and could use improvement.

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