World Science Scholars
3.2 Detecting Gravitational Waves
summary
Gravitational waves are both rare and difficult to detect.

• Binary systems are the best target source for detecting gravitational waves. The wave produced by a binary system will be most powerful just before the two bodies merge.
• These mergers happen only about once every 10,000 years in our galaxy. To see one per year, we need to look at tens of thousands of galaxies.
• A binary merger in the nearby Virgo cluster would distort spacetime around Earth by one part in $10^{21}$, an amount so tiny that Einstein thought they could never be measured.
• It turns out he was wrong. There are many different ways to measure gravitational waves, and in fact since this talk was recorded the binary merger of two black holes has been successfully detected by LIGO.
• Waves from different sources have different properties that affect our ability to detect them. Even though the primordial gravitational background has high amplitude, its low frequency makes it very difficult to measure. Remember that efforts to detect it in the cosmic microwave background have not yet been successful.

Pulsar timing arrays could help us measure powerful gravitational waves.

• Recall that pulsars are essentially very precise clocks. We can use the radio blips they emit to measure the distance between pulsars and the earth.
• If a gravitational wave passes between the earth and a pulsar, the distance between the two will change. This is detectable as a change in the timing of pulsar signals.
• Three pulsar timing arrays are actively searching for the primordial gravitational background as well as supermassive black hole mergers, both sources that produce high-amplitude, low-frequency gravitational waves.

How can we detect gravitational waves using interferometers?

• An interferometer works by splitting a laser down two paths, usually at 90 degree angles to each other. These paths have known lengths and end in mirrors, reflecting the lasers back.
• When the two lasers return they recombine. Depending on the pattern of interference, this recombined signal can tell us whether the length of one of the paths has changed relative to the other.
• Gravitational waves have quadrupolar character, meaning that a circle would stretch into an ellipse as a gravity wave passed through it. In other words, space distorts by different amounts in different directions.
• This allows us to measure gravitational waves using interferometers because the two path lengths will change by different amounts which will cause a detectable change in the pattern of interference.

Interferometers need to operate over large distances to measure gravitational waves.

• To make the distorting effect of gravitational waves measurable, long path lengths are necessary.
• A trio of satellites separated by millions of kilometers could act as a very sensitive space-based interferometer. Such a system could be able to detect low-frequency supermassive black hole mergers.
• One such project, called LISA, is being considered by the European Space Agency. A spacecraft called LISA Pathfinder was launched in late 2015 to test technology for future use in LISA.

Ground-based interferometers are now sensitive enough to detect gravitational waves.

• The Laser Interferometer Gravitational-Wave Observatory, LIGO, is a US national project that has built two ground-based observatories, one in Washington and the other in Louisiana.
• Each observatory consists of an interferometer with 4km path lengths. Spacetime distortions will change this path length by about 1/1000 of a proton’s diameter (~$10^{-16}$), a level of precision that LIGO has been able to achieve.
• Since 2010 upgrades called Advanced LIGO have begun to be installed and activated with the goal of increasing sensitivity by 10 times.
• LIGO could detect events in the local Virgo cluster, in which mergers happen about once every 100 years. Advanced LIGO will increase the search volume by 1000 times, which could increase the number of expected events to tens per year.

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