Chapter 3 Extrasolar tests of gravity

  The Solar System allows us to investigate a number of diferent gravitational efects. Many of them can be measured to high accuracy, because we have easy access to the nearby planets and satellites. They are, however, quite weak gravitational fields. This is because all of the objects in the Solar System are, relatively speaking, rather slow moving and not very dense. If we set our sights a little further though, we can find objects that are much more extreme than anything we have available nearby.

  Let’s start by considering the life of a star. First-generation stars are thought to form when the clouds of hydrogen gas that emerged from the Big Bang collapse under their own gravitational field, and become hotter and denser. Eventually nuclear reactions start occurring, and the outward pressure from these reactions becomes strong enough to balance the inward attraction of gravity.

  This results in a star: a hot ball of collapsed gas undergoing violent nuclear reactions. This process of collapsing gas and nuclear reactions is, of course, also a rough description of what happens in our own Sun.

  

  But this isn’t the end of the story. A star such as the Sun can only ever have a finite lifetime. Eventually the hydrogen required for nuclear fusion will run out, and the star will have to start burning other materials. This makes it swell into a red giant. In turn, even these alternative fuels must eventually run out, and the gravitational collapse of the star will resume. What stops the collapse at this point depends on the size of the star. A small star will settle down to become a white dwarf. This is a state in which the quantum mechanical properties of the electron prevent it from becoming any smaller. At this point it’s just not possible to fit any more electrons in the space that the star takes up.

  If a star is a bit bigger, then instead of becoming a white dwarf it will end up as a neutron star. In a star of this type, the end of nuclear fusion leads to a collapse of its core. The star then collapses, which in turn causes a colossal explosion, known as a supernova. During this process the gravitational force is strong enough to force the electrons and protons to combine into neutrons. The electron pressure is then absent, and the star collapses until the neutrons are so dense that no more can fit into the same space. The end result is a star that has a density that’s comparable to the nucleus of an atom. In a sense, a neutron star can be thought of as a giant atomic nucleus (but without any protons and without electrons orbiting it). Neutron stars are very small and very dense. They are denser than anything that exists in the Solar System, and tend to move at extremely high velocities.A neutron star isn’t the most extreme object that can result from a collapsing star though. That title goes to a type of object called a black hole. If a star is so large that even the pressure from neutrons can’t support it, then it will collapse to a black hole.

  A black hole is one of the most extreme objects that can exist in nature. All that is really left after a collapse of this type is the gravitational field itself. A black hole consists of a region of space-time enclosed by a surface called an event horizon. The gravitational field of a black hole is so strong that anything that finds its way inside the event horizon can never escape. Even light. Hence the name.In this section we are going to consider star systems that contain some of the objects just described. Astronomers have now discovered a large number of these systems, and observations of them have allowed us to explore gravity in ways that are simply impossible in our own Solar System. The extreme nature of these objects amplifies the efects of Einstein’s theory, so that, even though they are very far away, they ofer us a new and exciting window through which to see the efects of gravity.

  The Hulse–Taylor binary pulsar

  The Hulse—Taylor binary pulsar, or PSR B1913+16, is a star system that contains two neutron stars in orbit around each other. The remarkable thing about this system is that one of the neutron stars is what is known as a pulsar (an abbreviation of 『pulsating star』). These are stars that appear to emit regular pulses of radiation, when viewed from Earth. This radiation is the result of the strong magnetic fields that surround the star and that cause powerful beams to be projected outwards from its surface. Together with the rapid rotation of neutron stars, these beams appear as rapid 』ashes of radiation to distant astronomers, much like the signal from a lighthouse appears as 』ashes of light to nearby sailors.

  Pulsars were discovered for the first time in 1967, by Jocelyn Bell Burnell and Antony Hewish. These astronomers saw the characteristic 』ashes of radiation that are now known to signal the existence of a pulsar, but at the time were quite unexpected. Indeed, it was originally thought that these 』ashes could be signals from another civilization. The astronomers even went as far as to call the source of the signal LGM-1 (Little Green Men-1). Later, similar signals were discovered from other parts of the sky, and it was realized that the pulses were from a rapidly rotating neutron star. At present we know of the existence of thousands of pulsars. In the future we are likely to find many more.

  The significance of the discovery of PSR B1913+16 by Joseph Taylor and Russell Hulse in 1974 was not that it was a pulsar, but that it was a pulsar in orbit around another neutron star. This information was obtained by noticing that the arrival times of the pulses varied slightly. That is, the arrival times of the pulses were sometimes three seconds earlier and sometimes three seconds later. The period over which this change happened was about seven hours and forty-five minutes. As the pulsar emitted seventeen pulses a second, it was possible to make a smooth chart that showed a clear pattern. The only explanation was that the pulsar was in orbit around another object, and that the radius of the orbit was about three light seconds (that is, the distance light travels in a period of three seconds, equal to about a million kilometres).

  So the Hulse—Taylor pulsar was known to be part of a binary system, but it was still not possible to see the other object in the system. This meant it couldn’t be a regular star, but it had to be something with a similar mass to a star. It was decided that the most plausible explanation was that the pulsar was part of a binary system, with the other body in the system being a neutron star that wasn’t pulsating (or, at least, wasn’t sending any pulses of radiation in our direction). Such a system is of particular interest for the study of gravity because the objects involved are so dense and are orbiting each other at such extremely high velocities. This makes the small efects that are predicted from Einstein’s theory much more prominent. The fact that one of the neutron stars was emitting a signal that was as accurate as an atomic clock was the icing on the cake. Information could be extracted from this signal about the details of the gravitational interaction.

  Data has been collected from the Hulse—Taylor binary pulsar since its discovery in 1974. This has been done primarily with the Arecibo telescope in Puerto Rico, which is a 305-metre-wide radio antenna (and which will be familiar to anyone who has seen the film GoldenEye). It is this large collection of data that makes this particular binary pulsar system special. Later, I will discuss some other binary pulsar systems that are now known to exist, but none of these have been observed for as long as the Hulse—Taylor pulsar. The large database that has been constructed for this system allows for some very precise tests of gravity to be performed.

  Let’s now consider the specifics of how information about gravity is encoded in the pulsar’s signal. One way that this happens is through time delays and redshift efects that the signal experiences, as it travels through the gravitational field of the companion neutron star. You will recall that both of these efects have been measured in the Solar System. Now they can be measured in two distant neutron stars, which orbit each other at a distance that is similar to the radius of our own Sun. Another efect that will be familiar, and that is visible in the Hulse—Taylor binary system, is the precession of the orbit. Just as the orbit of Mercury precesses around the Sun so too the neutron stars in the Hulse—Taylor binary system precess around each other. To compare with similar efects in our Solar System, the orbit of the Hulse—Taylor pulsar precesses as much in a day as Mercury does in a century.

  A final efect which it is possible to measure with the binary pulsar, and which is impossible to measure in the Solar System, is the change in period of an orbit due to the emission of gravitational waves. The existence of gravitational waves has not yet been discussed, but it is a definite prediction of Einstein’s theory: there should exist ripples in space-time that can carry energy out of a system. This is a phenomenon that has no counterpart in Newton’s theory, and is therefore of particular interest for testing Einstein’s gravity. I will explain gravitational waves in more detail in Chapter 4, including attempts to measure them directly. For now, I just want you to keep in mind that they were predicted by Einstein, and that they should act to remove energy from the binary pulsar system, as they are emitted from the orbiting bodies.

  So there are three relativistic efects that can be measured in the arrival times of the pulses from the Hulse—Taylor system. These are the time delay efect from the gravitational field of the companion neutron star; the precession of the orbit of each star; and the decrease in orbital period due to the loss of energy through gravitational waves. Any two of these pieces of information can be used to infer the masses of the two neutron stars, which up until this point have not been measured in any way. The third piece of data can then be used to see if Einstein’s theory is correct.

  Using this method the masses of the two neutron stars in the Hulse—Taylor binary system can each be determined to be about 1.4 times that of the Sun. This is inferred using the size of the time delay efect, which can be measured to about 0.02 per cent accuracy, and the amount of precession of the orbit, which can be measured to an accuracy of about 0.0001 per cent. From the masses of the two stars, we can then calculate what Einstein’s theory predicts for the amount of energy lost through gravitational waves, and what this means for the orbital period. It turns out that Einstein’s theory predicts the orbits should decrease by about 3.5 metres per year. This is exactly what is measured, up to the accuracy of the observations, which is currently around 0.2 per cent. This is another spectacular confirmation of Einstein’s theory of gravity, and one for which Hulse and Taylor were awarded the Nobel Prize in Physics in 1993.

  One last efect that is expected to occur in the Hulse—Taylor pulsar, is geodetic precession (the change in direction of the axis of a spinning top). This efect will be encoded in the shape of the signals that arrive from the binary pulsar, because the pulsar itself acts as a spinning top in its orbit around its companion. Although it has probably been observed, the interpretation of this data is currently not good enough to give another precision test of Einstein’s theory. This is mainly due to the unknown details of the region that emits the pulses of radiation on the surface of the neutron star.

  The Hulse—Taylor binary pulsar ofers some excellent tests of gravity, but while it is unique historically, it is now no longer the only binary pulsar that we know about. Let us now consider newly discovered systems that in some cases can already rival the tests of gravity we can perform with the Hulse—Taylor system, and which promise to outstrip it in the future.

  Other binary pulsar systems

  Due to its historical significance, the Hulse—Taylor binary pulsar has the privilege of being named after its discoverers, as well as having a scientific name (PSR B1913+16). Other binary pulsar systems are usually just referred to by their scientific names. The convention that’s been adopted for this is to call the system PSR, for 』Pulsating Source of Radiation』, and then to write its position on the sky in terms of right ascension and declination (these are coordinates that indicate positions on the sky). The letter 『B』 or 『J』 is also used to denote whether the pulsar was discovered before or after 1993 (the ones discovered after this date usually have their position recorded to higher accuracy).

  Up until 2006, we only knew about the existence of eight other binary pulsar systems that had orbital periods of less than a day. Some of these systems have special properties that make them particularly interesting for studying gravity, and although they haven’t been observed for as long as the Hulse—Taylor pulsar, they still ofer new insights into how gravity works. In the rest of this section, I will give a very brief summary of some of the most interesting of these systems, before finishing of with a look forward at what the future holds for extrasolar tests of gravity.

  Let’s start with PSR B1534+12. As the name shows, this binary pulsar system was discovered before 1993. The remarkable thing about this system is that we see it almost exactly edge on. That is, our line of sight to the system lies almost exactly in the orbital plane of the two neutron stars. This amplifies the time delay of the radio signals, as at some points in the orbit the radio waves from the pulsar have to pass very close by to its companion before they can make their way to Earth to be observed by our astronomers. The pulsar also has particularly strong and narrow radio pulses, which makes it a very good clock. Unfortunately the distance to this system is not known with much accuracy, which limits the precision with which it can be used as a test-bed for gravity. To date, this system has therefore not provided as much information about gravity as the Hulse—Taylor pulsar.

  Another binary pulsar system of special interest is PSR J1738+0333. This system is thought to contain a pulsar in orbit around a white dwarf (the bigger brother of the neutron star, described earlier in this section). The special thing about this system is that the two objects involved are very diferent from each other. This allows for a new test of gravity. It just so happens that in Einstein’s theory the emission of gravitational waves from a binary system isn’t particularly sensitive to whether or not the two objects are similar or diferent. Most of the possible alternatives to Einstein’s theory do, however, predict sensitivity to this type of diference. By looking at how much energy is lost to gravitational waves in a system such as PSR J1738+0333, it is therefore possible to provide an additional test of Einstein’s theory. If Einstein were wrong, then we should expect PSR J1738+0333 to lose energy at an anomalously high rate. So far, no such anomaly has been detected, which provides still further verification of Einstein’s theory.

  However, probably the most exciting system that was known about before 2006 is PSR J0737-3039A/B. This system was discovered in 2003, and has a number of almost unbelievable properties. Chief amongst these is the fact that both the neutron stars in the system were observed to be emitting pulses of radiation leading to it being called the double pulsar. No longer was it the case that the second object in the system was simply a passive companion, providing only a gravitational field through which the radio signals of the pulsar travelled. In this system both objects were emitting pulses of radiation, which allowed both of their orbits to be tracked in ways that were not previously possible. As if this amazing discovery wasn’t enough, however, it also turned out that the two pulsars were moving at extremely high velocities (even by the standards of binary neutron stars), and that the system was almost exactly edge-on. This combination of properties greatly enhanced the efects of relativistic gravity in the system, to such an extent that by 2008 one of the pulsars had precessed so far that its radio pulses went completely out of view.

  No longer do we have to observe for many decades to see the subtle efects of Einstein’s gravity; with the double pulsar system we could see them in just a few short years. It is now the case that PSR J0737-3039A/B provides even better evidence for the existence of gravitational waves than does the Hulse—Taylor pulsar. While both pulsars were visible, this system provided six ways to measure the gravitational fields of the neutron stars compared with the three that are available for the Hulse—Taylor system. After determining the two unknown masses of the neutron stars, this leaves four independent tests of gravity in a single system. Yet again, Einstein’s theory passed these tests with 』ying colours.

  The future

  While astonishing discoveries have already been made by observing gravitational systems outside of the Solar System, it is highly likely that we have even more to look forward to in the future. The reason for this optimism is partly due to the construction of a new generation of telescopes, the largest of which is known as the SKA (Square Kilometre Array). The SKA will be a telescope designed to receive radio waves from distant sources, and it will be built on a scale never before seen on Earth.

  The SKA will consist of thousands of radio antennas and dishes, spread over distances of several thousand kilometres in South Africa and Australia as well as several other sub-Saharan states.

  The total collecting area of the telescope (the sum of all dishes and antennas combined) will be one million square metres. It will be fifty times more sensitive than any other radio telescope ever built, and will require a computer network with a capacity larger than all current internet traic combined. The estimated cost of the SKA, at the time of writing, is around €2 billion, which is being supplied by an international collaboration between Australia, New Zealand, Canada, China, India, South Africa, Italy, Sweden, the Netherlands, the UK, and Germany. By any standard, the SKA is a monumental undertaking.

  A project the size of the SKA takes a long time to plan and build, but when it starts taking data in 2020 it will allow experiments to be performed that were never previously possible. For the purposes of studying gravity, one of the most important of these will be the measurement of large numbers of pulsars. First of all, the SKA is very likely to discover a large number of new binary pulsar systems, each of which can be used to study gravity in the way just described. Second, and perhaps even more exciting, the SKA will likely detect hundreds of rapidly rotating microsecond pulsars (i.e. pulsars that rotate millions of times a second). The idea is that by carefully measuring the arrival times of the signals from each of these pulsars, the SKA will be able to directly measure the efect of long wavelength gravitational waves as they pass through our part of the Universe. In this way, the SKA promises to be a giant gravity wave detector (something I will explain in more detail in Chapter 4).

  It is expected that the observations of gravitational phenomena made by the SKA will be about a hundred times more accurate than those made by observing bodies within the Solar System. This will be a huge leap forward. At present, binary pulsar observations are just starting to overtake observations made in the Solar System as the best testing ground for gravity. The SKA will do considerably better. Beyond even this though, the SKA ofers a few more tantalizing possibilities for testing gravity. One of these involves using the SKA to test how gravity works over very large distance scales in the Universe. I will return to this in Chapter 5. Another is the possibility of discovering a pulsar in close orbit around a black hole. A black hole is expected to be the most extreme gravitational field that exists anywhere in the Universe. It is the result of a large star collapsing in on itself at such a rate that nothing can stop it. The existence of binary systems comprised of a pulsar and a black hole are expected to be rare, but if they do exist, then there’s a good chance the SKA will find them. Such a system would provide the opportunity to test gravity in the most extreme of all environments. It is a very exciting prospect.

  Another, more immediate, reason for being hopeful about the future of extrasolar gravitational physics is the recent discovery of another new type of pulsar system. In 2014, a team of astronomers announced that they had discovered a pulsar in orbit with not one, but two, white dwarfs. They named this triple system PSR J0337+1715. The orbits that are possible in a triple star system are much more varied than the possibilities in a binary system, and it looks as though the system is structured in a hierarchical way, such that the pulsar is in a close orbit with one of the white dwarfs, while the second white dwarf orbits them both at a larger distance. The outer white dwarf appears to be accelerating the orbits of the inner pair, providing a new type of laboratory within which strong gravitational physics can be studied.

  It’s expected that new telescopes such as the SKA will aid the study of both double and triple pulsar systems. It may even be the case that it allows astronomers to observe the frame-dragging efect (described in Chapter 2), in which space itself is dragged around with the rotating stars. Such a measurement would not only be of interest for the study of gravitational physics, but also for astrophysicists who want to know how matter inside neutron stars behaves. If such observations could be made, they would allow us to study a material with a density of around a trillion kilograms per cubic centimetre.