Spin history

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.

Fine, so 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. The process of wind accretion is a very complicated one, and numerical simulations of the process push the limits of computers. It appears that, in some circumstances, a disk may form briefly around the neutron star, only to be dissipated and replaced by a disk going the other way. One barrier to understanding this kind of accretion is that, even with today's computers, high-resolution 3D simulations just aren't feasible now, so we have to derive what insight we can from good two-dimensional calculations.

Misanthropic (aka isolated) neutron stars Neutrons were discovered in 1932, and very shortly afterward (in 1934) a suggestion was made by Walter Baade and Fritz Zwicky that neutron stars were formed in supernovae. But for many decades after that, neutron stars were just hypothetical phenomena that didn't attract much interest. Since the stars are so small, people felt that the prospects for observing them were minimal, and thus little effort was expended on theory or observation of neutron stars.

This changed dramatically in 1967, due to serendipity and the diligence of an Irish graduate student by the name of Jocelyn Bell. Bell and her advisor, Anthony Hewish, were working on radio observations of quasars, which had been discovered in 1963. Bell and some other graduate students constructed a scintillation array for the observations, then she got down to examining the charts of data produced (she had to analyze the miles of charts by hand, since this was in the days before powerful computers!). One day she noticed a bit of "scruff" that appeared on the charts every second and a third. The scruff was so regular that she first thought it must be artificial. However, careful checking showed that indeed the signal was extraterrestrial, and in fact that it must be from outside the solar system. This source, CP 1919, was the first radio pulsar to be discovered.

The discovery initiated a storm of activity that has still not abated. A number of other pulsars were discovered, including one in the Crab Nebula, site of a famous supernova in the year 1054 that was observed by Chinese, Arabic, and North American astronomers (but not recorded, as far as we know, by Europeans). Within a year or so of the initial discovery, it became clear that (1) pulsars are fast, with periods known in 1968 from 0.033 seconds (the Crab pulsar) to about 2 seconds, (2) the pulsations are very regular, with a typical rate of change of only a second per ten million years, and (3) over time, the period of a pulsar always increased slightly.

With this data, it was realized quickly that pulsars had to be rotating neutron stars. With certain exceptions that don't apply in this case, if a source varies over some time t, then its size must be less than the distance light can travel in that time, or ct (otherwise the variation would be happening faster than the speed of light). Thus, these objects had to be less than 300,000 km/s times 0.033 seconds, or 10,000 km, in size. This restricts us to white dwarfs, neutron stars, or black holes. You can get a periodic signal from such objects via pulsation, rotation, or a binary orbit. White dwarfs are large enough that their maximum pulsational, rotational, or orbital frequencies are more than a second, so this is ruled out. Black holes don't have solid surfaces to which to attach a beacon, so rotation or vibration of black holes is eliminated. Black holes or neutron stars in a binary could produce the required range of periods, but the binary would emit gravitational radiation, the stars would get closer together, and the period would decrease, not increase (and would do so very quickly, too!). Pulsations of neutron stars typically have periods of milliseconds, not seconds. The only thing left is rotating neutron stars, and this fits all of the observations admirably. Here's an animated gif of a pulsar.

There have now been more than 1000 radio pulsars discovered, with periods from about 1.4 milliseconds to more than 5 seconds. Their discovery is considered one of the three most important astronomical discoveries in the latter half of the twentieth century (along with quasars and the microwave background), and in part for his role in the discovery of pulsars Anthony Hewish shared the 1974 Nobel Prize in physics. Social (aka accreting) neutron stars Not all neutron stars are destined to lead a life of isolation. Some of them are born in binaries that survive the supernova explosion that created the neutron star, and in dense stellar regions such as globular clusters some neutron stars may be able to capture companions. In either case, mass may be transferred from the companion to the neutron star, as mentioned in the spin evolution section above.

If the companion star has less than the mass of our Sun, the mass transfer occurs via Roche lobe overflow. If part of the companion star's envelope is close enough to the neutron star, the neutron star's gravitational attraction on that part of the envelope is greater than the companion star's attraction, with the result that the gas in the envelope falls onto the neutron star. However, since the neutron star is tiny, astronomically speaking, the gas has too much angular momentum to fall on the star directly and therefore orbits around the star in an accretion disk. Within the disk, magnetic or viscous forces operate to allow the gas in the disk to drift in slowly as it orbits, and to eventually reach the stellar surface. If the magnetic field at the neutron star's surface exceeds about 10^8 G, then before the gas gets to the stellar surface the field can couple strongly to the matter and force it to flow along field lines to the magnetic poles. The friction of the gas with itself as it spirals in towards the neutron star heats the gas to millions of degrees, and causes it to emit X-rays. Some characteristic dimensions of this sort of system are displayed in the figure.

Here, from wwwastro.msfc.nasa.gov/xray/openhouse/ns/, is a cartoon of the inner region where the neutron star's magnetic field controls matter:

Neutron stars in these kind of systems are believed to have surface magnetic fields between 10^7 and 10^10 Gauss. This means that the accreting gas can spiral very close to the neutron star before it is grabbed by the magnetic field. At such a close distance, the orbital frequency is very high (hundreds of Hertz), so the neutron star is spun up rapidly. As mentioned earlier, this is how we think we get millisecond pulsars. Those millisecond pulsars, by the way, are extremely stable rotators; the best are at least as stable as atomic clocks! There have been suggestions that using millisecond pulsars as cosmic clocks could tell us about all sorts of exotic things, such as the presence of a background of gravitational radiation left over from the Big Bang.

Another fun phenomenon associated with neutron stars that have low-mass companions is X-ray bursts. These typically last a few seconds to a few minutes, and have a peak luminosity nearly a hundred thousand times our Sun's luminosity. The model for these bursts is that as hydrogen and helium is tranferred to the neutron star from the companion, it builds up in a dense layer. Eventually, the hydrogen and helium have been packed in a layer so dense and hot that thermonuclear fusion starts, which then converts most or all of the gas into iron, releasing a tremendous amount of energy. This is the equivalent of detonating the entire world's nuclear arsenal on every square centimeter of the neutron star's surface within a minute! Some of these binaries can be amazingly close to one another. Here's an artist's conception (from heasarc.gsfc.nasa.gov/Images/exosat/slide_gifs/exosat18.gif) of one particularly extreme case, that of 4U~1820-30, which has a binary period of just over eleven minutes! Too bad the distances are in miles...

If the companion to the neutron star has a mass between one and ten times our Sun's mass, the mass transfer is unstable and doesn't last very long, so there are few objects in this category.

If the companion to the neutron star has a mass more than about ten times our Sun's mass, the companion naturally produces a stellar wind, and some of that wind falls on the neutron star. The neutron stars in these systems have strong magnetic fields, around 10^12 Gauss (similar to typical isolated pulsars). At field strengths this high, almost all the accreting gas is forced to flow along field lines to the magnetic poles. This means that the X-rays primarily come from the resulting hot spots on the poles. It also means that if the magnetic axis and rotation axis of the star aren't co-aligned, the radiation sweeps past us once per rotation and we see X-ray pulsations. These systems are therefore called "accretion-powered pulsars", to distinguish them from the "rotation-powered pulsars" that Jocelyn Bell discovered.

For some recent results on accreting neutron stars, check out a poster from a science fair for grownups held at the University of Chicago.

What the @#$% makes gamma-ray bursts? Gamma-ray bursts have been known for more than 25 years, but there are still a lot of uncertainties about their origins. They were first discovered in the late 1960's as part of nuclear test ban verification; US satellites picked up bursts of gamma rays and there was a lot of concern that these might be due to Soviet nuclear explosions, but it was determined that the bursts originated outside the atmosphere. The "official" discovery came in 1973 (by Klebsedal, Olsen, and Strong). Since then, more than 2500 bursts have been detected, over 1800 by BATSE (the Burst and Transient Source Experiment aboard the Compton Gamma-Ray Observatory). Before tackling the question of what gamma-ray bursts are, we need to establish what they are observationally.

Loosely speaking, gamma-ray bursts are, well, bursts of energy that appear mostly in gamma rays and come from outside the Earth. The flux at earth is between 10^-8 erg/cm^2/s and 10^-3 erg/cm^2/s, the duration of the bursts is between 10 ms and 1000 s, and the photons typically have energies between 100 keV and 2 MeV, although energies down to 5 keV and up to 18 GeV have been seen from some bursts. The flux as a function of time varies from burst to burst, but often a spike within a burst follows the "fred" profile (fast rise, exponential decay). Here's an animated gif showing a simulation of a burst as we'd see it on a map of the Galaxy (left) and its brightness as a function of time (right). All in all, gamma-ray bursts are extremely heterogeneous, so it is tough to extract characteristic behaviors that would lead to easy classification (see a typical time profile for a GRB).

Can we at least tell how far away gamma-ray bursts are? Until recently, the answer was "no", not with any certainty. From the early 1970s it has been apparent that gamma-ray bursts come from all parts of the sky with approximately equal probability. Since other aspects of gamma-ray bursts (such as the fast rise time [<1 ms in some cases] and high photon energies) seemed consistent with a neutron star origin, most people prior to 1990 believed that gamma-ray bursts came from galactic neutron stars, and that instruments simply hadn't had the sensitivity to probe deeply enough to see a bias towards the galactic center and plane. However, since 1990 the Burst and Transient Source Experiment (BATSE) aboard the Compton Gamma-Ray Observatory has seen nearly one gamma-ray burst per day, and these too are nearly isotropic (click for the sky map of the first 921 bursts). It is believed that, if galactic neutron stars really are the sources of gamma-ray bursts, BATSE should be able to see them far enough away that the distribution should be more like a pancake than a sphere. Another piece of evidence comes from the number of sources seen with at least a given flux. If the universe were Euclidean and the sources were spread out uniformly, then out to a distance r there would be a number of sources proportional to r^3, and the dimmest sources would have fluxes proportional to 1/r^2. Thus, in a Euclidean universe with uniformly distributed sources of a given intrinsic luminosity, a plot of log N (N=number of sources at a flux greater than F) versus log F should have a slope of -3/2. At the highest fluxes this slope is seen, but at lower fluxes the slope becomes smaller, exhibiting a continuous rollover and becoming about -0.8 at the lowest fluxes BATSE can see.

What does that mean? The dropoff at lower fluxes, which corresponds to greater distances if the intrinsic luminosity is constant, means that in some sense there is an edge to the distribution. For example, if the sources were distributed in a thin plane instead of a sphere, the slope would be -1, and for sources in a line the slope is -0.5. Even if the source distribution is spherical, the slope will roll over if the sources become less dense at greater distances, or if the flux drops off faster than 1/r^2. Because of the isotropy of the distribution, many people believed that gamma-ray bursts are cosmological, at typical redshifts z=1, where the redshift would decrease the flux in about the right way to account for the log N - log F rollover. But until 1997 there wasn't any "smoking gun" to tell us for sure that the bursts were cosmological, and actually there were plausible models of gamma-ray bursts in which the bursts came from an extended halo around our own galaxy.

All this changed in 1997, when researchers using the Italian-Dutch satellite BeppoSAX made a tremendous breakthrough. A sticking point in our understanding of gamma-ray bursts was that they were always a "one and done" type of phenomenon, in which, after a brief flash of gamma-rays lasting a few seconds, that was all she wrote. The lack of any detectable emission in other frequencies (such as optical and radio) meant that these sources couldn't be localized with any certainty. This is where BeppoSAX came in. This satellite has the capability of detecting X-ray emission from half a dozen to a dozen gamma-ray bursts per year and localizing the emission to within about two arcminutes (a thirtieth of a degree, or a little less than the apparent size of a billiard ball at the far end of a football field). This is about 100 times better than the localization possible with BATSE. It allowed people to discover that most of the gamma-ray bursts observed with BeppoSAX have x-ray afterglows; here's an image of the first one, showing a bright spot (left) that fades away later (right). Many have optical and radio afterglows as well! The afterglows in optical and radio allowed the position to be nailed down to an arcsecond or better (the apparent size of an eyelash at the far end of a football field!). Further observations showed that, at least in projection and probably in reality, the gamma-ray bursts are in galaxies. Not only that, but redshifts have been measured for many of these galaxies, and some of them are really big: one was measured at a redshift greater than 3.4! So that settles at least part of the question: the bursts observed with BeppoSAX are definitely cosmological. If gamma-ray bursts are cosmological, their energy release must be gigantic. It is now thought that most bursts are tightly beamed (like a lighthouse) and emit a good 10^51 ergs in just gamma rays. It is still really puzzling how this could happen. The constraints on these models are really tight, and no detailed model yet suggested can circumvent all the constraints. No matter what these are, though, the energy release by itself guarantees that the central engine is one of the biggest blasts around! The two most popular current ideas are (1) the bursts are caused by the inspiral and merger of two neutron stars or a neutron star and a black hole, or (2) the bursts are caused by the collapse of a massive star (maybe 20 solar masses or more) into a rapidly spinning massive black hole. General opinion is that the longer bursts are of type (2), but there is still a question about the shorter bursts. Either way, it seems unavoidable that all that energy sails out into interstellar space and produces a serious blast wave.

Soft gamma-ray repeaters and whopping magnetic fields 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.

But first, we have to get more direct evidence that such high fields exist. Recent supporting evidence arrived in 1998, when several soft gamma-ray repeaters were active and when it was finally possible to measure (1) a spin period and (2) a rate of change of the spin period, which in the simplest approximation allow an estimate of the magnetic field of these sources. You guessed it, it seems like magnetic fields greater than about 10^14 Gauss are required, although there are still some subtleties. What would really be nice would be a signature in the energy spectrum of these ultrastrong fields. We don't have it yet, but there has been a lot of effort by many people. Tomek Bulik and I have proposed the one that I think is most promising. It relates to something called the vacuum resonance, and the spectral signature is a dip in the X-ray spectrum that moves to lower energies when the intensity is higher. If such a signature is seen, we will then have strong and direct evidence for the existence of these superstrong fields, and theorists such as myself will have a wonderful new playground!

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