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Neutron stars are left when a massive star expends itself in a supernova. Most become pulsars when rotation of the neutron star's magnetic field produces a repeating, clocklike signal in radio, light, even X-rays (right) and gamma rays. One mystery is why a large number of supernovas create magnificent nebulas yet leave no pulsar at the center. This anomaly poses a problem for theorists trying to calculate the rates of star births and deaths and, eventually, the ages of galaxies and the universe.

When a massive, rapidly rotating star explodes, it compresses its core to a diameter of about 20 km (12 mi) and having a density so great that a pinhead of neutron star material would weigh as much as a battleship. It's also so hot that for the first 30 seconds or so it circulates as hot neutron liquid rises to the surface, cools, and sinks. This motion generates a magnetic field. If the star is spinning at 200 rotations/second or more (more than 360 times faster than an old 33-1/3 record), it sets up a dynamo effect that generates a magnetic field 1,000 times stronger than that of "ordinary" neutron stars. A magnetar is born.^1z

After the neutron star cools, it forms a 1 km-thick (0.625 mi) crust of iron nuclei jam-packed with almost no space between each other. They have increasingly large atomic numbers, and are increasingly bloated with neutrons, with greater depth. as you go down deeper.

Right: A cross-section diagram shows a neutron star in its first seconds of life. It is still a superhot liquid with two or three layers of convection carrying heat to the surface. If the neutron star is spinning at more than 200 rotations/second, it sets up a dynamo effect that forms an intense magnetic field, and a magnetar is born.

Astrophysicists announced that the discovery of very rapid oscillations in the brightness of some X-ray-emitting neutron stars has yielded important new constraints on the properties of the superdense matter at the centers of these stars. These new results are based on the earlier dramatic discovery by Rossi that the brightness of many neutron stars varies more than a thousand times each second. This represents the first evidence for a unique effect of strongly curved space-time predicted by Einstein's theory of gravity but never before observed. The new measurements were made using NASA's Rossi X-Ray Timing Explorer satellite, which was designed to probe closer than ever before the strongly curved space-time near neutron stars and black holes.^76d These variations are the highest frequency oscillations ever detected in any astrophysical object. According to Einstein's theory of gravity, space-time near neutron stars is strongly curved - observation of the effects of strongly curved space-time would be the first confirmation of a strong-field prediction of general relativity.

Many neutron stars are found in binary systems with ordinary stars like the sun, but the stars orbit so closely that the neutron stars are devouring their companion stars. The strong gravitational field of the neutron star literally pulls gas off the surface of the companion star. The gas then spirals in toward the neutron star, and the observed high-frequency brightness oscillations are thought to be caused by clumps of gas hurtling around the neutron star just above its surface at relativistic speeds.

When gas from these clumps collides with the surface of the star, the gas reaches temperatures of 100 million degrees and emits X-rays. -- The neutron star becomes brighter when the heated gas is on the side facing us and dimmer when the heated gas is on the other side. Scientists using the Rossi satellite found that these neutron stars are playing cosmic chords, with two or three nearly pure tones. The pureness of these tones makes it possible to use them to investigate how matter moves in the strongly curved space-time near these neutron stars." Calculations showed how the X-ray brightness oscillations could be used to determine the masses and dimensions of neutron stars and to look for evidence of the innermost stable orbit - a key prediction of general relativity.

The innermost stable orbit is a qualitatively new prediction of Einstein's theory of gravity. According to Newton's theory, gas can orbit a compact star at any distance, in contrast, Einstein's theory predicts that if the star is sufficiently massive and compact, there is a region of space around it where space-time is so strongly curved that there are no stable circular orbits. Gas orbiting this close to the star unavoidably plunges to its surface.

The frequency of the X-ray brightness variations should increase as the gas flow onto the neutron star rises, until the clumps producing the oscillations are at the innermost stable orbit. At this point the oscillation frequency should become constant as the X-ray power continues to rise. Astronomers observed the neutron star called 4U 1820-30 over several months^76d and found that as its X-ray power rises, the frequency of its brightness oscillation increases until it is oscillating about 1,050 times a second. As the X-ray power increases further, the frequency remains constant, indicating that the innermost stable orbit has been reached.

There is a good possibility that the Rossi Explorer has provided the first evidence supporting the predictions of Einstein's theory of gravity about how matter moves in strongly curved space-time - all previous tests of general relativity have been made in regions where space-time is curved only very, very weakly. Searching for effects of strong gravitational fields is of fundamental importance, however, if this evidence for the existence of an innermost stable orbit is confirmed, it will be a major advance. Studying how matter moves in the strongly curved space-time near neutron stars also has allowed us to extract interesting new bounds on the masses and dimensions of these stars and on the stiffness of the superdense matter inside them. The new evidence reported suggests that the strong nuclear force is more repulsive than many nuclear physicists had expected and that the superdense matter in neutron stars is rather stiff. While these new findings represent a very important and exciting development, they will require confirmation, Lamb cautioned.

A powerful numerical simulation developed at the University of Illinois has revealed that gravitational waves play a major role in the coalescence of neutron stars, which may aid in the future detection of gravitational waves. General relativity predicts that a pair of neutron stars orbiting one another will radiate energy in the form of gravitational waves. It is believed that this loss of energy will cause the stars to move closer and closer together, until they eventually collide.The gravitational waves produced in such events are expected to be observed by highly specialized detectors -- such as the Laser Interferometric Gravitational-Wave Observatory.^76e

Gravitational waves are extremely weak, however, and theoretical templates of the anticipated waveforms will be necessary to extract the signal from the noisy background. By using computer simulations and scientific visualization to study the merger of two neutron stars, it is possible to make predictions in anticipation of detectors coming on line to actually measure the waveforms.

To run the simulation an SGI/Cray Origin2000 supercomputer from the National Computational Science Alliance was used. The researchers initially ran the simulation with only Newtonian hydrodynamics; then they added a post-Newtonian "correction" in the form of a relativistic radiation reaction. It is reported that the radiation reaction dramatically altered the dynamics of the merger - the reaction caused the stars to coalesce much faster, and led to very different gravitational waveforms. It was found that the final coalesced objects differed both in structure and in total angular momentum.

One particularly striking feature seen in the simulation is the formation of tidal arms during the merger that transport a substantial amount of material into a rapidly rotating disk surrounding the merger. Most of the energy that is being radiated in the form of gravitational waves comes from these tidally distorted regions, not from the most massive or most dense parts of the stars. Although post-Newtonian methods are extremely useful for predicting gravitational waveforms during the early stages of the inspiral, predicting the later stages will require a fully relativistic simulation.^76e

Astronomers using NASA's Hubble Space Telescope have taken their first direct look, in visible light, at a lone neutron star. This offers a unique opportunity to pinpoint its size and to narrow theories about the composition and structure of this bizarre class of gravitationally collapsed, burned-out stars.In successfully characterizing the properties of an isolated neutron star, astrophysicists have an opportunity to better understand the transitions matter undergoes when subjected to the extraordinary pressures and temperature found in the intense gravitational field of a neutron star.

The Hubble results show the star is very hot, and can be no larger than 16.8 miles (28 kilometers) across. Some scientists think that these results prove that the object must be a neutron star, for no other known type of object can be this hot and small. This puts the neutron star uncomfortably close to the theoretical limit of how small a neutron star should be. ^76g With this observation it is possible to rule out some of the many models of the internal structure of neutron stars.

Neutron stars, which are created in some supernovae, are so dense because the electrons and protons that form normal matter have been squeezed into neutrons and other exotic subatomic particles. Neutron star matter is the densest form of matter known to exist. Theoretically, a piece of neutron star surface weighing more than a fleet of battleships would be small enough to be held in the palm of your hand.

The Hubble observations, combined with earlier data, promise to help astronomers refine the equation of state of the complex transformations matter undergoes at extraordinary densities not found on Earth. Equations of state are well understood for "everyday" matter such as water, which can transition between gaseous, liquid and solid states, but the behavior of matter under extreme temperature and pressure found on a neutron star is not understood to anyones satisfaction.

There are several hundred million neutron stars thought to exist in our galaxy, and all neutron stars now known have either been found orbiting other stars in X-ray binary systems or emitting machine-gun blasts of radio energy as pulsars. The neutron star seen by Hubble is not a member of a binary system, and is not known to pulse at X-ray or radio wavelengths.

Pulsars are young neutron stars born with moderately strong magnetic fields; non-pulsing neutron stars may be old, dead pulsars, with ages of more than a million years, or they may never have been pulsars. Only a few lone neutron star candidates have been pinpointed through X- ray observations. This is the first optical counterpart to be identified.

The first clue that there was a neutron star at this location came in 1992, when the ROSAT (the Roentgen Satellite) found a bright X-ray source without any optical counterpart in optical sky surveys.^76g It drew the attention of astronomers because objects this hot and bright, without counterparts at other wavelengths, are extremely rare. Hubble's Wide Field Planetary Camera 2 was used in October 1996 to undertake a sensitive search for the optical object, and found a stellar pinpoint of light within only 2 arc seconds (1/900th the diameter of the Moon) of the X-ray position.

Astronomers haven't directly measured the neutron star's distance but fortunately the neutron star lies in front of a molecular cloud known to be about 400 light-years away in the southern constellation Coronae Australis. Using the distance to the cloud as an upper limit, the astronomers calculated a diameter by next comparing the neutron star's brightness and color as measured by Hubble, along with X- ray brightness from the ROSAT and EUVE (Extreme Ultraviolet Explorer) satellites.

-- The object is brightest at X-ray wavelengths. In two Hubble images, the object is brighter at ultraviolet wavelengths than at visible wavelengths. It has been concluded they are directly seeing an ultracompact surface sizzling at about 1.2 million degrees Fahrenheit. To be so hot, yet so dim (below 25th magnitude in visual light) and relatively close to Earth, the object must be extremely small - smaller than a white dwarf, a more common stellar remnant. It has been estimated to be only 16.8 miles in diameter ! A hot white dwarf at this magnitude would lie 150,000 light-years away (outside our galaxy), and have 1/70,000 as much X-ray emission.

The 16.8-mile diameter estimate comes from assuming the neutron star is at the farthest it can be, just in front of the obscuring "wall" of the molecular cloud. If instead the neutron star is significantly closer to us it would be smaller still, and present an even bigger challenge to the theories of the equation of state of nuclear matter. Although neutron stars in binary systems allow astronomers to measure their mass, which turn out to be consistent with theory, it's much harder for astronomers to estimate the diameter of the neutron stars. Since the neutron stars "feed" on their companion stars in these systems, the light does not come exclusively from the surface but from jets, disks and other phenomenon that occur around the star. This can lead to inaccurate size estimates. Over the next year, the HST will be used in an attempt to determine exactly how far away and how large the star is.

Magnetic Fields in Neutron Stars

Neutron stars are very hot when they first form. Simulations show that the dense fluid of neutrons inside them boils turbulently to help carry out heat - heat-driven circulation like this is called "convection." Hot neutron star fluid also can conduct electricity, because it contains a trace of free electrons and protons, which are electrically charged. This means that any magnetic field lines caught in the fluid initially are swept along by the convective motions - the fluid acts as a thermal and electrical conductor.

If the star is born rotating fast enough, the combination of rotation and convection dragging the field lines through the star can build up the star's overall magnetic field---a complicated process known as "dynamo action." This same dynamo action operates in the interior of the Earth and the Sun, giving them their magnetic fields. If a dynamo worked with ideal efficiency in a hot, newborn neutron star, it would generate a field of at least 10¹⁶ Gauss - 10,000 times stronger than was actually found in pulsars.

As the star cools, convection and dynamo action cease. This happens after only about 20 seconds in a neutron star, but 20 seconds is enough time for a VERY strong field to build up. After that, the field can remain trapped by the heavy, stratified liquid of neutrons and protons inside the neutron star. This led scientists to conclude that the familiar radio pulsars were neutron stars in which large-scale dynamos had essentially FAILED to operate, probably because they were not born rotating fast enough.¹⁷

The spin period of the Crab pulsar at birth was about 20 milliseconds; scientists found that it needed to be considerably less than that for the dynamo action to work. The question of why a pulsar field was 10¹² Gauss thus turned out to involve some subtle details of the residues of magnetism left over after a large-scale dynamo fails.

Is this a new kind of Star?

Scientists have estimated that, at the pole of a dynamo-active young neutron star, the magnetic field could realistically reach 10¹⁴ - 10¹⁵ Gauss--- 100 to 1000 times stronger than in ordinary pulsars.¹⁷ What would such a strongly-magnetized neutron star, or `magnetar' look like ?Although it is born spinning somewhat faster than a pulsar, a magnetar spins down MUCH more quickly, because the magnetic waves (and the related, magnetically-powered winds of charged particles) which carry off the star's rotational energy are very efficient when the field is strong. This means that magnetars rarely send out "lighthouse" beams as do radio pulsars: except in a fleeting interval just after it is formed, a magnetar spins so slowly that its radio beams are probably turned off - radio beams in an ordinary pulsar come from a rotation-driven outflow of charged particles above the magnetic poles; when the rotation rate drops this ceases.

The emissions of ordinary radio pulsars are powered by a slow loss of the rotational energy that the star is born with, and a radio pulsar's magnetic field is essentially stable; its main role is to passively facilitate the loss of rotational energy. In a magnetar, the rotational energy quickly becomes negligible, but the magnetic field itself can provide an energy source for potentially observable emissions. A magnetar's field is strong enough to push material around in the star's interior and crust, dissipating a significant amount of magnetic energy during the first ten thousand years.

This has several consequences:

Why does the star have a crust?

The crust is comprised of a crystalline substance that is the "nuclear fluid" of a neutron star, which contains a trace of protons and electrons, is mostly made of a dense liquid of neutrons: the pure stuff of the atomic nucleus. It is more than 10¹⁴ times more dense than liquid water is on Earth. The ultra-dense nuclear fluid would explode like a nuclear bomb if you brought it to Earth, but inside a neutron star it is stable because it is held under tremendous pressure.

In the outer layers of a neutron star (as in the outer layers of all stars) the pressure and the temperature both drop. Here the fluid solidifies into a heavy crust, about 1/2 mile in depth. This is made of a solid lattice of heavy nuclei, with electrons flowing between, somewhat like a terrestrial metal but much more dense. The surface is made of iron.

In a pulsar this outer, solid shell is essentially stable, but in a magnetar, it is stressed by unbearable magnetic forces as the field drifts through it. This deforms the crust and often cracks it. At the instant it cracks, pent-up energy is released, just like in an earthquake. Violent seismic waves then vibrate the crust, driving magnetic waves outward which energize clouds of particles above the surface of the star. This is thought to produce a burst of hard X-rays (soft gamma rays), and that such "starquakes" are observable as normal SGR bursts. Note that magnetic forces may also deform a radio pulsar's crust, but a typical pulsar's field is not strong enough to break the crust. - the field must be roughly 10¹⁴ Gauss or more to break the crust all the way through. Note also that the "shaking-type" magnetic waves driven by starquakes are different from the steady, rotation-powered, "twisting-type" magnetic waves which help cause a neutron star to spin down. However, in the case of active magnetars, shaking-type waves can also accelerate the spindown.