Neutron starsIntroduction to neutron stars M. Coleman MillerAssociate Professor of Astronomy, University of Maryland Welcome to my neutron star page! Ineed to emphasize that the stuff I have here represents my opinions,and errors aren't the fault of those patient pedagogues who tried tocram this information into my head. I'll try to indicate when there isa dispute in the community, but I won't always be successful, so don'tuse only this page to study for your candidacy exams! For those withserious interest in neutron stars and other compact objects,an excellent reference is "Black Holes, White Dwarfs, and Neutron Stars",by Stuart Shapiro and Saul Teukolsky (1983, John Wiley and Sons).For those who want a quick intro to selected cool things about neutron stars and black holes, check out a posterI made for a science fair at the University of Chicago. If you'd likemore detail about quasi-periodic oscillations in particular, I wrotea pedagogical review based on my summer school lectures in Dubna,Russia, in August 2004. Here are the Postscript andPDF documents.I also have a link to some questions I have received about neutronstars, and myanswers.Here are the topics in this page: The basics Neutron star formation Neutron star internal structure Neutron star thermal and spin evolution Isolated neutron stars (including pulsars) Accreting neutron stars (e.g., X-raybursters) Classical gamma-ray bursts Soft gamma-ray repeatersGetting started on neutron starsNeutron stars are the collapsed cores of some massive stars.They pack roughly the mass of our Sun into a region the size ofa city. Here's a comparison with Chicago: At these incredibly high densities, you could cram all of humanityinto a volume the size of a sugar cube. Naturally, the people thuscrammed wouldn't survive in their current form, and neither doesthe matter that forms the neutron star. This matter, which startsout in the original star as a normal, well-adjusted combination ofelectrons, protons, and neutrons, finds its peace (aka a lowerenergy state) as almost all neutrons in the neutron star. Thesestars also have the strongest magnetic fields in the known universe.The strongest inferred neutron star fields are nearly a hundredtrillion times stronger than Earth's fields, and even the feeblestneutron star magnetic fields are a hundred million times Earth's,which is a hundred times stronger that any steady field we cangenerate in a laboratory. Neutron stars are extreme in many otherways, too. For example, maybe you get a warm feeling when youcontemplate high-temperature superconductors, with critical temperaturesaround 100 K? Hah! The protons in the center of neutron starsare believed to become superconducting at 100 million K,so these are the real high-T_c champs of the universe.All in all, these extremes mean that the study of neutron starsaffords us some unique glimpses into areas of physics that wecouldn't study otherwise.So, like, how do we get neutron stars?Neutron stars are believed to form in supernovae such as the one thatformed the Crab Nebula (or check outthis cool X-ray image of thenebula, from the Chandra X-ray Observatory). The stars thateventually become neutron stars are thought to start out with about8 to 20-30 times the mass of our sun. These numbers are probably goingto change as supernova simulations become more precise, but it appearsthat for initial masses much less than 8 solar masses the star becomesa white dwarf, whereas for initial masses a lot higher than 20-30 solarmasses you get a black hole instead (this may have happened with Supernova 1987A, althoughdetection of neutrinos in the first few seconds of the supernova suggeststhat at least initially it was a neutron star). In any case, the basic idea isthat when the central part of the star fuses its way to iron, it can'tgo any farther because at low pressures iron 56 has the highest bindingenergy per nucleon of any element, so fusion or fission of iron 56requires an energy input. Thus, the iron core just accumulates untilit gets to about 1.4 solar masses (the "Chandrasekhar mass"), at whichpoint the electron degeneracy pressure that had been supporting it against gravity gives up the ghost and collapses inward.At the veryhigh pressures involved in this collapse, it is energetically favorableto combine protons and electrons to form neutrons plus neutrinos. Theneutrinos escape after scattering a bit and helping the supernovahappen, and the neutrons settle down to become a neutron star, withneutron degeneracy managing to oppose gravity. Since the supernovarate is around 1 per 30 years, and because most supernovae probablymake neutron stars instead of black holes, in the 10 billion year lifetimeof the galaxy there have probably been 10^8 to 10^9 neutron stars formed.One other way, maybe, of forming neutron stars is to have a whitedwarf accrete enough mass to push over the Chandrasekhar mass, causinga collapse. This is speculative, though, so I won't talk about itfurther.The guts of a neutron starWe'll talk about neutron star evolution in a bit, but let's say you takeyour run of the mill mature neutron star, which has recovered from itsbirth trauma. What is its structure like? First, the typical mass ofa neutron star is about 1.4 solar masses, and the radius is probably about 10 km. By the way, the "mass" here is the gravitational mass (i.e.,what you'd put into Kepler's laws for a satellite orbiting far away).This is distinct from the baryonic mass, which is what you'd get if youtook every particle from a neutron star and weighed it on a distant scale. Because the gravitational redshift of a neutron star is so great,the gravitational mass is about 20% lower than the baryonic mass.Anyway, imagine starting at the surface of a neutron star and burrowingyour way down. The surface gravity is about 10^11 times Earth's, andthe magnetic field is about 10^12 Gauss, which is enough to completelymess up atomic structure: for example, the ground state binding energyof hydrogen rises to 160 eV in a 10^12 Gauss field, versus 13.6 eVin 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 nucleiare mostly iron 56 and lighter elements, but deeper down the pressure ishigh enough that the equilibrium atomic weights rise, so you might findZ=40, A=120 elements eventually. At densities of 10^6 g/cm^3 the electronsbecome degenerate, meaning that electrical and thermal conductivities arehuge because the electrons can travel great distances before interacting.Deeper yet, at a density around 4x10^11 g/cm^3, you reach the "neutrondrip" layer. At this layer, it becomes energetically favorable forneutrons to float out of the nuclei and move freely around, so the neutrons "drip" out. Even further down, you mainly have free neutrons,with a 5%-10% sprinkling of protons and electrons. As the densityincreases, you find what has been dubbedthe "pasta-antipasta" sequence. At relatively low (about 10^12 g/cm^3)densities, the nucleons are spread out like meatballs that are relativelyfar from each other. At higher densities, the nucleons merge to formspaghetti-like strands, and at even higher densities the nucleons looklike sheets (such as lasagna). Increasing the density further bringsa reversal of the above sequence, where you mainly have nucleons butthe 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 factorof 2 or 3, really exotic stuff might be able to form, like pion condensates,lambda hyperons, delta isobars, and quark-gluon plasmas. Here's agorgeous figure (from http://www.astroscu.unam.mx/neutrones/NS-picture/NStar/NStar-I.gif) thatshows the structure of a neutron star: Yes, you may say,that's all very well for keeping nuclear theorists employed, but howcan we possibly tell if it works out in reality? Well, believe it ornot, these things may actually have an effect on the cooling historyof the star and their spin behavior! That's part of the next section.The decline and fall of a neutron starThermal historyAt the moment of a neutron star's birth, the nucleons that compose it haveenergies characteristic of free fall, which is to say about 100 MeV pernucleon. 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 thetemperature is below 10^11 K and falling fast. In this early stage ofa neutron star's life neutrinos are produced copiously, and since if theneutrinos have energies less than about 10 MeV they sail right throughthe 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] andp+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 neutronsthan 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 theneutron stars to neutrinos due to the modified URCA processes goes likeT^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 thermalphoton cooling, which has a power proportional to T^4. Another exampleis thermal pair bremsstrahlung in the crust, where an electron passes bya nucleus and, instead of emitting a single photon as in standardbremsstrahlung, emits a neutrino-antineutrino pair. This has a powerthat goes like T^6, but its importance is uncertain. In any case, thequalitative picture of "standard cooling" that has emerged is that thestar first cools by URCA processes, then by modified URCA, then byneutrino pair bremsstrahlung, then by thermal photon emission. In sucha picture, a 1,000 year old neutron star (like the Crab pulsar) wouldhave 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 statethe density can get up to several times nuclear density. This is aregime that we can't explore on Earth, because the core temperatures of10^9 K that are probably typical of young neutron stars are actuallycold by nuclear standards, since in accelerators when highdensities are produced it's always by smashing together particles withhigh Lorentz factors. Here, the thermal energies of the particles aremuch less than their rest masses. Anyway, that leaves us with onlytheoretical predictions, which (as you might expect given the lack ofdata to guide us) vary a lot. Some people think that strange matter,pion condensates, lambda hyperons, delta isobars, or free quark mattermight form under those conditions, and it seems to be a general rulethat no matter what the weird stuff is, if you have exotic matter thenneutrino cooling processes proportional to T^6 can exist, which wouldmean that the star would cool off much faster than you thought. Iteven appears possible in some equations of state that the proton andelectron fraction in the core may be high enough that the URCA processcan operate, which would really cool things down in a hurry. Addingto the complication is that the neutrons probably form a superfluid(along with the protons forming a superconductor!), and depending onthe critical temperature some of the cooling processes may get cut off.So how do we test all this? We expect that after a hundred years orso the core will become isothermal (because it is then superfluid), andwe can estimate thermal conductivities in the crust, so if we couldmeasure the surface temperatures of many neutron stars, then we couldestimate their core temperatures, which combined with age estimates andan assumption that all neutron stars are basically the same would tellus about their thermal evolution, which in turn would give us a hintabout whether we needed exotic matter. Unfortunately, neutron starsare so small that even at the 10^6 K or higher temperatures expected foryoung neutron stars we can just barely detect them. Adding to thedifficulty is that at those temperatures the peak emission is easilyabsorbed by the interstellar medium, so we can only see the high-energytail clearly. Nonetheless, ROSAT has detected persistent X-ray emissionfrom several young, nearby neutron stars, so now we have to interpretthis emission and decide what it tells us about the star's temperature.This ain't easy. The first complication is that the X-ray emissionmight not be thermal. Instead, it could be nonthermal emission from themagnetosphere. That could carry information of its own, but it makestemperature determinations difficult; basically, we have to say that,strictly, we only have upper limits on the thermal emission. Even ifit were all thermal, we need to remember that we only see a section ofthe spectrum that is observable by an X-ray satellite, so we could befooling ourselves about the bolometric luminosity. In fact, someearly simulations of radiation transfer through a neutron star atmosphereindicated that a neutron star of effective temperature T_eff wouldyield far more observed counts than a blackbody at T_eff. Thus, ablackbody fit would overestimate the true temperature. These simulationsused opacities computed for zero magnetic field. Thus, especially forlow atomic number elements such as helium, there weren't any opacitysources at 500 eV (where the detectors operate), so in effect we wouldbe seeing deeper into the atmosphere where it was hotter. Such simulationsmay be relevant for millisecond pulsars, which have magnetic fieldsin the 10^8 G to 10^10 G range.Most pulsars, though, have much stronger fields, on the order of 10^12 G.In fields this strong, the binding energies of atoms go up (as mentionedbefore, the ground state binding energy of hydrogen in 10^12 G is 160 eV),meaning that the opacity at those higher energies rises as well. Thus,the X-ray detectors don't see as far down into the atmosphere, and theinferred temperature is less than in the nonmagnetic case. The detailsof the magnetic calculations are very difficult to do accurately, as theyrequire precise computations of ionization equilibrium and polarizedradiative transfer, and these are nasty in strong fields and dense, hot,matter. It seems, though, that when magnetic effects are included ablackbody isn't too bad an approximation. Stay tuned.So what does all this mean with respect to neutron star composition?Yep, you guessed it, we don't have enough data. If you squint and looksideways at a graph of estimated temperature versus age, you mightconvince yourself that there is some evidence of rapid cooling, whichwouldn't fit with the standard cooling scenario. But, unfortunately,the error bars are too large to be definite. We really need a largearea detector that can pick up more stars. Features inthe spectra would be nice, too, but at the moment that's just a dream.In the meantime, here's some recent data, plotted against severalrepresentative cooling curves that make various assumptions aboutthe internal composition (this graph is fromwww.physik.uni-muenchen.de/sektion/suessmann/astro/cool/: Spin historyNeutron stars rotate very rapidly, up to 600 times per second. But howare they spinning when they are born? They may be born rotating very fast, with periods comparable to amillisecond (although evidence is ambiguous). After that, they spin down ever after because of magnetictorques. This seems to be supported by the fact that some of theyoungest 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, withtypical 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, theycan undergo very brief periods of spinup. These events are called "glitches", and they can momentarily change the period of a pulsar byup to a few parts in a million. The effects of glitches decay awayin a few days, and then the pulsar resumes its normal spindown. Incurrent models of glitches, the superfluid core and normal crust arepresumed to couple impulsively, and since the crust had been spun downby the magnetic field while the superfluid kept rotating at its originalrate, this coupling would speed up the crust, leading to the observedspinup. It is very difficult to treat this process from first (nuclear)principles, because the critical angular velocity difference at whichthe crust and superfluid finally couple depends sensitively on variousill-determined properties of neutron superfluids, and since theseproperties aren't directly accessible by experiments we may have to besatisfied by our current phenomenological description. Incidentally,the glitch should also heat up the crust, and late in the lifetime ofthe neutron star heating by rotational dissipation can actually becomea 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 themass of our Sun or lower, accretion tends to proceed by Roche lobeoverflow (more on that later). This type of flow has a lot of angularmomentum, so the matter forms a disk around the star. The radius of theinner 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 thematter at the inner edge of the accretion disk. This means that neutronstars with relatively small (10^8 to 10^9 Gauss) magnetic fields can bespun up to high frequencies, and this is the accepted picture of howwe get millisecond pulsars.If the companion of the neutron star is a high-mass star (over 10 solarmasses) instead, then the matter that makes it onto the neutron stargoes in the form of a low angular momentum wind. Therefore, the neutronstar isn't spun up to such high frequencies; in fact, some pulsars thatare in high-mass systems have periods longer than 1000 seconds. Theprocess of wind accretion is a very complicated one, and numericalsimulations 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. Onebarrier to understanding this kind of accretion is that, even with today's computers, high-resolution 3D simulations just aren't feasiblenow, so we have to derive what insight we can from good two-dimensionalcalculations.Misanthropic (aka isolated) neutron starsNeutrons were discovered in 1932, and very shortly afterward (in 1934)a suggestion was made by Walter Baade and Fritz Zwicky that neutronstars were formed in supernovae. But for many decades after that,neutron stars were just hypothetical phenomena that didn't attractmuch interest. Since the stars are so small, people felt that theprospects for observing them were minimal, and thus little effortwas 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 JocelynBell. Bell and her advisor, Anthony Hewish, were working on radioobservations of quasars, which had been discovered in 1963. Belland some other graduate students constructed a scintillation arrayfor the observations, then she got down to examining the charts ofdata produced (she had to analyze the miles of charts by hand, sincethis was in the days before powerful computers!). One day shenoticed a bit of "scruff" that appeared on the charts every secondand a third. The scruff was so regular that she first thought itmust be artificial. However, careful checking showed that indeedthe signal was extraterrestrial, and in fact that it must be fromoutside the solar system. This source, CP 1919, was the firstradio pulsar to be discovered.The discovery initiated a storm of activity that has still notabated. A number of other pulsars were discovered, including onein the Crab Nebula, site of a famous supernova in the year 1054that was observed by Chinese, Arabic, and North American astronomers(but not recorded, as far as we know, by Europeans). Within ayear 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 arevery regular, with a typical rate of change of only a second per ten million years, and (3) over time, the period of a pulsaralways increased slightly.With this data, it was realized quickly that pulsars had to berotating neutron stars. With certain exceptions that don't applyin this case, if a source varies over some time t, thenits size must be less than the distance light can travel in thattime, or ct (otherwise the variation would be happeningfaster than the speed of light). Thus, these objects had tobe less than 300,000 km/s times 0.033 seconds, or 10,000 km, insize. This restricts us to white dwarfs, neutron stars, or blackholes. You can get a periodic signal from such objects via pulsation, rotation, or a binary orbit. White dwarfs are largeenough that their maximum pulsational, rotational, or orbitalfrequencies are more than a second, so this is ruled out. Blackholes don't have solid surfaces to which to attach a beacon, sorotation or vibration of black holes is eliminated. Black holesor neutron stars in a binary could produce the required range ofperiods, but the binary would emit gravitational radiation, thestars would get closer together, and the period would decrease,not increase (and would do so very quickly, too!). Pulsations ofneutron stars typically have periods of milliseconds, not seconds.The only thing left is rotating neutron stars, and this fits allof the observations admirably. Here's an animated gif of a pulsar.There have now been more than 1000 radio pulsars discovered, withperiods from about 1.6 milliseconds to more than 5 seconds. Theirdiscovery is considered one of the three most importantastronomical discoveries in the latter half of the twentiethcentury (along with quasars and the microwave background), andin part for his role in the discovery of pulsars Anthony Hewishshared the 1974 Nobel Prize in physics.Social (aka accreting) neutron starsNot all neutron stars are destined to lead a life of isolation.Some of them are born in binaries that survive the supernovaexplosion that created the neutron star, and in dense stellarregions such as globular clusters some neutron stars may be ableto capture companions. In either case, mass may be transferredfrom the companion to the neutron star, as mentioned in thespin evolution section above.If the companion star has less than the mass of our Sun, themass transfer occurs via Roche lobe overflow. If part of thecompanion star's envelope is close enough to the neutron star,the neutron star's gravitational attraction on that part ofthe envelope is greater than the companion star's attraction,with the result that the gas in the envelope falls onto theneutron star. However, since the neutron star is tiny, astronomicallyspeaking, the gas has too much angular momentum to fall on thestar directly and therefore orbits around the star in an accretiondisk. Within the disk, magnetic or viscous forces operate toallow the gas in the disk to drift in slowly as it orbits, andto eventually reach the stellar surface. If the magnetic fieldat the neutron star's surface exceeds about 10^8 G, then beforethe gas gets to the stellar surface the field can couple stronglyto the matter and force it to flow along field lines to themagnetic poles. The friction of the gas with itself as it spiralsin towards the neutron star heats the gas to millions of degrees,and causes it to emit X-rays. Some characteristic dimensions ofthis sort of system are displayed in the figure.  Here, from wwwastro.msfc.nasa.gov/xray/openhouse/ns/, is a cartoon ofthe inner region where the neutron star's magnetic field controlsmatter: Neutron stars in these kind of systems are believed to have surface magnetic fields between 10^7 and 10^10 Gauss. Thismeans that the accreting gas can spiral very close to the neutron star before it is grabbed by the magnetic field. Atsuch 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 millisecondpulsars. Those millisecond pulsars, by the way, are extremelystable rotators; the best are at least as stable as atomicclocks! There have been suggestions that using millisecondpulsars as cosmic clocks could tell us about all sorts ofexotic things, such as the presence of a background of gravitationalradiation left over from the Big Bang.Another fun phenomenon associated with neutron stars that havelow-mass companions is X-ray bursts. These typically lasta few seconds to a few minutes, and have a peak luminositynearly a hundred thousand times our Sun's luminosity. Themodel for these bursts is that as hydrogen and helium is tranferred to the neutron star form the companion, it buildsup in a dense layer. Eventually, the hydrogen and helium havebeen packed in a layer so dense and hot that thermonuclearfusion starts, which then converts most or all of the gas intoiron, releasing a tremendous amount of energy. This is theequivalent of detonating the entire world's nuclear arsenalon every square centimeter of the neutron star's surface withina minute! Some of these binaries can be amazingly close to oneanother. Here's an artist's conception (fromheasarc.gsfc.nasa.gov/Images/exosat/slide_gifs/exosat18.gif)of one particularly extreme case, that of 4U~1820-30, which hasa binary period of just over eleven minutes! Too bad the distancesare in miles... If the companion to the neutron star has a mass between one andten times our Sun's mass, the mass transfer is unstable anddoesn't last very long, so there are few objects in this category.If the companion to the neutron star has a mass more than aboutten 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). Atfield strengths this high, almost all the accreting gas isforced to flow along field lines to the magnetic poles. Thismeans that the X-rays primarily come from the resulting hotspots on the poles. It also means that if the magnetic axis and rotation axis of the star aren't co-aligned, the radiationsweeps 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" thatJocelyn Bell discovered.For some recent results on accreting neutron stars, check outa poster from a science fair for grownupsfair 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 arestill a lot of uncertainties about their origins. They werefirst 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 ofconcern that these might be due to Soviet nuclear explosions, but itwas 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 ComptonGamma-Ray Observatory). Before tackling thequestion of what gamma-ray bursts are, we need to establishwhat they are observationally.Loosely speaking, gamma-ray bursts are, well, bursts of energy thatappear mostly in gamma rays and come from outside the Earth. The fluxat earth is between 10^-8 erg/cm^2/s and 10^-3 erg/cm^2/s, the durationof the bursts is between 10 ms and 1000 s, and the photons typically haveenergies between 100 keV and 2 MeV, although energies down to 5 keV andup to 18 GeV have been seen from some bursts. The flux as a function oftime varies from burst to burst, but often a spike within a burst followsthe "fred" profile (fast rise, exponential decay). Here's ananimate gif showing a simulation ofa burst as we'd see it on a map of the Galaxy (left) and its brightnessas a function of time (right). All in all, gamma-raybursts are extremely heterogeneous, so it is tough to extract characteristicbehaviors that would lead to easy classification (see a typicaltime 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 thatgamma-ray bursts come from all parts of the sky with approximately equalprobability. Since other aspects of gamma-ray bursts (such as the fastrise time [ |
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