Behind the Curtains of the Cosmos 2: Gravitational Waves

by Shane L. Larson

Nearly every picture you have ever seen of galaxies and nebulae and stars, and virtually everything that we know about the Cosmos, has been obtained with light.  Light is plentiful and easily created, so it is natural to use it as a probe of the Universe. Vision is, for most of us, the primary sense by which we interact with the world, so again light is an obvious probe for us to lean on.

Three dimensional gravitational wave emission from colliding black holes (NASA-Goddard).

But there are other physical phenomena in Nature, and technology enables us to probe those phenomena, whether we can personally sense them or not. One such phenomena, first predicted by Albert Einstein in 1916, are gravitational waves. Gravitational waves are propagating disturbances of gravity — in the modern language of gravity, they are ripples in the fabric of space and time.  If a massive object moves, it takes time for the gravitational field to respond because nothing can travel faster than light.  Heuristically then, gravitational waves are the shifting of gravitational fields, in response to dynamical motion of mass.

When two massive objects (like stars or black holes) orbit one another, the information about how the gravitational field is changing moves outward at the speed of light. These ripples spiraling outward are gravitational waves, and carry detailed information about the source. Click to animate. [Image by S. Larson]

Most of us are familiar with the idea of a spectrum from light, produced by a prism or seen as a rainbow after a storm passes. The “electromagnetic spectrum” encompasses more than just those few colors we can see with our eyes; it also includes kinds of light our eyes can’t see, like gamma rays, ultra-violet light, radio waves, and microwaves.

The electromagnetic spectrum — light in all its varieties, illustrated in the many different ways that scientists describe the properties of a specific kind (or “color”) of light.

Gravitational waves also form a complete spectrum, independent of the electromagnetic spectrum. Since we can’t sense gravitational waves with our bodies, we have no sensory experience to describe them, and have no names for the different parts of the spectrum, so we simply identify the waves by their wavelength (the distance between peaks of the wave) or alternatively their frequency (how often a peak passes by you, if you just stand still and let the waves wash by). As astrophysicists, we have thought hard about the Universe, and can easily imagine Nature creating “high frequency waves” (short wavelength), where thousands of wave peaks pass by you every second, all the way down to “very low frequency waves” (long wavelength), where a wave peak may only pass by once every 30 million years.

There are many different sources of gravitational waves that we expect to see. These include (clockwise from upper left): Colliding neutron stars, merging supermassive black holes, white dwarf binaries, supernova explosions, the Big Bang, and the capture of compact stars by supermassive black holes.

Gravitational waves are generated by all kinds of different astrophysical systems, and as such the waves themselves are as varied as the phenomena that created them. From the simplest viewpoint, the astrophysical system making the waves defines how big they are. Systems that have large spatial extent and large masses tend to make much longer wavelength waves than small, super-compact systems. To develop some intuition about this, consider one of the bread-and-butter source for modern gravitational wave observatories, a binary black hole — two black holes, locked in a mutual gravitational dance, orbiting one another the way the planets orbit the Sun. When the black holes are far apart (larger orbit) they complete their orbits more slowly. As a result the gravitational waves emitted have low frequencies. Suppose the orbit shrinks. What happens? The black holes orbit each other more quickly, so the frequency of the gravitational waves increases.  What we see here is that the size of the orbit influences the size of the gravitational waves. Similar arguments can be made for other physical properties that influence the shape and form of the gravitational waves, which makes them useful for doing astronomy.

A simple example of how the properties of the source change the structure of the gravitational waves. If we can detect and measure the waves, that will tell us something about the sources. [Image by S. Larson]

Astronomy is a game of detection — as I like to say, “astronomy, unlike life, IS a spectator sport!”  Our job as astronomers is to watch the Cosmos and record what we see. We build instruments to help us accomplish that mission, instruments with cool names that you can use to impress your mother or a date: telescope, observatory, detector, bolometer, radiometer, and so on. If you want to build an instrument to look for some form of putative radiation, then you need to know how it interacts with your detector. The basic behaviour we exploit with light is that it bounces off of appropriately designed surfaces, whether the light is radio waves, optical light, or x-rays, it bounces off of surfaces, a fact that humans have exploited to gather light for more in depth experiments.

The effect of a PLUS (+) polarized gravitational wave on a grid of particles. Click to animate. [S. Larson]

The effect of a CROSS (X) polarized gravitational wave on a grid of particles. Click to animate. [S. Larson]

So what do gravitational waves do? Gravitational waves change the proper distance between particles. There is a very nice way to visualize this. Imagine a grid of particles — little marbles or marshmallows, arranged on this screen.  Now imagine a gravitational wave shooting straight through the screen: from your eyes, through the middle of your grid, and out the back.  What happens? The distances between all the marshmallows changes in a very specific way, illustrated in the animated images here.  At the start, in one direction all the marshmallows are stretched farther away from each other, while at the same time marshmallows in the perpendicular direction are pulled closer together. If you wait a while, the gravitational waves move a bit farther on in its cycle and it returns the grid to its original appearance. But it doesn’t stop there! On the “downside” of the wave cycle, the stretching and pulling swap directions!  This pattern repeats itself for as long as the gravitational wave is flying through the grid of marshmallows. There are two different “flavors” of gravitational waves (what astronomers call “polarizations”) that both distort our grid of marshmallows, just in different directions.  One flavor is called “PLUS” because the pattern of deformation looks like a + sign.  The other flavor is called “CROSS” because the pattern of deformation looks like a X sign.

So if we want to detect gravitational waves, we need a way to see this distortion. Like other radiation we encounter in astronomy (particularly electromagnetic radiation — light), gravitational waves carry energy which can affect other objects in the Cosmos. A “detector” is a device which extracts some of that energy to let us know the wave is passing by. But gravitational waves have one big problem —- they interact very WEAKLY with matter! That means it is hard to get them to deposit energy in a detector, and that means they are hard to detect.  This is a fact that Einstein appreciated full-well — he knew if we were ever going to see gravitational waves, technology was going to have to get better — much better. It would not be until the 1960s that any serious effort to detect gravitational waves would begin.

The gravitational wave interferometer concept is to measure the changing proper distance between points using lasers.

If you look at our particle grids, you see the effect is more pronounced for particles that are farther apart, so the bigger the instrument is the better.  Today, the premiere technology for gravitational wave searches is a classic physics instrument called a “laser interferometer” —  a device that times how long it takes a laser to fly in two different directions and very precisely compares the results to tell you if the two directions have different lengths! This is perfect for gravitational wave detection! Laser interferometers are easy to build in the lab (or at home, if you can acquire a few parts — try these instructions), but it is easier to detect gravitational waves over larger distances, because the stretching effect is larger.  So we’ve built HUGE laser interferometers, that stretch 4 kilometers (2.5 miles) from one end to the other! We’ve built two of them here in the United States — they are called LIGO.  The Pictionary style picture of LIGO is three mirrors — one at a corner, and two at the far ends of two long arms. Think of any three marshmallows in our grid — those are the functional locations of the mirrors in LIGO that the lasers are measuring distances between. When gravitational waves change the distances between the mirrors, we can measure those changes with our lasers.

(L) Aerial view of LIGO-Hanford Observatory [top] and in Google Maps [Bottom]. (R) Aerial view of LIGO-Livingston Observatory [top] and in Google Maps [Bottom].

Just as in traditional photon astronomy, we have to build different kinds of detectors to detect different kinds of gravitational waves. As a general rule, when the wavelengths of the gravitational waves we want to see are longer, we have to build bigger detectors. A laser interferometer could be built in space by imagining the mirror locations being free-flying spacecraft. Such a concept exists, known as LISA, where the spacecraft are 5 million kilometers apart (that’s 13 times the distance from the Earth to the Moon; it will take the lasers 16.6 seconds to fly between the spacecraft!).

Spacecraft concept for a gravitational wave detector in space [eLISA Consortium]

Eventually it becomes impractical to imagine building bigger and bigger interferometers. Does that mean there are parts of the gravitational wave spectrum that we simply will never be able to observe? No; astronomers are clever folks and have devised ways to use astrophysical systems as gravitational wave detectors by measuring the imprints the gravitational waves leave behind them.

There are two primary ways we monitor astrophysical systems to detect gravitational waves. One way is we watch pulsars — the spinning dead hulks of massive stars that died in supernova explosions, and now spin relentlessly, periodically flashing the Earth with a bright beam of electromagnetic radiation.  Many pulsars spin in a very stable manner, shining their spinning light on us at very precise intervals, which we can time and write down.  If a gravitational wave passes between us and a pulsar, then it stretches the space between us, and it takes the pulses longer or shorter amounts of time to reach us! We can detect gravitational waves by watching for changes in the arrival time of pulsar pulses!  This is called pulsar timing.

We can detect gravitational waves by monitoring the arrival times of pulses from many pulsars in different directions on the sky.

The second astrophysical method for gravitational wave detection is to look very closely at the Cosmic Microwave Background, and see if gravitational waves left very tiny distortions in the microwaves. There are many different distortions that can and do appear in the Microwave Background radiation, but the signature of gravitational waves is unlike just about every other kind of known distortion. They are of intense interest because if that signature could be detected, it would mean the gravitational waves came from the other side of the Curtain! This is exactly what the BICEP2 experiment was all about, and will be the theme of our discussion in the next and final post of this series.

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This is the second installment in a 3-part series about the March 2014 BICEP2 announcement about the detection of a putative signal from inflation in the Cosmic Microwave Background.  Part 1 can be found here.