Music of the Spheres

Scott A. Hughes

In a distant galaxy, long ago, a pair of black holes, each about thirty times more massive than our sun, began to orbit one another. Over the next several hundred million years, gravitational waves generated by their motion caused them to spiral together, slowly at first but gathering speed as they came closer and closer, until they were whirling about one another at the same rate as the blades in a kitchen blender. They eventually slammed together at about a third of the speed of light, emitting a last burst of gravitational waves before settling down to the sedate life of an ‘ordinary’ black hole.

Those gravitational waves passed through our solar system on 14 September 2015. They were picked up by the Laser Interferometer Gravitational-Wave Observatory, only days after the new Advanced LIGO detectors had come into operation. Over the following months, more than 900 scientists worked together to study the event. On 11 February, they announced that we have, at last, detected gravitational waves. My colleagues and I have been celebrating ever since.

Einstein first predicted gravitational waves – ripples in gravity produced by rapidly accelerating masses – in 1916. He botched the first analysis. He corrected his mistakes in 1918, but remained confused, vacillating about the nature and even the existence of gravitational waves several times in his life. Indirect evidence for these waves finally came following the discovery in 1974 by Russell Hulse and Joseph Taylor of a binary system containing two neutron stars. Over many decades of observation, these neutron stars have been observed to slowly spiral towards one another at exactly the rate predicted by the laws of gravitational wave emission.

But gravitational waves were not directly detected until this month. The discovery event has been described as a ‘chirp’. ‘Hearing’ this signal is somewhat metaphorical. Sound is a pressure wave that propagates through a material medium like air or water. Gravitational waves are ripples of gravity propagating through space and time. The oscillation frequencies of the waves that LIGO measures correspond precisely to the range of pitch to which the human ear is sensitive. Although we did not directly hear the collision of two black holes, it is fair to say that LIGO converted the gravitational signal into an audio one, much as a radio converts electromagnetic signals into audio.

Astronomy has largely been a science of images: we point telescopes at objects in the sky and study the images we find. Astronomy with gravitational waves is a different endeavour. We cannot use gravitational waves to make an image of the source that produces them. Instead, the theory of general relativity tells us how the dynamics of a gravitational-wave source is imprinted on the waves that we measure. General relativity tells us how the pitch and strength of the waves change as their source wiggles here and wobbles there. It tells us how the properties of the two black holes – their masses, their spins, the shape of their orbits – influences the waves that come out.

When we listen to the waves that LIGO first played for us, we can tell that the system is quite heavy, since the signal ends a bit lower than middle C on the piano. If the system were lighter, the waves would have ended at a higher pitched note. We can tell that the two objects are about the same mass because the waves sweep across the band of frequencies that LIGO is sensitive to quite fast. If the masses were less equal, they would have moved through this band more slowly.

We can also tell that the two black holes appear not to be spinning very quickly, though we are less confident of this. If they were spinning rapidly and their axes were misaligned, each black hole would wobble in its orbit. The wobbling would imprint a distinct warble on both the strength and the pitch of the waves it produces. We don’t hear this warble, so either they aren’t spinning very fast or their axes are aligned quite closely.

However, there are gravitational-wave homonyms: two systems with slightly different properties might sound just the same if our detectors can hear only a few cycles of their waves. It reminds me of trying to understand a friend with a heavy accent in a noisy pub. Did he just say ‘Want another beer?’ or ‘Wanda’s mother’s fear’? ‘Beer’ makes a lot more sense; but Wanda’s mother does seem to be afraid of her own shadow.

We know we can hear these waves now, and we want to make our ears better. We want to reduce the noisy hiss inherent to our detectors as much as possible, and open up the range of pitches we can hear. We want to hear more of the wave packet, so we can listen for the wobbling warble of spinning black holes as they move through the last steps of their inspiralling dance. We want to hear binary neutron stars, and search for the explosion that is sure to follow in gamma rays and infrared. We want to hear the ghostly whispers of the earliest moments of the universe’s expansion. We want to listen without prejudice and to hear things that for now we can barely imagine.

Virgo, an antenna in Italy, will join the search later this year, to be joined by detectors in Japan and India in the next few years (both LIGO’s detectors are in the United States). A planned detector in space, eLISA, will extend our ears from the soprano and tenor of neutron stars and stellar mass black holes to the baritone of black holes with a million times the mass of the sun. The bass of even more massive black holes will be revealed using a network of pulsars, rapidly rotating neutron stars that emit regular radio pulsars. The basso profundo of the universe’s earliest moments has left its mark on the cosmic microwave background radiation. With sufficient care, effort and patience, we will disentangle it from the interference that currently masks it from our detectors. The universe has been talking to us for a long time. Until 14 September 2015, we didn’t have the ears to hear. Now that we do, it is time to listen to its story.


  • 24 February 2016 at 10:41am
    mototom says:
    I find all this simultaneously fascinating and nonsense.

    I appreciate the effort to communicate what gravitational waves are and why they're important, but my brain is anesthetised by the whole thing.

    Most recently I heard that the latest understanding is that gravity does not actually exist, it is an illusion caused by the curvature of space/time (and no I don't understand what that means.)

    One other thing, describing such stellar systems as "heavy" or "light" does not encourage me to really trust the rest of the article - I mean, "heavy" (and "light") refers to weight and that is a force (in this case gravity acting on mass). Seeing as we are talking about the gravity caused by the mass of the system, what gravity is acting on that system to cause weight?

    I suppose what I really want to know is, is it possible to understand any of this without understanding the mathematics?

    • 25 February 2016 at 1:16am
      Graucho says: @ mototom
      You are in good company as the nature and behaviour of waves have baffled some of the greatest minds in physics and we are talking light waves never mind gravitational ones.
      As I would understand it, a phenomenon can be described as a wave if it pulses, that is rises and falls when measured at a fixed location over time, and this is what the physicists must have detected in this case.

    • 26 February 2016 at 11:33am
      mototom says: @ Graucho
      Thanks for your gentle words.

      Another enigmatic puzzle I'm struggling to grasp is if gravity is real rather than simply a misunderstanding of some other real phenomena, what have gravitational waves got to do with gravity? Are these waves involved in my persistent attraction to the earth?

    • 29 February 2016 at 10:37pm
      DARKNRG says: @ mototom
      Heavy does not only refer to the weight of something. It can also refer to the mass. In simplest terms, that is related to the number of neutrons and protons it has, and it can be defined by the object's inertia or its gravitational effect on other objects. So in that sense, Earth is "heavier" than the moon because it has more mass, even though both are "weightless" in space.

      Black holes have the mass of all the neutrons and protons that have fallen into them, but the mass is expressed only through its spacetime curvature. So one can infer a mass for them by the gravitational field (from the Newtonian perspective) that they create at large distances, or by their inertias. This is the same process you use to infer the mass of other large objects, like the Sun and Earth.

      These two black holes would both behave dynamically like ~30 solar mass objects if you were far away from them. In this case, "far" means much larger than their "sizes," or Schwarzschild radii, which are around 100 kilometers, give or take.

  • 24 February 2016 at 11:40am
    Alan Benfield says:
    A nice analogy to how gravity works is to imagine space-time as a two-dimensional rubber sheet, under normal gravity, of course, dotted with spheres of various sizes. Obviously these spheres will distort the rubber sheet by differing amounts depending upon their mass.

    Now imagine a marble which is set to roll across the rubber sheet. If it stays well away from any of the spheres, its trajectory will not be affected, but the nearer is comes to any of them, the more likely its trajectory is to be deviated. In the extreme case, if it passes too close to an object, it will be 'captured', either to orbit the object or to collide with it. This is, of course, a very poor model in that everything apart from the moving marble is static, whereas probably in the real universe all objects are moving to some extent. But as an analogy it gives some indication of how in three dimensions space-time can be distorted in the vicinity of massive bodies to produce what we experience as 'gravity'. It has been known for some time that light (which normally travels in straight lines) experiences this effect in the vicinity of massive bodies. In the vicinity of black holes, the light is not just deviated but actually captured, which is why they are black.

    General Relativity posits that the movement of massive bodies will disturb the surrounding space-time to produce gravitational waves; again, to use an illustration, as two-dimensional waves are created by dropping a stone into a pond. This effect, however, is so small that only very massive objects are likely to produce a measurable effect. That is why the recent results are so exciting: finally an object (actually two objects) massive enough (and rotating) has produced an effect large enough to be measurable, so confirming an essential prediction of General Relativity.

    I hope this helps.

    • 25 February 2016 at 2:44pm
      Rikkeh says: @ Alan Benfield
      See also:

    • 1 March 2016 at 10:58am
      Alan Benfield says: @ Rikkeh
      Well, there are limits to any analogy...


    • 3 March 2016 at 11:23pm
      Timothy Rogers says: @ Alan Benfield
      The limits to the analogy of the rubber sheet, which is a good one, is that the curvature of space-time by mass is omni-directional. In the rubber-sheet picture we are looking at a flat, two dimensional plane that now gets dimples into a third (orthogonal) direction when it is distorted by mass. But there are actually a virtually infinite number of imaginary planes that are affected by mass, "radiating out" from the center of mass of the object that is affecting space-time. This is really hard to picture, though you could approximate it through a series of pictures that show you inserting more sheets at different angles that pass through the center of mass of the object distorting them.

      The zooming marble traveling across the sheet is a little easier to picture and even replicate with simple materials. Take a stainless steel salad bowl put a marble in it (or a popcorn kernel), and with two hands start moving the bowl around in a circular motion - at the slow speed the marble travels in a circular path near the bottom, but as you increase the speed of your circular motion (which is being transferred to the marble), it creeps up the side of the bowl, and, if you make it go fast enough it goes flying out. This certainly illustrates both the "dimple" in space time and the fact that objects can move at velocities that allowthem to be captured in orbits and velocities that escape that orbit (moving, when they escape, at a tangent to the circle which touches it at the point where the marble hits its escape velocity - it will now go in a straight line with respect to the bowl, though of course curve down toward the floor).

    • 4 March 2016 at 9:32am
      Alan Benfield says: @ Timothy Rogers
      Quite right. I think the problem with the analogy is that it can only ever be a hint at the nature of gravity in that the mind is incapable of doing the thought experiment required to visualise the extension of the 2-D model to a 3-D space-time. So, not 'really hard', but probably impossible to picture.

      But it hints in the right direction. While I like your salad bowl potential well visualisation, it ultimately suffers from a similar limitation. But it demonstrates the idea of escape velocity nicely.


  • 2 March 2016 at 8:47pm
    Aethelbald says:
    >> the explosion that is sure to follow in gamma rays and infrared

    Presumably this should be at the exact same time.

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