What Are the Limits of Physical Law?
Chapters 3 through 5 describe the quest for new physical laws under circumstances in which it is already known that current understanding is incomplete. What of the familiar laws of physics that human beings use on a regular basis? Particle accelerators and telescopes, and bridges and airplanes, are designed and built through the confident application of principles that have been used and tested over centuries. However, this testing has, for the most part, taken place only under the physical conditions that are accessible to humans working on Earth, and there is an intense curiosity about whether these basic principles of physics are valid under more intense conditions.
The opportunity provided by contemporary astrophysics is to subject essentially all of this “secure” physics to scrutiny in extreme environments, under pressures, temperatures, energies, and densities orders of magnitude greater than those that can be created within a terrestrial laboratory. What makes this opportunity so timely is a new generation of astronomical instruments (made possible by technological advances) that can measure with precision the conditions that exist in the extreme environments found in the universe.
There are two quite separate reasons for carrying out this program. The first is to check the basic assumptions made when analyzing exotic cosmic objects like white dwarfs, neutron stars, and black holes. For example, the wavelengths of the spectral lines that are emitted by common atoms on Earth have been measured with great precision. Do similar atoms orbiting a massive black hole at nearly the speed of light emit at exactly the same wavelengths? Although there is no strong reason today to doubt this assumption, it must be checked: If it did turn out to be false, then much of the current understanding of the evolving universe and its contents would be seriously undermined.
The second reason for subjecting the laws of physics to extreme tests is even more important—it affords us the chance to discover entirely new
laws. For example, when Albert Einstein thought hard about the most basic principles of kinematics, not just in the everyday world but at speeds near that of light, he was led to the special theory of relativity, with its bizarre melding of space and time. Later, once particle accelerators were built, it became possible to give particles extremely high energies and thus to show that supposedly fundamental particles like the proton actually had substructure—quarks and gluons. Accelerators gave birth to the whole new field of particle physics, whose laws are so different from those of classical physics. It will be quite remarkable if more “new” physics is not uncovered by probing matter under more extreme conditions.
Fortunately, the approaches to satisfying these twin reasons are identical. The problem must be attacked from both ends on the one hand by using the universe as a giant cosmic laboratory and watching it perform experiments and on the other by carrying out controlled experiments on Earth that are tailored to simulate, as closely as possible, astrophysical conditions. Neither approach by itself is complete. The cosmic laboratory includes the astrophysicist only as a silent witness, a decoder of distant events from fragmentary clues, rather like a historian or an archaeologist. The experimental physicist has more immediate control but cannot recreate the extraordinary range of conditions that occur in the universe. The two approaches are therefore complementary and should be pursued in parallel.
Particle accelerators exist on Earth that can raise protons to energies 1,000 times greater than their energies at rest. Many trillions of particles can be accelerated, from which a few very rare and valuable events are culled. However, for the foreseeable future, building a terrestrial accelerator with sufficient energy to explore directly the unification of all the forces is inconceivable. By contrast, cosmic ray protons are created in distant, astronomical sources with energies some 300 million times greater than those produced by the largest particle accelerators on Earth (see Box 6.1). These collide with atoms in the upper atmosphere, and the products of these collisions are observed on the ground as sprays of particles called air showers. Thus, cosmic ray protons can be used to explore physics at much higher energies, but only with rather primitive diagnostics. Both accelerators and cosmic ray experiments are needed to obtain a complete picture.
EXTREME COSMIC ENVIRONMENTS
Many cosmic environments for testing physical laws are associated with stars or their remnants. The interiors of stars have temperatures of several millions of degrees, hot enough to drive the nuclear reactions that
make them shine. When a star’s fuel is exhausted, it shrinks under the pull of gravity, becoming even hotter in the process. Relatively small stars like the Sun come to rest as dense white dwarfs—one teaspoon of a white dwarf weighs several tons. Yet this density pales in comparison with that of neutron stars, formed by the spectacular supernova explosions of more massive stars, that have density beyond that of nuclear matter, 1,000 trillion times that of normal matter and initial temperatures of over 100 billion degrees (see Box 6.2). Neutron stars themselves have a maximum mass (less than three solar masses), and the most massive supernovae have no option but to
BOX 6.1 ULTRAHIGH-ENERGY COSMIC RAYS
“Cosmic ray” is the name given to high-energy particles arriving at Earth from space, including protons and nuclei. Of particular interest are the highest-energy particles, whose source is currently unknown. Such particles are so rare that their detection requires huge, many square-kilometer arrays on the ground to collect air showers, the cascades of particles that are created as cosmic rays strike the upper atmosphere. The event rate is so low at the highest energies that it is still not clear whether the spectrum actually shows the predicted high-energy cutoff predicted due to degradation by interactions with the cosmic microwave background radiation (see text). There is some evidence, still not conclusive, that the spectrum of cosmic rays extends past the cutoff energy, at 5 x 1019 eV. The handful of events above this energy are of exceptional interest because of their extraordinarily high energy coupled with the fact that they must come from relatively nearby sources, cosmologically speaking.
Current data indicate that the flux of particles above the cutoff energy is only about five particles per square kilometer per century. The main challenge is therefore simply to collect a sufficiently large sample. Several experiments are under way or proposed to address this problem. Their aim is to discover a characteristic pattern that reveals the nature of the sources. An important technical aspect of all the new experiments is the atmospheric fluorescence technique, by which profiles of individual air showers can be observed from a relatively compact array of telescopes that track the trajectory across the sky—the socalled Fly’s Eye technique. The technique can be used alone or in hybrid mode with a giant array of particle detectors on the ground. The ultimate use of this technique would be to monitor huge areas of the atmosphere from space to detect giant cascades. To detect the high-energy neutrinos that may accompany the production of ultrahigh-energy cosmic rays, a large array of detectors deep in water or ice is needed to record the characteristic flashes of light from neutrino interactions while suppressing the background from low-energy cosmic rays that bombard Earth’s surface. Some strategies for detecting ultrahigh-energy cosmic rays and neutrinos are illustrated in Figure 6.1.1.
BOX 6.2 NEUTRON STARS AND PULSARS
When a star has exhausted its nuclear fuel, a runaway collapse of the core and ejection of the mantle in a supernova explosion mark its demise. In stars more than about 15 times the mass of the Sun, nothing can arrest the collapse of the core into a black hole. When the initial mass is some 6 to 15 times the solar mass, matter in the core is crushed only to nuclear density and the collapse stops. Electrons and protons combine to make neutrons and neutrinos, the neutrinos escape, and the remnant is a bizarre “nucleus” some 10 km in radius—a neutron star. Following the ejection of the mantle in a supernova, a neutron star is formed. Not all neutron stars have the same mass; many do have well-determined masses of around 1.4 solar masses. A neutron star of mass greater than about 3 solar masses cannot support itself against gravity, and collapse to a black hole is inevitable. Neutron stars are hot, rapidly spinning, highly magnetized objects. Radiation is channeled and emitted in searchlight beams along the magnetic axes. When the spin and magnetic axes are not aligned, the beams rotate rapidly through the sky, giving rise to regular pulses
FIGURE 6.2.1 Schematic of the interior of a neutron star showing the layers of packed and compressed matter. Condensed matter physics can tell us many things about the forms that matter takes, except at the very center of the neutron star, where densities exceed those of nuclear matter.
as they briefly illuminate Earth. Such spinning neutron stars are called pulsars.
The neutron star is as exotic an environment as one could wish for (Figure 6.2.1). On the star’s surface, a sugar cube would weigh as much as the Great Pyramid of Egypt. The surface is most likely made of metallic iron. Below, the pressure increases rapidly, and electrons are captured by protons to make increasingly neutron-rich nuclei. The nuclei become large droplets and take on strange shapes—strings, sheets, and tubes. This region, down to a depth of about 1 km, is whimsically known as the “pasta” regime. Below that, there are mostly neutrons, with a few protons and electrons. But the pressure continues to grow with depth, and it is possible that some of the electrons may be replaced by heavier particles called pions or kaons, which can combine into a collective state called a condensate. Finally it is likely that a quark-gluon plasma may form at several times nuclear density at the very center.
The response of nuclear matter to these incredible pressures is not well understood. Measurements of the masses, radii, and surface temperatures of neutron stars provide a window onto their interiors and reveal much about how nuclear forces behave under extreme conditions.
collapse all the way to infinite density, forming black holes (see Box 6.3). Such collapses may also trigger a gamma-ray burst—an explosive burst of gamma rays lasting only a few seconds but with an apparent power that may for a brief instant approach the power of the entire visible universe. The pressures inside these sources may exceed a trillion trillion atmospheres, comparable to the pressure encountered in the expanding universe when it was only about 10 milliseconds old. (By contrast, the most powerful lasers for creating astrophysical conditions can only create pressures of about a billion trillion atmospheres.)
Far from marking the permanent death of a star, any of these compact objects may herald its rebirth in a more active form. This may happen, for example, if a remnant has a regular star as a binary companion and the star swells and dumps its gas onto the compact object. The gas may swirl around the compact object for a time on its way down, forming a hot accretion disk, moving with a speed approaching that of light, and emitting x rays, or it may settle onto the surface of the compact object, providing fresh fuel for nuclear explosions. Young, rapidly spinning neutron stars called pulsars can radiate very intense radio and gamma-ray radiation (see Box 6.2). Their power derives from the spin of the neutron star, which has a magnetic field over a million times larger than can be sustained on Earth and which acts like a giant electrical generator capable of producing over 1,000 trillion volts and more than 10 trillion amperes. Other pulsars are powered by gravity, through their accretion of matter from a nearby companion.
Even larger black holes are found in the nuclei of galaxies. Essentially all galaxies, including our own, harbor in their centers black holes with masses between a million and billion times that of the Sun. These black holes are the engines for the hyperactive galactic nuclei called quasars, which for a time in the early universe outshone whole galaxies by up to a thousandfold. Quasars, too, are powered by accretion disks, fueled by gas supplied by their host galaxies. In addition, they often form “jets”—moving beams of high-energy particles and magnetic fields—which radiate across the whole spectrum from the longest radio waves to the highest-energy gamma-rays. It appears that these jets are formed very close to the central black hole, but understanding in detail how they are formed remains a major puzzle.
One of the most intriguing questions involves cosmic rays, mentioned above. It is believed that cosmic rays are energized by the shock waves associated with cosmic explosions like supernovae. However, this explanation is challenged to account for the fastest particles, with individual
BOX 6.3 BLACK HOLES
Any object whose radius becomes smaller than a certain value (called the Schwarzschild radius) is doomed to collapse to a singularity of infinite density. No known force of nature can overcome this collapse. The Schwarzschild radius (or event horizon) is proportional to the object’s mass and corresponds to that distance where even light cannot escape the gravitational pull of the central matter. Because of this property, these collapsed singularities are called black holes. Just outside the Schwarzschild radius, outwardly traveling photons can barely escape to infinity. It has even been speculated that there could be “naked singularities,” which are not shrouded by an event horizon.
Properly describing the geometry of space-time (which dictates the motion of both particles and light) near a black hole requires Einstein’s theory of general relativity. Particle as well as light trajectories become severely distorted, or curved, compared with those predicted by the Newtonian description. Geometrically, space near a black hole can be exactly described by simple formulae, the Kerr solutions to Einstein’s equations. The gravitational field depends on only two parameters, the mass and spin of the hole. The radius of the event horizon and the smallest orbit that matter can have without falling in depend on how fast the hole is spinning—the faster the spin, the closer material can get.
Einstein’s theory of general relativity is only just now beginning to be tested (e.g., by measurements made by the Rossi X-ray Timing Experiment) in regions of strong gravity, where gravitational forces accelerate matter to speeds close to the speed of light. The most straightforward test would be to observe matter directly as it swirls into a black hole, measuring the particle trajectories and comparing them with the predictions of theory. This may be possible someday with the extremely high resolution achievable with x-ray interferometers. However, nature has provided an indirect tracer of black holes at the centers of galaxies that is already being exploited. As heavy elements like iron spiral inward toward a black hole, they reach high orbital velocities and temperatures in the tens of millions of degrees. Transitions of electrons between discrete atomic energy levels generate radiation of specific wavelengths that can be observed in the x-ray band. The wavelengths of these spectral lines are altered by several effects: a Doppler shift due to each atom’s orbital velocity around the hole (the shift can be positive or negative, depending on whether the motion is toward or away from the observer); an overall shift to longer wavelengths that occurs for all radiation struggling to escape from black holes; and another longward shift due to the time-dilating effects of high-speed motion near the hole. The net result is that the lines are shifted and broadened, with “wings” whose shape depends on the atoms’ trajectories as determined by the geometry of space-time. Recent observations of broad lines from the nuclei of active galaxies believed to contain massive black holes are consistent with solutions in which the black hole is spinning rapidly.
energies comparable to that of a well-hit baseball; it may be that scientists are seeing evidence for completely new forms of matter. Very-high-energy neutrinos, some of which may be produced by jets, can also be created, and experiments are on the threshold of being able to detect these, too.
Finally, the most penetrating signals of all are gravitational waves, first predicted by Einstein in 1918 (see Box 6.4). Scientists know that these waves really do exist because the energy they carry off into space affects the orbits of binary pulsars in a manner that matches well with precision measurements of observed binary pulsar systems. However, they have not yet been detected directly. The most promising sources of gravitational waves, which involve the collisions and coalescences of large black holes, are even more luminous than gamma-ray bursts.
NEW CHALLENGES IN EXTREME ASTROPHYSICS
Four problem areas, drawn from the physics-astronomy interface, are ready for a concerted attack.
Black Holes and Strong Gravity
Isaac Newton’s theory of gravity has been superseded by Albert Einstein’s general theory of relativity, which is widely believed to be the “true” theory of gravity as long as quantum mechanical corrections are unimportant. The subtle differences between Newton’s and Einstein’s theories have been tested in the solar system by monitoring the motions of the Moon, the planets, and light. So far general relativity has passed every test with a quantitative precision that in several cases exceeds 1 part in a 1,000. Outside the solar system, the first binary pulsar, PSR1913+16, provided a test in stronger fields. By monitoring the arrival time of regular radio pulses from this source, it was possible to measure the orbital decay caused by the power lost as the two orbiting neutron stars radiated gravitational radiation. Theory and observation agree within about 3 parts per 1,000. The tests of general relativity have been so significant that few scientists doubt its validity in the regimes probed.
However, in both the solar system and pulsar tests, gravity is still relatively weak in the sense that the characteristic speeds of bodies are less than roughly one-thousandth the speed of light. Therefore the critical limit of the theory in which objects move at near-light speeds has not yet been tested. It is a basic tenet of physics that, if a physical law is truly understood and has been verified to very high accuracy in at least one location, it should be
BOX 6.4 GRAVITATIONAL RADIATION AND GRAVITY-WAVE DETECTORS
The general theory of relativity posits that matter (and energy) introduces curvature into four-dimensional space-time and that matter moves in response to this curvature. The theory admits wave solutions in which gravitational ripples in the fabric of space-time propagate with the speed of light. Such waves are an inescapable consequence of general relativity (and indeed of most theories of gravity). However, there are also some very important differences from electromagnetic radiation. Electromagnetic waves accelerate individual charged particles, and this property underlies their detection in, for example, radio antennas. Similarly, gravitational waves are detected by measuring the relative acceleration induced between a pair of test masses as the wave passes by. In addition, when gravitational wave amplitudes are large, as in some cosmic sources, the wave energy of gravitational radiation itself becomes a source of gravity, which is not true for electromagnetic waves. This nonlinearity complicates the theory of wave generation, necessitating extensive numerical computation to calculate the expected wave intensity from a given source.
The best-understood sources of gravitational radiation are binary stars. Two white dwarfs or neutron stars in close orbit lose energy via gravitational radiation and spiral in toward each other. A good example is the first binary pulsar discovered, PSR 1913+16, which comprises two neutron stars in an 8-hour orbit. One of these neutron stars emits a radio pulse every 59 milliseconds, and by monitoring very accurately the arrival times of these pulses at Earth, radio astronomers have followed the inspiral and consequent change of orbital period. As the speeds of these neutron stars are much less than the speed of light, it is possible to compute their orbits very accurately. The measurement agrees with general relativity to a precision of 3 parts per 1,000 and effectively rules out most other theories. So, in a sense, researchers have already verified the existence of gravitational waves.
Testing the theory when gravity is strong requires measuring gravitational waves directly. There are several likely strong sources of gravitational radiation: inspiraling binary neutron stars, supernova explosions, and merging supermassive black holes in galactic nuclei. In all cases, the goal is to measure the gravitational wave profile as the mass falls together and compare it with nonlinear predictions using general relativity. A peculiarly relativistic effect called Lense-Thirring precession arises when space is “dragged” by the spinning black hole. Measuring this effect would also indicate how rapidly black holes spin. In general, if the comparison between observation and theory is successful, it will constitute an impressive validation of the fundamental theory of gravity.
More exotic sources of gravitational radiation have also been proposed. A particularly important one is primordial gravity waves generated soon after the big bang in the early universe. One particular epoch proposed is that in which quarks changed into ordinary nucleons, the so-called quarkhadron transition. If this happened abruptly, in a manner similar to that by which water changes into steam, then the gravity-wave intensity may be detectable. Other such phase transitions in the early universe associated
FIGURE 6.4.1 Aerial photographs of the interferometers used in the Laser Inteferometrer Gravitational Wave Observatory (LIGO). The long tunnels house the evacuated laser chambers, in which laser beams travel a 4-km path length. At the vertex of the L, and at the end of each of its arms, are test masses that hang from wires and that are outfitted with mirrors. Ultrastable laser beams traversing the vacuum pipes are used to detect the ultrasmall change in the separation of a pair of test masses caused by the passage of a gravitational wave. Images courtesy of the LIGO Laboratory.
with the unification of the forces have also been discussed. Inflation is perhaps the most compelling source of gravitational waves from the early universe. Detection of gravity waves from the early universe would allow us to look back at extremely early times and to study physics that is simply not accessible in a terrestrial lab.
Two distinct types of classical gravitational wave detector have been proposed. The first is a ground-based laser interferometer designed to measure tiny changes in the separations of pairs of test masses (suspended by wires) due to the passage of gravitational waves. A prominent example is the Laser Interferometer Gravitational Wave Observatory (LIGO), which comprises two sites (for redundancy), one in Washington state and the other in Louisiana (Figure 6.4.1). At each site, three test masses are spaced 4 kilometers apart; it is hoped eventually to measure relative displacements between the masses as small as 10−19 meters. This facility, which began operation in 2002, will be especially sensitive to waves with periods in the range from 3 to 100 milliseconds and is therefore tuned to collapsing sources of stellar mass. To detect the gravitational radiation from the formation of more massive black holes, a larger detector that is sensitive to lower frequencies is required. Because of natural size limitations as well as seismic noise, such a detector would have to be deployed in space. Studies for a space-based gravitational wave detector to complement LIGO are under way in the United States and in Europe (see Figures 6.4.2 and 6.4.3).
possible to use it anywhere it is claimed to be valid. Thus, if general relativity is the correct theory of gravity, researchers already know what should happen when the field is strong, even though they have not tested it there yet. However, it is conceivable that general relativity may not be a comprehensive theory of gravity. Moreover, one of its most impressive predictions, the existence of cosmic points of no return—black holes—has not been fully tested. It is therefore imperative to test relativity where gravity is strong. There is no better cosmic laboratory than a black hole (see Box 6.3).
It is now clear beyond all reasonable doubt that black holes are abundant in the universe. They appear to be present in the nuclei of most regular galaxies and to have masses ranging from millions to billions times that of the Sun. In addition, much smaller black holes (5 to 15 solar masses) are being found, commonly in x-ray binary star systems in our galaxy. Recent evidence suggests a class of black holes with masses between 30 and a million times that of the Sun. Astrophysical black holes are defined by two parameters: (1) mass, which sets the size of the black-hole space-time and (2) spin, which determines the detailed geometry of the black-hole space-time. Spin is important because, as noted in the case of pulsars, rotational energy provides a reservoir of extractable energy rather like a giant fly-wheel, and it can act as a prime mover for much of the dramatic high-energy emission associated with black holes.
Observational knowledge of black holes has advanced remarkably in the last 5 years. Masses have been measured with increasing precision, and scientists are starting to understand how the sizes of black holes relate to their host galaxies or stellar companions. In addition, at least two approaches to measuring black hole spins appear to be promising, although they are yet to be convincingly exploited. Massive holes in galactic nuclei are often orbited by accretion disks of gas that spiral inward, eventually crossing the event horizon—the surface from which nothing, not even light, can escape.
The spectral lines from atoms such as iron orbiting the black hole are quite broad because they are subjected to a variable Doppler shift relative to an Earth-based observer. They are also shifted to lower energy because photons lose energy in climbing out of the hole’s deep potential well. It turns out that gas can remain close to the black hole and produce such a strongly broadened and redshifted line only if the hole spins nearly as fast as possible. On this basis, at least some active galactic nucleus black holes are already thought to rotate very rapidly.
It may be possible to use x-ray flares to map out the immediate environments of black holes only light-hours from their centers. This technique makes use of the fact that it takes a finite amount of time for high-energy x rays from
the flare to travel to the disk and excite iron emission; different parts of the disk will therefore be observed at different times, allowing the space-time around the black hole to be probed. Alternatively, if astronomers are lucky enough to catch one, a star in orbit around a black hole could also provide a powerful probe of the space-time as it is drawn in and torn apart.
There is a serious obstacle to carrying out this program. The wavelengths and the strengths of all of the spectral lines emitted by the accretion disks, which are at very high temperatures, are simply not known. (In fact it is not yet possible to identify half of the lines in the solar spectrum.) Although the quantum mechanical principles necessary to calculate these effects are understood, the atoms are so complex in practice that it is necessary to mount a focused program in experimental laboratory astrophysics to make the most of existing observations of accretion disks.
A second approach to measuring a black hole’s spin comes from monitoring the rapid quasi-periodic oscillations of the x-ray intensity from selected galactic binary sources. These are almost certainly influenced by both the strong deviations from Newtonian gravity that are present close to the event horizon, independent of the spin, and a peculiarly spin-dependent effect called the dragging of inertial frames (see Figure 6.1). Frame-dragging requires that all matter must follow the black hole’s spin close to the event horizon. In addition, if the matter follows an orbit that is inclined with respect to the black hole’s spin, the orbit plane must rapidly precess. Both effects change the oscillation frequencies. Although it has been argued that
the consequences of both of these effects are already being observed (e.g., in quasiperiodic oscillations seen in neutron star accretion disks), neither approach is understood well enough to allow confidence that it is the spins that are being measured, let alone testing general relativity.
An even bigger challenge is to image a black hole directly. Two ambitious approaches are currently under investigation. The first involves constructing a spaceborne x-ray interferometer to resolve the x-ray-emitting gas orbiting the black hole. By combining beams from x-ray telescopes far apart, it is possible in principle to produce images with microarcsecond angular resolution—300,000 times better than the best optical mirrors in space. This resolution is sufficient to enable seeing the event horizon of a supermassive black hole in the nucleus of a nearby galaxy. A second method involves submillimeter-wave interferometry, perhaps also prosecuted from space. This approach is useful for observing sources like our own galactic center, which, although not a powerful x-ray source, does emit submillimeter radiation bright enough to permit resolving the radio source that envelops the central black hole.
A quite different and more comprehensive approach to testing general relativity is to measure directly the gravitational radiation emitted by a pair of merging compact objects. Ground-based facilities in Louisiana and Washington, the Laser Interferometric Gravitational Wave Observatory (LIGO), are designed to detect merging stellar-mass compact objects in nearby galaxies. To measure gravitational radiation from forming or merging massive (or intermediate-mass) black holes, it will be necessary to construct a facility in space. Nearly as difficult as building these observatories, however, is the task of computing the gravitational waveforms that are expected when two black holes merge. This is a major challenge in computational general relativity and one that will stretch computational hardware and software to the limits. However, a bonus is that the waveforms will be quite unique to general relativity, and if they are reproduced observationally, scientists will have performed a highly sensitive test of gravity in the strong-field regime.
Finally, neutron stars also provide an astrophysical laboratory for testing the predictions of general relativity in strong gravitational fields. The quasiperiodic oscillations (QPOs) seen in association with the accretion of material onto neutron stars may be useful in probing effects predicted by general relativity, such as Lense-Thirring precession.
Neutron Stars as Giant Atomic Nuclei
Atomic nuclei are held together by nuclear forces. At the simplest level these forces act between protons and neutrons, but at a more fundamental
level they involve their constituent quarks and are mediated by the carriers of the strong force, the gluons. The gross structure of natural nuclei is comparatively well understood (with some conspicuous problems remaining, e.g., understanding the effect of the underlying quark structure on nuclei), because it is fairly well understood how nucleons interact when they are about 2 femtometers (10−15 m) apart, as they are in normal nuclei. However, what happens when matter is compressed to greater baryon density or heated to a higher temperature?
To address this question, a major facility, the Relativistic Heavy Ion Collider (RHIC), has been constructed at Brookhaven National Laboratory. Using this facility, it will be possible to collide heavy nuclei, like gold, so that they momentarily attain a density roughly 10 times that of nuclear matter. Under these circumstances, it may be possible to form a quarkgluon plasma—a denser version of the state of matter that is thought to have existed in the universe earlier than about 10 microseconds after the big bang. A strong experimental program at RHIC will be carried out over the next few years to see what the states of matter are at extreme energy density.
Nature has performed a complementary experiment by making neutron stars in supernova explosions. Neutron stars are about one and a half times as massive as the Sun and have radii of about 10 km. They can be considered as giant nuclei, containing roughly 1057 nucleons with an average density similar to that of normal nuclei. However, as gravity provides an additional strong attractive force, the densities at the centers of neutron stars are almost certainly well above nuclear, as in the heavy ion collisions. There is one crucial and important difference between colliding heavy ions and neutron stars. In the former case, the dense nuclear matter is extremely hot, about 1012 K, whereas neutron stars usually have temperatures of less than 109 K, which from a nuclear standpoint is cold. Scientists are still quite unsure about the properties of cold matter at densities well above nuclear matter density.
One good way to see what really happens is to measure the masses and radii of neutron stars with high precision. The masses of a handful are known to exquisite precision (1 part in 10,000), and a number of others are known to within a few percent, from the study of their binary orbits. Promising ways to measure neutron star radii involve high-resolution x-ray spectroscopy or the study of so-called quasi-periodic oscillations. The most direct approach is to observe the wavelengths and shapes of spectral lines formed within a hot neutron star atmosphere immediately following a thermonuclear explosion beneath the star’s surface. (These explosions, called x-ray bursts, are commonly observed from neutron stars that are fed with
gaseous fuel at a high rate.) The central wavelengths of the x-ray lines provide a measurement of the gravitational redshift—essentially the depth of the gravitational potential well—and the widths and strengths of the lines measure the rotation speed near the neutron star’s surface. Together with a good understanding of the neutron star atmosphere, these two quantities fix the mass and the radius. In addition, if the distance to the neutron star is known, it is possible to estimate the radius yet another way by knowing that the observed flux strength varies in proportion to the surface area of the star (although one must assume that the entire star is being observed). Given an accurate determination of the radius of a neutron star of known mass, it will be possible to constrain the compressibility of cold nuclear matter and thus the nature of its underlying composition and particle interactions.
An even more direct approach to learning the composition of highly compressed nuclear matter involves neutron star cooling. Neutron stars are born hot inside supernovae, which also create shells of expanding debris known as supernova remnants (see Figures 6.2 and 6.3). The size of this remnant is a measure of the neutron star’s age, and the star itself yields its surface temperature. New theories in condensed matter physics can then be used to relate the surface temperature to the temperature inside. In sum, by observing neutron stars of different ages, astronomers can measure how fast they cool.
It turns out that if the interior of a neutron star contains just neutrons and a small fraction of protons and electrons, it ought to cool quite slowly, but if it contains a significant fraction of protons or other particles like pions or kaons or even free quarks, it will cool much more quickly. Thus it is possible to learn about a neutron star’s interior simply by measuring its surface temperature. In addition, neutron star interiors are believed to be in a superfluid state, with their protons superconducting, and this too would influence the cooling. Neutron stars can serve as excellent cosmic laboratories for testing physical ideas in this new territory.
As explained in Chapter 2, quantum electrodynamics (QED) is a highly quantitative quantum theory of the electromagnetic interaction of photons and matter. It makes predictions that have been tested with great precision in regimes accessible to laboratory study. In particular, it has been tested in static magnetic fields as large as roughly 105 G.
However, ever since the discovery of pulsars, it has been known that fields as large as 1012 G are commonly found on the surfaces of neutron stars. More recently it has been concluded that a subset of neutron stars, called “magnetars,” have magnetic field strengths of 1014 to 1015 G, well above the QED “critical” field, where the kinetic energy of an electron
spiraling in the magnetic field exceeds its rest mass energy. QED should still be a correct description above this critical field, but the physics is quite different from what is normally considered. For example, when an x ray propagates through a vacuum endowed with a strong magnetic field, QED predicts that electron-positron pairs will be created in such a way that the emergent x-ray radiation will become polarized. It may therefore be possible to observe QED at work in magnetars by observing x-ray polarization and mapping out the neutron star magnetic field. Measuring x-ray polarization is difficult, but, encouragingly, it has recently become possible to measure the circular polarization of x rays from laboratory synchrotrons. Perhaps these techniques can also be used in space x-ray observatories.
Supernova Explosions and the Origin of the Heavy Elements
The big bang produced the lightest elements in the periodic table— hydrogen, helium, and lithium. Planets and people are made not only of these elements but also of carbon, nitrogen, oxygen, iron, and all the other elements in the periodic table. It is believed that the elements beyond lithium are made in the contemporary universe by stars and stellar explosions. There is a good understanding of the origin of elements up to the iron group (nickel, cobalt, and iron). The iron-group elements have the greatest binding energies, so the elements up to the iron group can be made by nuclear reactions that fuse two nuclei to make a heavier nucleus and release energy. However, producing the elements heavier than iron requires energy input, and astrophysicists have looked to stellar explosions as the likely production sites. The details of how the heaviest elements are made are still not fully known.
Supernovae mark the violent deaths of the most massive main-sequence stars and also of close binaries with one highly condensed member (e.g., a white dwarf). These cataclysmic explosions, which can be seen far across the cosmos, can be used as markers of time and distance (see Figure 5.7 for a gallery). Supernovae occur because stars become unstable either as they evolve or as they accrete matter. A main-sequence star of several solar masses can produce energy by successively combining elements up to iron. After nuclear burning has turned the core to iron-group elements, no more energy can be produced. This impasse triggers the collapse of the core and the explosion of the mantle in a supernova. Thermonuclear runaway also occurs when a white dwarf accretes too much mass from a main-sequence companion.
Supernovae are classified theoretically by mechanism—core collapse or accretion—and observationally by whether hydrogen is present in the ejecta. Type I supernovae lack hydrogen, while Type II do not. (The categories are further subdivided into Ia, Ib, Ic, II-P, II-L, II-n, and IIb according to the pattern of heavy elements ejected.) The two means of classification do not necessarily coincide, and we lack a detailed theoretical understanding of how to make the correspondence. Nevertheless, Type Ia supernovae are observed to have very similar intrinsic luminosities and have provided convincing evidence that the expansion of the universe is speeding up (see Chapter 5). Discovering whether Type Ia supernovae are truly a homogeneous class and learning what spread is to be expected in their properties are high-priority objectives of supernova research.
Supernovae are clearly the factories in which the elements up to and slightly above the iron group of elements are made. Not only are the detailed abundances of the elements lighter than iron quantitatively under-
stood with the aid of nuclear theory and laboratory data, but the telltale signatures of radioactive isotopes also are seen in the expanding shell of debris following a supernova explosion.
When it comes to understanding the origin of elements much heaver than iron, however, scientists can reconstruct much of what must have happened, but the astrophysical factory has not been clearly identified. Intermediate-mass elements are made in a neutron-rich environment in which successive neutron captures occur slowly, and neutron-rich nuclei undergo beta decay back to more stable elements. Still heavier nuclei must have been made by a succession of rapid neutron captures, referred to as the r-process. A dense, highly neutron-rich environment must exist for the r-process to occur. Also seen in the abundances are the traces of other mechanisms, including possible evidence of nucleosynthesis induced by neutrinos. The element fluorine, for example, can be made by neutrinos interacting with supernova debris. In fact, it is strongly suspected that supernovae, once again, must be the place where the remaining elements up to uranium are built, but there is no detailed understanding of how the process occurs. Resolving this problem requires observational data from supernova remnants, experimental data from both nuclear physics and neutrino physics, and the ability to make detailed, fully three-dimensional, theoretical calculations of supernova explosions.
To begin with, theoretical models of supernovae are still incomplete. Simply producing a reliable “explosion” (in the computer) has proven to be an enormous challenge. Recently, the importance of convection driven by neutrino heating from the nascent neutron-star core was confirmed by numerical calculations. The key was to do calculations in two dimensions instead of one (convection in one dimension is impossible). However, not until it is possible to do a full three-dimensional calculation with full and complete physics will the combined role of rotation and convection be clear. A full three-dimensional calculation with proper inclusion of neutrino transport will require the terascale computing facilities that are just now being realized. There is reason to hope that such a calculation will distinguish the site of the r-process and at the same time illustrate the properties neutrinos must have to match what is currently known about the elements, resolving with a single stroke two important questions in modern physics.
To make this step in computational prowess, however, theory will call upon experiment to provide solid ground for the r-process. In equal measure, progress will come from measurements in neutrino physics and in nuclear physics. Neutrino oscillations can dramatically alter the synthesis of the elements in a supernova, because the muon and tau neutrinos made in
a supernova are much hotter (more energetic) than the electron neutrinos. Normally neutrino effects are muted because muon and tau neutrinos do not interact so easily with nuclei, while electron neutrinos are not produced so hot. But if oscillations scramble the identities, the hot muon and tau neutrinos can turn into hot electron neutrinos and readily disintegrate nuclei just built by the r-process.
The nuclei built in rapid neutron capture lie at the boundary of nuclear stability, the neutron “drip line.” To trace the path of nucleosynthesis, researchers need to know the masses and lifetimes of nuclei far from the ones that can be reached with existing technology. The binding energy of such exotic nuclei can be calculated well for nuclei nearer the “valley of stability” (the region in the diagram of all possible nuclei described by their numbers of neutrons and protons where the most stable nuclei are found). How well those equations serve in extrapolation to r-process nuclei is completely unknown. In the last few years it has been realized that these nuclei can be produced and measured in a two-stage acceleration, isotope-production, re-acceleration facility. With a suitably designed facility, every r-process nucleus may be accessible for direct measurement.
Finally, there will be in the coming decades the opportunity to observe directly the synthesis of heavy elements where it is believed that synthesis occurs—that is, in the explosions of stars. These explosions create radioactive nuclei, which decay over time, usually with the emission of a gamma ray of specific energy. Future sensitive high-energy x-ray and gamma-ray space experiments will allow these decays to be observed and monitored over time soon after the explosion and the distribution of newly synthesized material in the remnant matter expelled in the explosion to be mapped with high fidelity. These remnants can “glow” for tens of thousands of years in observable radiation. Such observations can be used to constrain the theoretical models for the explosions, directly measure the quantities of synthesized material, and observe how it gets distributed into the space between stars.
Cosmic Accelerators and High-Energy Physics
Earth is continuously bombarded by relativistic particles called cosmic rays, which are known to originate beyond the solar system. Cosmic rays with energies up to at least 1014 eV are probably accelerated at the shock fronts associated with supernova explosions, and radio emissions and x rays give direct evidence that electrons are accelerated there to nearly the speed of light. However, the evidence that high-energy cosmic-ray protons and nuclei have a supernova origin is only circumstantial and needs confirma-
tion. Most puzzling are the much higher energy cosmic rays with energies as large as 3 x 1020 eV. In fact, it would seem that they ought not to exist at all, because traveling through the sea of CMB photons for longer than roughly 100 million years would rob them of their ultrahigh energy.
Accounting for these particles—probably mostly protons—is one of the greatest challenges in high-energy astrophysics. Among the many suggested origins are nearby active galactic nuclei, gamma-ray bursts, and the decay of topological defects or other massive relics of the big bang.
Protons are not the only type of ultrahigh-energy particle that might be observed from these sources—many models also imply the associated production of high-energy neutrinos. In models involving decaying massive particle relics from the big bang, such neutrinos would emerge from cascades of decaying quarks and gluons that set in at the energy scale of grand unification. In models involving particle acceleration, they could be produced in interactions of protons with dense photon fields or gas near the emitting object. The ability to detect high-energy neutrinos from energetic astrophysical sources would open an entirely new window onto the high-energy universe. In particular, since most sources are relatively transparent to their own neutrinos, these particles allow “seeing” the particle acceleration mechanism directly, deep inside the source.
Studying neutrinos is difficult because they interact only through the weak force, so they usually pass through detectors without leaving a trace. One technique for achieving a large effective volume is to detect upward-moving muons created by neutrinos interacting in the material below the sensitive volume of the detector. Upward trajectories guarantee that the parent particles must be neutrinos, because no other particles can penetrate the whole of the Earth. The atmospheric neutrinos, whose behavior provides the current evidence that neutrinos have mass, are detected in a similar way, through their interactions with detectors in deep mines; so far, however, only upper limits have been achieved up to now for energetic astrophysical neutrinos.
Gamma-ray photons, a third type of high-energy particle, have been observed from the cosmos with energies as high as 50 TeV. As is the case for the high-energy cosmic rays, the sources of such energetic photons must all be relatively local on a cosmological scale, since photons of this energy also tend to be destroyed in traveling through space by combining with background infrared photons from starlight to create electron-positron pairs. Many of the highest-energy gamma rays are probably emitted as a by-product of the acceleration of the mysterious ultrahigh-energy cosmic rays. Whether they are produced in cascades initiated by high-energy protons or
radiated by electrons could in principle be decided by determining whether or not the high-energy gamma rays are accompanied by neutrinos, a frequent by-product of high-energy proton collisions.
Understanding the origin of the highest-energy particles will require better understanding of the sites where they are accelerated. Gamma-ray bursts produce flashes of high-energy photons, and theory predicts that very-high-energy neutrinos and cosmic rays will accompany the flash. Although significant progress in locating and studying gamma-ray bursts has been made recently, the sources of these enormous explosions is still a matter of debate. Another class of energetic sources, the highly variable but long-lived jets of active galactic nuclei, in some cases emit gamma rays with energies as high as 10 TeV, which directly implies the presence of charged particles of at least this energy. Although quite different in origin, both jets and gamma-ray bursts are thought to involve highly relativistic bulk motion, ultimately powered by accretion onto massive black holes. Scientists only have quite speculative theories to offer at this stage, but future observations, in particular of high-energy radiation, can provide important constraints.
To date, much of the information about powerful cosmic accelerators has come from gamma-ray photons of all energies. Much more information may come from measuring the primary accelerated particles, as well as secondary photons and neutrinos. For example, the observation of a coincident gamma-ray and high-energy neutrino signal from a gamma-ray burst would directly test the existing theories of the shock mechanism in these sources. Identifying accelerated cosmic rays from a particular source is difficult, because intervening magnetic fields scramble the directions of charged particles as they travel. So far, it has only been possible to identify particles coming from solar flares. In contrast, neutrinos and photons, being neutral, are undeflected by magnetic fields and thus can be traced back to individual sources, provided they are bright enough. With projects currently under way or proposed, the ultimate goal of detecting high-energy protons, photons, and neutrinos from specific energetic sources may be within reach.
At the highest energies, it may be possible to identify and study cosmic accelerators by backtracking to the accelerated protons themselves. This is possible because the amount of bending in a given magnetic field is inversely proportional to the energy of the particle, and the highest-energy particles must come from relatively nearby sources to avoid having been degraded by interaction with photons of the microwave background. The aim is to accumulate enough events so that the pattern of their arrival directions and energies will reveal the identity of the specific sources. Ultimately, the highest-energy cascades would be studied from space with detectors able to view a
huge section of the atmosphere from above and thus overcome the extremely low occurrence rate of the highest-energy events. “Shower” detectors that view a sufficiently large volume of the atmosphere can also detect ultrahigh-energy neutrinos, which can make horizontal cascades starting deep in the atmosphere or even in the crust of Earth.
Further understanding of the conditions within ultrahigh-energy sources may also come from measurements made on Earth. Although the conditions within these sources cannot be reproduced here in the laboratory, the behavior of bulk matter under unexplored regimes of pressure and temperature can be examined using high-performance lasers. It is already possible to sustain pressures of 10 million atmospheres and magnetic field strengths of 10 megagauss and to create, impulsively, electron-positron pair plasmas with relativistic temperature at these facilities. These investigations are valuable because they provide a much stronger basis for scaling from the laboratory to cosmic sources. They can be particularly useful for understanding giant planets, the dynamics of various types of supernova explosions, and the relativistic flows and shock waves associated with quasars and gamma-ray bursts.
It is possible to summarize the discussion above in the form of five fundamental questions that cut across the problem areas discussed as well as the issues identified in the previous chapters.
Did Einstein Have the Last Word on Gravity?
There is a striking opportunity to begin testing general relativity in the strong-field regime using observations of astrophysical black holes. Observations of disks and outflows would test the form of the standard Kerr geometry of a spinning black hole; those of coalescing black holes would test a far more intricate dynamical space-time. The needed observations include x-ray line Doppler shifts and linewidths from black holes, quasiperiodic fluctuations of x-ray intensity from oscillating accretion disks, and gravitational radiation from mergers of compact objects.
What Are the New States of Matter at Exceedingly High Density and Temperature?
Understanding the equation of state and phase transitions of dense nuclear matter is one of the great challenges in contemporary many-body
physics. Cold neutron stars and hot supernova explosions provide two quite different ways to obtain unique experimental data and to test theoretical understanding. The opportunities include (1) measuring neutron-star radii from x-ray line gravitational redshifts and from absolute distance and x-ray intensity measurements, neutron-star rotation speeds from x-ray linewidths, x-ray timing measurements from quasi-perioidic oscillations, and the cooling rate of neutron stars in expanding supernova remnants and (2) theoretical work on the nuclear equation of state and the transition between nuclear matter and the quark-gluon plasma (see Figure 6.4).
Is a New Theory of Matter and Light Needed at the Highest Energies?
The committee believes that QED is the most successful theory of physics and that there is, as yet, no good reason to doubt it within its domain of applicability. However, it has not been tested in environments in which the magnetic field strengths are very strong and the energy densities very great,
nor have the applicable physical principles in these environments been elucidated. Observing the polarization of x rays from pulsars, magnetars, and perhaps gamma-ray bursts would allow just this.
How Were the Elements from Iron to Uranium Made?
The production of the light elements in the big bang and of the elements up to iron in supernovae is in quantitative agreement with observation. Beyond iron, the general conditions needed to make the elements seem clear, but the locale and means of production are unknown. Supernovae or neutron stars are thought to be likely sites for the origin of the heavy elements. By combining full three-dimensional calculations of supernova explosion in a terascale computation, experimental measurements of neutrino-oscillation physics, experimental data on the r-process and rp-process nuclei far from stability, and x-ray and gamma-ray observations of newly formed elements in supernovae, it may be possible to pin down the source of the heaviest elements.
How Do Cosmic Accelerators Work and What Are They Accelerating?
On both spectral and astrophysical grounds, it seems that ultrahigh-energy protons are formed in extremely powerful yet local sources. Perhaps these sources have already been identified with active galaxies or gamma-ray bursts. Alternatively, a completely new constituent of the universe could be involved, like a topological defect associated with the physics of grand unification. Only by observing many more of these particles, or perhaps the associated gamma rays, neutrinos, and gravitational waves, will scientists be able to distinguish these possibilities. To realize this opportunity, large cosmic-ray air shower detector arrays and observations of high-energy gamma rays and neutrinos will be needed, as described in Box 6.1.