Tuesday 27 March 2012

Why should You love Neutron Stars

The strongest inferred neutron star fields are nearly a hundred trillion times stronger than Earth's fields, and even the feeblest neutron star magnetic fields are a hundred million times Earth's, which is a hundred times stronger that any steady field we can generate in a laboratory.
The surface gravity is about 10^11 times Earth's, and the magnetic field is about 10^12 Gauss, which is enough to completely mess up atomic structure: for example, the ground state binding energy of hydrogen rises to 160 eV in a 10^12 Gauss field, versus 13.6 eV in no field. In the atmosphere and upper crust, you have lots of nuclei, so it isn't primarily neutrons yet. At the top of the crust, the nuclei are mostly iron 56 and lighter elements, but deeper down the pressure is high enough that the equilibrium atomic weights rise, so you might find Z=40, A=120 elements eventually. At densities of 10^6 g/cm^3 the electrons become degenerate, meaning that electrical and thermal conductivities are huge because the electrons can travel great distances before interacting. Deeper yet, at a density around 4x10^11 g/cm^3, it becomes energetically favorable for neutrons to float out of the nuclei and move freely around, so the neutrons "drip" out. Even further down, there are free neutrons, with a 5%-10% sprinkling of protons and electrons. As the density increases, we find what has been dubbed the "pasta-antipasta" sequence. At relatively low (about 10^12 g/cm^3) densities, the nucleons are spread out like meatballs that are relatively far from each other. At higher densities, the nucleons merge to form spaghetti-like strands, and at even higher densities the nucleons look like sheets (such as lasagna). Increasing the density further brings nucleons but the holes form (in order of increasing density) anti-lasagna, anti-spaghetti, and anti-meatballs (also called Swiss cheese). When the density exceeds the nuclear density 2.8x10^14 g/cm^3 by a factor of 2 or 3, really exotic stuff might be able to form, like pion condensates, lambda hyperons, delta isobars, and quark-gluon plasmas.
At the moment of a neutron star's birth, the nucleons that compose it have energies characteristic of free fall, which is to say about 100 MeV per nucleon. That translates to 10^12 K or so. The star cools off very quickly, though, by neutrino emission, so that within a couple of seconds the temperature is below 10^11 K and falling fast. In this early stage of a neutron star's life neutrinos are produced copiously, and since if the neutrinos have energies less than about 10 MeV they sail right through the neutron star without interacting, they act as a wonderful heat sink. Early on, the easiest way to produce neutrinos is via the so-called "URCA" processes: n->p+e+(nu) [where (nu) means an antineutrino] and p+e->n+nu. If the core is composed of only "ordinary" matter (neutrons, protons, and electrons), then when the temperature drops below about 10^9 K all particles are degenerate and there are so many more neutrons than protons or electrons that the URCA processes don't conserve momentum, so a bystander particle is required, leading to the "modified URCA" processes n+n->n+p+e+(nu) and n+p+e->n+n+nu. The power lost from the neutron stars to neutrinos due to the modified URCA processes goes like T^8, so as the star cools down the emission in neutrinos drops sharply.
When the temperature has dropped far enough (probably between 10 and 10,000 years after the birth of the neutron star), processes less sensitive to the temperature take over. One example is standard thermal photon cooling, which has a power proportional to T^4. Another example is thermal pair bremsstrahlung in the crust, where an electron passes by a nucleus and, instead of emitting a single photon as in standard bremsstrahlung, emits a neutrino-antineutrino pair. This has a power that goes like T^6, but its importance is uncertain. In any case, the qualitative picture of "standard cooling" that has emerged is that the star first cools by URCA processes, then by modified URCA, then by neutrino pair bremsstrahlung, then by thermal photon emission. In such a picture, a 1,000 year old neutron star (like the Crab pulsar) would have a surface temperature of a few million degrees Kelvin.
But it may not be that simple...
Near the center of a neutron star, depending on the equation of state the density can get up to several times nuclear density. This is a regime that we can't explore on Earth, because the core temperatures of 10^9 K that are probably typical of young neutron stars are actually cold by nuclear standards, since in accelerators when high densities are produced it's always by smashing together particles with high Lorentz factors. Here, the thermal energies of the particles are much less than their rest masses.
Neutron stars rotate very rapidly, up to 600 times per second. But how are they spinning when they are born? They may be born rotating very fast, with periods comparable to a millisecond (although evidence is ambiguous). After that, they spin down ever after because of magnetic torques. This seems to be supported by the fact that some of the youngest pulsars, such as the Crab pulsar (33 ms) and the Vela pulsar (80 ms) have unusually short periods. After a pulsar is born, its magnetic field will exert a torque and slow it down, with typical spindown rates of 10^-13 s/s for a young pulsar like the Crab.
Although overall the tendency is for isolated pulsars to slow down, they can undergo very brief periods of spinup. These events are called "glitches", and they can momentarily change the period of a pulsar by up to a few parts in a million. The effects of glitches decay away in a few days, and then the pulsar resumes its normal spindown. In current models of glitches, the superfluid core and normal crust are presumed to couple impulsively, and since the crust had been spun down by the magnetic field while the superfluid kept rotating at its original rate, this coupling would speed up the crust, leading to the observed spinup. It is very difficult to treat this process from first (nuclear) principles, because the critical angular velocity difference at which the crust and superfluid finally couple depends sensitively on various ill-determined properties of neutron superfluids, and since these properties aren't directly accessible by experiments we may have to be satisfied by our current phenomenological description. Incidentally, the glitch should also heat up the crust, and late in the lifetime of the neutron star heating by rotational dissipation can actually become a significant source of heat and affect the temperature evolution.
That's an isolated neutron star. If the star has a companion, it can accrete from the companion and have its rotational frequency altered that way. If the companion is a low-mass star, say half the mass of our Sun or lower, accretion tends to proceed by Roche lobe overflow (more on that later). This type of flow has a lot of angular momentum, so the matter forms a disk around the star. The radius of the inner edge of the disk is determined by the strength of the magnetic field; the stronger the field, the farther out it can control the accretion flow (for a given accretion rate). The star then (more or less) tries to come to equilibrium with the Keplerian angular velocity of the matter at the inner edge of the accretion disk. This means that neutron stars with relatively small (10^8 to 10^9 Gauss) magnetic fields can be spun up to high frequencies, and this is the accepted picture of how we get millisecond pulsars.
If the companion of the neutron star is a high-mass star (over 10 solar masses) instead, then the matter that makes it onto the neutron star goes in the form of a low angular momentum wind. Therefore, the neutron star isn't spun up to such high frequencies; in fact, some pulsars that are in high-mass systems have periods longer than 1000 seconds.
Another (somewhat less) mysterious type of bursting events believed to come from neutron stars is the soft gamma-ray repeater bursts. These typically last from 0.1 seconds to 3 seconds and have spectral peaks in the 10 keV to 30 keV range. Soft gamma-ray repeaters have in the past been identified with supernova remnants, but with the possible exception of the single source in the Large Magellanic Cloud (SGR 0525-66) these identifications are now considered dubious (see Gaensler et al. 2001, ApJ, 559, 963). Caution is especially appropriate because there are only four (!) SGRs known (SGR 0525-66, SGR 1900+14, SGR 1806-20, and SGR 1627-41, where the numbers give the right ascension and declination in B1950 coordinates). Despite the paucity of these sources, interest has focused on them because (1) they have observational properties distinct from that of any other known astronomical phenomenon, (2) they have some tantalizing links to gamma-ray bursts, and (3) one current model of SGRs involves neutron stars with 10^14 Gauss to 10^15 Gauss surface magnetic fields, in which a variety of exotic microphysical processes could be important. One particular burst from SGR 0525-66, which occurred on March 5, 1979, has attracted so much attention that it is usually called just the "March 5 event". This was the highest intensity gamma-ray event seen up to that point. It started with a hard spike that lasted a quarter of a second and had a rise time less than a millisecond, then continued emitting softer radiation for another 200 seconds. The emission during this extended tail had a clear period of 8 seconds, and was consistent with rotational modulation. Because of the high intensity and rapid onset of this event, nine different satellites throughout the Solar System recorded this event, and the relative timing between the satellites allowed the direction of the event to be determined very accurately. It was determined that the event came from a direction consistent with the N49 supernova remnant in the Large Magellanic Cloud, putting it at a distance of somewhat more than 50 kiloparsecs. At this distance, the initial hard spike had a peak luminosity of more than 10^45 ergs per second. That is to say, in the first quarter second of the burst, this source put out as much energy as the Sun radiates in 3000 years! This is also the event that makes some astronomers think that SGRs are related to classical gamma-ray bursts. If the hard spike is analyzed by itself, then its duration, light curve, and energy spectrum are indistinguishable from classical GRBs. Indeed, if the event had occured ten times as far away as it did (so that we would have missed the extended soft emission), we would have considered this another ho-hum gamma-ray burst.
Observations of other bursts from SGR 0525-66 (none as spectacular as the March 5 event) and bursts from SGR 1900+14 and SGR 1806-20 suggested initially that all are associated with supernova remnants, but as mentioned above this has been challenged. Even if they are associated with the remnants, the sources are not at the center of the remnants; instead, they are off to the side, by distances that would imply a velocity of 500-1500 kilometers per second. The typical peak luminosity of a SGR burst is 10^40 to 10^42 ergs per second. This information can be put together as follows:
  • The March 5 event displayed an 8 second rotational period. Black holes don't have solid surfaces to give such a coherent rotational period, therefore it must be a neutron star.
  • SGRs may (or may not!) be associated with supernova remnants. If they aren't, most bets are off. On the other hand, if they are:
  • Supernova remnants leave behind neutron stars or black holes, so SGRs must be related to neutron stars or black holes.
  • If the supernova remnant were more than about 100,000 years old, it would have dissipated so we couldn't see it. We can, thus the compact object producing the SGR must be relatively young.
Thus, if SGRs are associated with supernova remnants then they come from young neutron stars. The next question is what is the energy source for the bursts? One naturally thinks of accretion or rotation, but strong magnetic fields have also been considered.
If SGRs are associated with supernova remnants they are moving at high speeds, because they are not at the center of the remnants. Accretion then has serious problems, because the high velocities inferred for all three SGRs mean that the neutron star can't pick up enough mass from the interstellar medium. Also, it turns out that accretion from, e.g., asteroids would be expected to last tens of thousands of seconds instead of the observed tenths of seconds. Rotation has even greater problems. A neutron star spinning at an 8 second period, such as the one that produced the March 5 event, has only about 3 times 10^44 ergs in rotational energy available. But the March 5 event itself released about 4 times 10^44 ergs, and the X-ray energy released since then in persistent emission is another 3 times 10^44 ergs, so there isn't enough rotational energy to do the job.
Starting about 1992, Chris Thompson and Rob Duncan started proposing another energy source, that of very strong magnetic fields. They were drawn to this in part because the March 5 event implies a very long rotational period (8 seconds) compared to the expected birth spin period of neutron stars (less than a second). If, as usually thought, the neutron star spins down by magnetic braking, then to get to that long period in the 5,000 year age of the N49 supernova remnant requires that the field be nearly 10^15 Gauss! Thompson and Duncan noticed that this would imply a total magnetic energy in the star of about 10^47 ergs, which is easy enough. They also found that this model is consistent with the other properties of SGR bursts.
So, maybe some neutron stars have magnetic fields of 10^15 Gauss. So what? Given that we're sure that some neutron stars have fields of 10^12 to 10^13 Gauss, which already sounds unbelievably large, what's the big deal with another two orders of magnitude?
The difference comes at the subatomic level. In a magnetic field, a charged particle such as an electron or proton will spiral around the field at a preferred frequency, the cyclotron frequency, that is proportional to the strength of the field. This principle is used in magnetic resonance imaging, where the preferred frequency (of nuclei) is in the radio wavelengths. When magnetic fields of neutron star strength are introduced, the electron cyclotron frequency is in the X-rays, and when the field is 4.414 times 10^13 Gauss the electron cyclotron energy (the cyclotron frequency times Planck's constant) equals the electron rest mass energy. This field turns out to be a critical field in quantum electrodynamics, such that (essentially) above that field there are a number of bizarre processes (e.g., single photon pair production, photon splitting) that can be very important, whereas below the critical field those processes are negligible. We don't have a prayer of accessing this regime of ultrastrong fields in the laboratory, and we only have our quantum mechanical predictions to guide us. So, if we can establish that such fields exist in astronomy, then by studying those objects we can test our quantum mechanical theories in a new physical regime.
Observations by the Swift gamma-ray-burst (GRB) mission located short GRBs in (or near) elliptical galaxies, that are no longer active in star formation. This suggested that short GRBs are produced when neutron stars (NSs) merge with other NSs or with black holes (BHs). However, the spatial offset of some short GRBs from their host galaxies is not consistent with double-neutron-star (DNS) systems formed from massive binary stars, which appear to remain in galactic disks. Instead, short GRBs may arise from NS mergers in compact binary systems that are naturally produced in globular clusters, in which extreme densities of very old stars can create and exchange compact binaries efficiently.
A collision of two neutron stars can naturally produce the magnetic structures thought to power the high-speed particle jets associated with short gamma-ray bursts (GRBs). The study provides the most detailed glimpse of the forces driving some of the universe's most energetic explosions.
GRBs longer than two seconds are the most common type and are widely thought to be triggered by the collapse of a massive star into a black hole. As matter falls toward the black hole, some of it forms jets in the opposite direction that move near the speed of light. These jets bore through the collapsing star along its rotational axis and produce a blast of gamma rays after they emerge. Understanding short GRBs, which fade quickly, proved more elusive. Astronomers had difficulty obtaining precise positions for follow-up studies.

That began to change in 2004, when NASA’s Swift satellite began rapidly locating bursts and alerting astronomers where to look.

"For more than two decades, the leading model of short GRBs was the merger of two neutron stars," said co-author Bruno Giacomazzo at the University of Maryland and NASA's Goddard Space Flight Center in Greenbelt, Md. "Only now can we show that the merger of neutron stars actually produces an ultrastrong magnetic field structured like the jets needed for a GRB."

A neutron star is the compressed core left behind when a star weighing less than about 30 times the sun's mass explodes as a supernova. Its matter reaches densities that cannot be reproduced on Earth -- a single spoonful outweighs the Himalayan Mountains.

The simulation began with a pair of magnetized neutron stars orbiting just 11 miles apart. Each star packed 1.5 times the mass of the sun into a sphere just 17 miles across and generated a magnetic field about a trillion times stronger than the sun's.

In 15 milliseconds, the two neutron stars crashed, merged and transformed into a rapidly spinning black hole weighing 2.9 suns. The edge of the black hole, known as its event horizon, spanned less than six miles. A swirling chaos of superdense matter with temperatures exceeding 18 billion degrees Fahrenheit surrounded the newborn black hole. The merger amplified the strength of the combined magnetic field, but it also scrambled it into disarray.

Over the next 11 milliseconds, gas swirling close to the speed of light continued to amplify the magnetic field, which ultimately became a thousand times stronger than the neutron stars' original fields. At the same time, the field became more organized and gradually formed a pair of outwardly directed funnels along the black hole's rotational axis.

This is exactly the configuration needed to power the jets of ultrafast particles that produce a short gamma-ray burst. Neither of the magnetic funnels was filled with high-speed matter when the simulation ended, but earlier studies have shown that jet formation can occur under these conditions.

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