Gravitational Wave detection – the technical achievement

The gravitational wave signal detected by LIGO. Image credit: LIGO Scientific Collaboration

Well, what an exciting week it’s been! I’ve been lucky enough to be working with the Gravitational Physics group here in Cardiff, and the wider international LIGO Scientific Collaboration, for the last few months on the plans for the big announcement last week of the first detection of gravitational waves. I should make it clear that I’ve not been involved in any of the scientific analysis of the results, but in the outreach activities associated with them.

The detection

As a quick summary, for those who’ve been under a bush for the last week, on 14th September 2015, at about 09:50 GMT, the twin LIGO detectors picked up a signal indication a gravitational wave passing through the Earth. The signal was incredibly strong – much stronger than anyone on the team could have hoped to detect.

The fact that both detectors picked it a strong signal simultaneously alerted the online automatic software within about three minutes. Following that, a comparison of the signal with numerical simulations models of expected sources established the properties of the source of the emission: a pair of black holes in a very tight orbit, spiralling in as they radiate away energy in the form of gravitational waves, and finally merging with a final, huge blast of energy – I’ll talk about the astrophysical event in a later post

The astrophysical consequences of this are astonishing, but the technical achievement is, frankly, staggering. LIGO was proposed in the 1970, and built in the 1990s. But the first version, called “initial LIGO” wasn’t really expected to detect any astrophysical signals, with a further upgrade required to created “Advanced LIGO”, which is the instrument we see today. In fact, the upgrade isn’t quite complete – there are more improvements to come which will increase the sensitivity further.

Precision measurements

LIGO Schemtic

Schamatic of a LIGO interferometer. LIGO/Cardiff Uni./C. North (CC-BY-SA)

It’s often stated that LIGO is the most sensitive ruler ever made by humanity. The units on the image above the right are strain – the relative change in length. These number are around 10-21, that’s one part in a thousand trillion trillion. The trick to making such a tiny change in length is to make the length you are measuring as long as possible. In the case of LIGO, with arms 4km long, the actual change in length is about 4×10-18 m (that’s 4 attometres, or 4 trillionths of a trillionth of a nanometer) – or about 1/1000th the size of a proton.

Even if that distance were larger, the problem doesn’t get much easier. A relative change in distance of 10-21 is equivalent to changing the diameter of the Earth’s orbit by the diameter of a single atom, or the distance to the nearest star (Proxima Centauri, 4.24 light years away) by the width of a human hair.

A matter of timing

LIGO has a couple of tricks up its sleeve. Firstly, it doesn’t measure the distance directly – that would be practically impossible – but measuring the phase difference between laser beams sent along each of the two perpendicular arms and back before being recombined – it’s essentially a Michaelson Interferometer. The laser beam is split into two and sent down each arm exactly in sync. The arms of of exactly equal length, and the setup is such that when the laser light reflects back and the two recombined, they produce an interference patter. The setup is such that in these circumstances there is almost (but not quite) no signal reaching the detector.

A gravitational wave passing through the detector will stretch one arm and shrink the another, with the stretching and squeezing oscillating with the wave. With a laser wavelength of about 1μm (10-6m), a change of 10-18m is about 10-12 wavelengths (a millionth of a millionth!). But as the wave passes through, the wavelength of light also changes, so the number of wavelengths along the arms stays the same. The trick is that the speed of light is constant, so if an arm gets longer, the light takes longer to travel along it, so when it gets back to the beam splitter it’s every so slightly out of phase with the other arm. The phase difference means that the interference pattern changes, and a small signal reaches the detector. LIGO is actually a timing experiment, but timing to an accuracy of around a femtosecond!

Another trick is that the laser beam is reflected back along the arms around 400 times before being recombined, so the “effective” length of the arms is about 1600km. That increases the phase difference by a factor of about 400 – though it’s still less than a billionth of a wavelength. That means the laser has to be incredibly stable, in both intensity and wavelength – a change in either would affect the interference pattern and create unwanted fluctuations at the detector. One of the major upgrades to Advanced LIGO was to increase the stability and coherence of the laser. There was also an increase in laser power from 10W to 200W – though for this observing run it was actually running lower than design power.

A busy background

A measurement like this isn’t just about precision – it’s also about picking out the signal above the background noise – that is, . That’s an incredibly difficult task for LIGO, which is measuring such a tiny change in length. Anything that changes the position of the mirrors could be mistaken for a real signal. That includes thermal fluctuations in the mirrors, such as those caused when a powerful laser hits them – the upgrade to Advanced LIGO included replacement of the mirrors with larger, thicker and more massive versions, complete with systems to compensate for the ever-so-slight distortions that occur when the laser (which carries about 1 MW of power in the arms, after reflections are taken into account) hits them.

Then there’s the physical motion of the mirrors from environmental effects. The ground motion due to seismic motion and waves crashing into the distant shore, is around 1μm – a million million times larger than the signal LIGO is searching for. There;s also the vibrations caused by trains and trucks going past, trees falling down during logging operations, and even wind hitting the buildings. These effects tend to be at relatively low frequencies, and are mitigated by incredibly complex seismic isolation systems (in which the University of Glasgow had strong involvement). The quadruple-pendulum system removes many of these vibrations.

Final sensitivity

Advanced LIGO sensitivity curves, showing the proposed evolution with future upgrades. Image credit: LIGO Scientific Collaboration

None of these systems are perfect, and there comes a point at which the quantum limit of sensitivity is reached – where it’s physically impossible to do any better. But they can be tuned as best as possible. LIGO is most sensitivity to gravitational waves which have a wavelength roughly double its effective arm length (that’s actually a common feature of a huge number of detectors of electromagnetic waves) – so that’s about 3000 km. A wave with a wavelength of 3000 km, travelling at the speed of light, has a frequency of around 100 Hz, and it’s this range to which LIGO is most sensitive At lower frequencies, it is dominated by thermal and seismic noise, while at high frequencies it’s by noise associated with the laser itself.

The image on the left shows how the sensitivity will evolve. The key also indicates the distance at which it’s expected that LIGO will be able to detect a binary neutron star coalescence – the most common event expected. Note that an increase in distance of 3, which is what’s expected by 2019, corresponds to an increase in the volume being observed of 30. The event seen in September 2015 was actually around twice as far away as any of those predicted distances, but that’s because it was the collision of two rather massive black holes, which produces a much louder signal.

In a future post I’ll discuss the black hole collision…