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Gamma-ray bursts and glitching neutron stars
PHYSICS REPORTS (Review Section of Physics Letters) 163, Nos. I-3 (1988) 155-166. North-Holland, Amsterdam
GAMMA-RAY BURSTS AND GLITCHING NEUTRON STARS Richard I. EPSTEIN Space Astronomy and Astrophysics Group, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Abstract: Gamma-ray bursts, short flashes of nonthermal radiation, may shed light on the structure and formation rate of neutron stars. At least one and possibly all gamma-ray bursts originate from neutron stars, and the study of the mechanisms for generating bursts may elucidate the internal structure of these stars and, hence, the properties of high-density matter. This report summarizes salient observations of gamma-ray bursts and considers whether there is more than one class of gamma-ray burster and in what ways other astronomical systems have observed properties that resemble gamma-ray bursts. It then examines physical constraints on neutron star models of gamma-ray bursters and explores a particular model in which crustal glitches in neutron stars produce gamma-ray bursts.
I. Introduction
Above a few tens of keV the sky is "dark"; a satellite borne gamma-ray detector typically measures a total flux of less than 10 -7 ergcm -2 s -~ (this radiation does not penetrate the earth's atmosphere). A few hundred times each year, however, the darkness is pierced for several seconds or less by a gamma-ray burst which appears much brighter than the sum of all other sources in the sky. The brightest of these bursts exceed 10 -5 erg cm -2 s -~. The origin and nature of gamma-ray bursts has been an outstanding mystery in astrophysics since the announcement of their discovery in 1973 [1]. This report summarizes the observed properties of the bursts, some general physical constraints which are largely model independent, and one approach to modeling gamma-ray bursters. Gamma-ray bursts, fascinating and perplexing phenomena in their own right, hold out the possibility of augmenting our understanding of supernovae. First, there is good reason to believe they originate from neutron stars which are the products of supernova explosions. Thus, the statistics of gamma-ray bursters reveal the rate and distribution of supernovae. Second, the physics of dense matter, crucial in understanding supernovae during the core collapse phase, is manifest in the structure and evolution of neutron stars and possibly in gamma-ray bursts. In particular the stiffness of dense matter and the presence of pion or kaon condensates [2-6] directly affect the size of the neutron star crust and the stellar cooling rate [7-10]. In some gamma-ray burster models that involve neutron star glitches, the crustal thickness and the stellar temperature play crucial roles.
2. What if anything is a gamma-ray burster?
In discussing the observations of gamma-ray bursts, one must consider whether there is such a thing as a gamma-ray burster. That is, does one unique class of events produce gamma-ray bursts or are gamma-ray bursts the products of several diverse and possibly unrelated phenomena? If the former possibility were true, then all the reliable burst observations should be used to constrain and construct 0 370-1573/88/$4.20 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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burster models. In the latter case it would be as unrealistic to try to develop one physical model to explain all the observed gamma-ray bursts as it would be to invent a single model to explain all apparently star-like objects such as main-sequence stars and quasars. In the fourteen years since the discovery of gamma-ray bursts were reported, researchers have amassed a rich collection of data on several hundred events. Readers may consult the proceedings of several workshops [11-14] and some recent review articles [15-20] for detailed discussions of the data and attempts to model them. Here we will only mention observations which are new, which bear on the question of the uniqueness of the gamma-ray bursters, or which clearly constrain theoretical models. Some researchers have suggested that there are at least two types of gamma-ray burst sources: the "classical" bursters, which include the vast majority of the observed events, and the "repeating" bursters, which include three sources which are known repeaters and perhaps other sources with similar spectra and durations [21, 22]. The classical bursters typically emit most of their energy above 300 keV in bursts that are observable for the order of one second, though some are detected for less than 100 ms and one was followed for over 1000 s [23, 24]. The gamma-ray intensity during a classical burst often fluctuates widely with significant variations on the minimum resolvable time scales of a few ms [23]. The classical bursts have not been seen to repeat; there is no strong indication that any two of the - 9 0 well-localized gamma-ray bursts originated from the same source. This lack of observed repetitions has been used to establish a minimum recurrence interval of - 8 years for classical bursts brighter than --10 -6 ergcm -2 s -~ [25]. The three known repeating sources are the 1979, March 5 source, which has been reported to have repeated 16 times [26], the 1979, March 24 source with three detected recurrences [27], and the 1979, January 7 source, the most recent addition to this class, which appears to be the most prolific repeater (searches of archival records from the ISEE/ICE satellite have turned up 111 recurrences of the 1979, January 7 source between August 1978 and June 1986 [22]). The intervals between bursts from the 1979, January 7 source range from I s to over one year, and they show no obvious correlations with burst intensity, in contrast to the X-ray "Rapid Burster" [28]. The bursts from all three of the repeating sources are softer and shorter than the average classical burst; most of the energy from a repeating burst is emitted around 50 keV and persists for - 0 . 1 - 0 . 4 s. The phenomenally intense 1979, March 5 event, however, was detected above 1 MeV, and produced faint, but measurable, radiation for >~180 s [29]. Even though an intriguing case can be made that the classical and the repeating bursters are distinct types of sources, the argument is not compelling. There is no clear division between the classical bursts and the repeaters. The spectra of the various bursts span a broad range with the repeaters at the soft end of this range. However, the repeaters are not necessarily the softest of the gamma-ray bursts nor are they grossly different from many other bursts. The range of the distribution of gamma-ray burst spectra is illustrated in fig. 1, which gives schematic spectra of the 1979, January 7 burst and four other bursts in terms of P, the power per logarithmic energy interval, and E, the photon energy. All the gamma-ray burst spectra rise steeply at low energies and then decline gradually. At energies well below the peak the spectral index a (defined by P ~ E ~) is greater than 1, and in some events exceeds 2 [31]. Above the peak the spectral indices are often less steep than - 1 ; the high-energy portions of the spectra above - 1 MeV do not terminate abruptly. The spectra of the repeating sources peak at - 5 0 keV, whereas most of the other bursters peak above 200 keV; nevertheless, spectral considerations by themselves do not allow one to separate gamma-ray bursts into two groups. In the KONUS catalog of gamma-ray bursts [32] we find that - 1 5 % of all spectra peak near or below 100 keV and - 2 5 % have their maximum values of P below 150 keV. Given the continuity of spectral properties that are found for gamma-ray bursters, the repeaters need not be
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treated as a separate class. The more appropriate conclusion to draw is that the softer sources burst more frequently.
3. Bursting neutron stars After the initial flurry of unbridled speculation following the discovery of gamma-ray bursts [1], most theoretical work has focussed on neutron star models of gamma-ray bursts. Direct observations provide compelling evidence that at least one gamma-ray burst source is a neutron star. This evidence is the periodic intensity variations in the long tail of emission from the 1979, March 5 event. Following an intense initial spike, the gamma-ray flux varied periodically for at least 22 eight-second cycles [29]. Periodicity of this sort is a signature of rotation or pulsations of a compact star (a neutron star or a white dwarf, but not a black hole), and the rapid rise of the initial spike of radiation (<0.25 ms) and the hard X-ray emission for the 1979, March 5 event [29] rule out a white dwarf. The case for all gamma-ray bursts originating from neutron stars would be stronger if the 1979, March 5 burst were not such a peculiar event. It is a soft, repeating source, and it was the most intense and rapidly rising burst yet seen. Because it occurred at a propitious time when the full interplanetary network of satellites was functional, its position is known to -0.1 arcmin 2 and is consistent with that of the - 2 arcmin 2 supernova remnant N49 in the Large Magellanic Cloud (LMC) [39]. If this source actually is in the LMC, it is - 5 5 kpc from the Earth, the luminosity of the March 5 burst would have exceeded 10 44 erg s -1, and the subsequent bursts would have been in the range 1041-42 erg s -1. The task of plausibly explaining repeating bursts of these intensities in terms of neutron star events has stifled
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theorists, though it has been suggested that these events may originate on a sister of a neutron star, a "strange star" [40]. Perhaps the simplest hypothesis is that, despite the small sizes of the positional error box and the supernova remnant, the superposition of the two is coincidental, and the 1979, March 5 burster is located in our galaxy [41]. The reported existence of spectral features in a significant fraction of the gamma-ray burst spectra suggests that the bursts originate from the surfaces of neutron stars. Mazets et al. [42-44] report that - 7 % of the spectra they measured have bumps or wiggles near 400 keV and that about a fourth of them have similar deviations from a smooth continuum at 50-100 keV. The former features have been interpreted as 511 keV electron-positron annihilation lines redshifted in the gravitational field of a neutron star and the latter as emission or absorption lines from cyclotron resonances in magnetic fields of several times 1012 G. If either of these interpretations were correct, it would essentially prove that many gamma-ray bursts arise from near the surface of neutron stars. However, the experimental evidence for the spectral features is inconclusive [45], and their theoretical interpretations are not without difficulties. Several attempts to confirm the KONUS observations of the 400 keV features with other instruments have been negative or ambiguous [45]. In the case of the lower-energy features, the observations appear to be more secure, but the interpretation in terms of cyclotron resonances is suspect. The UCSD HEAO-1 observations of the 1978, March 25 event found an absorption feature near 55 keV which, if interpreted as a cyclotron absorption, implies a field of - 5 x 1012 G [33]. On the other hand, much of the power from this source escapes at energies above 1 MeV (see fig. 1), and these high-energy photons would have been destroyed if they encountered transverse magnetic fields of greater than 3 × 1011 G. One might suppose that this apparent contradiction could be reconciled by assuming a two-component model in which the emission near -60 keV is generated in a region close to the star where the magnetic field is - 5 × 1012 G and high-energy emission is generated in a larger region with weaker magnetic field far from the star [46]. However, to be consistent with the "cyclotron" absorption line this model must be more elaborate. Since the radiation from the high-energy emitting region cannot have a -55 keV cyclotron absorption feature, the two-component model must explain why the radiation from the larger region does not swamp the radiation from the region near the star. Some physical mechanism is needed that would allow the large region to dominate the spectrum at ~>1 MeV but not at ~<100keV; none has been proposed. If neutron stars actually make gamma-ray bursts, what can be deduced about the morphology of the source, its power, and the emission mechanisms? The shape of the burst continuum, which often exhibits a deficiency of X-ray emission below the peak and an abundance of photons above 1 MeV, supplies much information about these questions. To understand the issues involved, consider the schematic bursting neutron star model shown in fig. 2. In this model an isotropic source of gamma rays of characteristic dimension - h is located a distance - h above the surface of neutron star. The dimensions and luminosity of the source region are seriously constrained by considering two processes which degrade the gamma radiation. First, some of the radiation impinges on the star and heats the stellar surface. The surface reradiates the energy as lower-energy photons in the X-ray or UV range. Since the observed spectra fall off rapidly at the X-ray energies below the peak in P, the re-emitted radiation from the neutron star surface cannot be too large. Laros et al. [47] made a careful study of the X-ray emission from four bursts and found that the emission in the 3-10 keV band was - 2 % of the emission above 30 keV. Requiring that the thermal emission from the stellar surface obeys this bound, restricts the luminosity and the dimension h in the schematic model to the region to the right of the band marked "L x > 0.02Lv" in fig.
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3 [31]. (If the surface becomes hotter than the "Eddington temperature" TE, radiation pressure drives a wind so that energy that would otherwise emerge as electromagnetic energy is transformed to kinetic energy of mass motion. The region in fig. 3 where this occurs is to the left of the line marked T~rf> TE.) Second, the highest-energy photons leaving the source can interact with each other to produce electron-positron pairs. The observations that the burst spectra do not cut off above a few MeV [48] indicate that few high-energy gamma rays are eliminated by photon-photon pair production. (Gammarays can regenerate by the reverse process but the energy of these gamma rays is on the average lower
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because positrons tend to annihilate with the more abundant lower-energy electrons.) The condition that the high-energy spectrum above - 2 MeV does not suffer appreciable degradation due to photonphoton interactions, restricts acceptable models to the region to the right of the band labeled ~ + ~ / ~ e + + e - [49]. Figure 3 illustrates that the characteristic dimension of a gamma-ray producing region must be larger than or comparable to the stellar radius. Even though this constraint was derived for the geometry of fig. 2, in which the source region is on one side of the neutron star, other geometries, such as a source region that surrounds the neutron star should give similar results. If the emission is collimated rather than isotropic, the emission region could be, in principle, much smaller since high-energy photons would not necessarily intersect at large enough angles to produce pairs and the gamma radiation could be beamed away from the surface of the neutron star. Nevertheless, if the emission were from a small region near the neutron star surface, the beaming and collimation would have to be very precise to satisfy the constraints indicated in fig. 3. On the other hand, if the source region is located far from the stellar surface, it is difficult to understand how the putative cyclotron or annihilation features could arise. As an approach to modeling gamma-ray bursters, one can try to draw analogies with other high-energy sources while bearing in mind the specific constraints implied by the gamma-ray burst spectra. The lower part of fig. 1 shows sketches of the spectra for a number of different types of sources: XB1724-30, an X-ray burster; Vela X-I, an accretion-powered pulsar; the low state of Cyg X-l, which is probably an accreting black hole; and the rotation-powered pulsar in the Crab Nebula. All of these high-energy sources have higher ratios of X-ray to ~/-ray emission than the typical gamma-ray burst. This is not necessarily a problem for making an analogy with gamma-ray bursters. For example, Zdziarski and Lamb [50] have studied a gamma-ray burster model that has common features with the accretion-powered sources. They invoke a large cloud of plasma containing hot electrons which engulfs a neutron star and has an outer dimension which is at least several stellar radii (this model is consistent with the constraints of fig. 3). The predicted spectra are in agreement with the typical gamma-ray burst spectrum below 500 keV, but the origin and energization of the electron cloud has not yet been elucidated. Rotation-powered pulsars are attractive prototypes of very nonthermal gamma-ray sources. Their gamma rays are thought to originate from "outer gap" regions which are at ~ 1 0 3 stellar radii [51], in agreement with the constraints of fig. 3. The gamma-ray emission from these objects is not necessarily intimately related to the X-ray emission, so it may be possible to devise a gamma-ray burster model that is similar to a rotation-powered pulsar with the X-ray emitting regions "turned off". The analogy between rotation-powered pulsars and gamma-ray bursts will be examined in more detail in what follows.
4. Glitching neutron stars
In a rotation-powered pulsar the braking of the rotation of the neutron star by the magnetic field frozen into the stellar surface powers the observable electromagnetic radiation. This process produces a fairly continuous stream of radiation, which appears pulsed because the star is rotating. The striking difference between pulsars and gamma-ray bursters is that gamma-ray bursters appear to lie dormant for years, radiate intensely for a few seconds, and then return to dormancy. The key to developing a pulsar-like model for gamma-ray bursters is understanding how the energy source is turned on for such
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brief intervals. Observations of the period changes of pulsars provide a clue: the periods occasionally undergo glitches, which are sudden decreases that must be due to violent readjustments in the internal structure of the neutron star. One approach to modeling gamma-ray bursters is to hypothesize that the energy released in a glitch is somehow transferred to gamma radiation [52-56]. Most of these models posit that glitches excite oscillations which jiggle the stellar surface. The motion of the magnetic field that is frozen in the surface then produces low-frequency electromagnetic radiation which damps the oscillations and accelerates high-energy particles which in turn produce gamma rays. To assess the possibility that glitches produce gamma-ray bursts, one must first examine mechanisms for known glitches in radio emitting pulsars. The glitch, a sudden decrease in the pulse period, is universally interpreted as an abrupt increase in the rotational velocity of the crust of the neutron star. The stellar crust contains nuclei in a Coulomb lattice. The "inner crust", the denser part of the curst extending from densities of - 4 x 1011 to - 2 x 1014 g cm -3, contains a free neutron gas that coexists with the nuclei [57]. Several hypotheses have been put forward to explain glitching. An initially popular interpretation was that star quakes produce glitches [58]. As the rotation rate of a neutron star slows due to magnetic braking, its equatorial bulge would decrease if the crust were not solid. Instead, stresses build in the solid crust until it cracks. The cracking or star quake decreases the crustal moment of intertia and, by conservation of angular momentum, spins up the crust. This was an attractive theory when the only known repeating glitches were from the Crab pulsar with small relative changes in the angular velocity, A/2/O = 10 -8 [59]. The subsequent discoveries of ~>100 times larger glitches from the Vela pulsar recurring on time scales of years [60] dealt a death blow to this model; the required strains could not be built up in a neutron star crust between glitches. Even though neutron star quakes should occur, they cannot explain the most outstanding glitches. Recent efforts to understand glitches have focused on mechanisms for transferring angular momentum from the free neutron gas in the inner crust of the neutron star to the solid crust [61-63]. An analogous process perturbs the earth's rotation period; angular momentum is exchanged between the solid earth and the atmosphere. Relative shifts in the earth's rotation rate of the order of AO/I2 = 10 -7.5 are compensated by changes in the atmospheric jet stream velocity [64]. In a neutron star the only component which may be sufficiently decoupled from the rest of the star to be able to play the role of the "neutron star jet stream" is the free neutron gas in the inner crust. Throughout much of the inner crust the free neutrons pair to create a superfluid which moves through the nuclear lattice with very little dissipation. The superfluid can impart momentum to the crust if it has an angular velocity Osr which is larger than that of the crust Ocr. This differential motion is possible because the rotating superfluid contains vortices which interact with the crustal nuclei. Even though superfluid flow is irrotational, i.e., the curl of its velocity is zero, its circulation, the line integral of the velocity around a closed loop, need not be zero. The circulation can equal NK, where N is an integer and K = h / m is the quantum of circulation (h is Planck's constant and m is the mass of a Cooper pair, which is twice the neutron mass). For each quantum of circulation there is a small region, a vortex core, in which the superfiuidity vanishes. At small distances r from each core the azimuthal velocity of the superfluid around the core varies as K/(2~rr). Since a vortex core contains a normal neutron gas rather than a superfluid, pairing energy is expended in forming a core. On the other hand, the kinetic energy density of the superfluid flow increases as 1/r 2 near the vortex core. Minimization of the total kinetic plus condensation energy determines the size of the vortex core; it is of the order of 10 fm in the neutron star crust. The energy of the vortex core can be further decreased if the vortex core is positioned to take advantage of the inhomogeneities created by the nuclei. Depending on the superfluid and nuclear parameters in the
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different layers of the star, the energy of a core is lowered by either threading through the nuclei or by avoiding the nuclei. By finding a minimum energy path through or between the nuclei, a vortex line pins itself to the nuclear lattice [78]. In the regions of the star where vortex lines are pinned, the motion of the superfluid can be decoupled from that of the crust. This may sound paradoxical, but pinning the vortex lines to the crust is far different from coupling the superfluid flow to the crust. In fact, the distribution of the quantized vortex lines determines the rotation rate of the superfluid throughout the star. When the neutron star crust rotation slows due to magnetic braking, the superfluid rotation in the inner crust is largely unchanged because the pinned vortex lines cannot be easily moved. The velocity difference between the crustal nuclei and the neutron superfluid thus grows. Current models of neutron star glitches exploit the excess angular momentum and free energy of the rotating superfluid. How does the superfluid lose angular momentum during a glitch? One possibility is that the angular velocity of the superfluid decreases due to the displacement of some vortex lines away from the rotation axis. A proposed mechanism of this type invokes catastrophic unpinning of vortex lines when the differential velocity between the crust and the superfluid approaches a critical value [61, 62]. An alternative explanation is that the stresses on the crust from the pinned vortex lines crack the crust, thereby displacing the lines without unpinning them [63]. Another possibility is that the distribution of vortex lines and the superfluid velocity do not change during a glitch, but rather the mass of the superfluid decreases. An analogous phenomenon would occur in the laboratory if rapidly rotating superfluid He II in a slowly rotating bucket is heated to the critical h-temperature. As the ratio of superfluid to normal helium decreases, angular momentum would be transferred from the superfluid to the normal matter, and the bucket would rotate more quickly. A neutron star glitch similarly can be "thermally driven" if a sudden energy input - perhaps from a crust . . .neutron . superflmd . .to above ~ts crlucal temperature, - 1 0 9-1o K. The q u a k e - heats rapidly rotating normal (nonsuperfluid) neutron gas quickly grinds to a halt relative to the crustal material and the excess angular momentum is imparted to the crust. In such a thermally driven glitch the energy for destroying the superfluidity is supplied by a separate mechanism such as a crust quake; the rapidly rotating superfluid in the inner crust is merely a passive reservoir of angular momentum. A perhaps more attractive model is a "velocity-dissipation" glitch mechanism. In this model the relative velocity between the superfluid and the crust provides both the angular momentum and the energy for a glitch. When the relative velocity difference between a superfluid and the crustal nuclei exceeds a critical velocity, the flow of the neutron gas around and through the nuclei becomes dissipative. The dissipation can be due to the emission of excitations somewhat analogous to rotons or to the generation of superfluid turbulence [65]. The critical velocity for roton emission can be estimated by scaling from the conditions in He II to be - - 1 0 9 c m s -~ [66], and the critical velocity for the onset of superfluid turbulence could be many orders of magnitude smaller [65]. Several of the above glitch mechanisms (the vortex-unpinning model, the crust-cracking model, and the velocity-dissipation model) are induced when the differential velocity between the superfluid and the crust attains a critical value, but only the one with the lowest threshold velocity can actually occur. Hybrid models are also possible. For example, crust cracking (due to changing stellar figure or to vortex-pinning stresses) could nucleate the onset of superfluid turbulence. If this were so, then seismically quiet stars might have fairly evenly spaced glitches whereas crust-quake prone stars might have numerous quakes that trigger many glitches. The glitches observed in radio pulsars speed up the crust on time scales shorter than one day. If glitches power gamma-ray bursts, the glitches must be excited on time scales considerably shorter than a
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day, typical gamma-ray burst time scales are a fraction of a second. This time scale is a significant constraint on glitch models for gamma-ray bursts. In the vortex line unpinning model the glitch time scale is set by the rate at which vortex lines unpin and impart angular momentum to the crust. Angular momentum may be transferred by electron scattering from vortex cores. If the electrons are scattered only by the neutron magnetic moments [67], the glitch time scale is ~years, which is not adequate to explain the radio pulsar data and is totally unacceptable for gamma-ray bursters [79]. Inclusion of other dissipation processes may significantly shorten this time scale. For example, since the vortex lines tend to attract or repel nuclei (depending on the neutron gas density), they are charged so that Coulomb scattering of electrons is significant [79]. The other glitch mechanisms discussed above (crust-cracking and velocity-dissipation glitches) function on the characteristic dynamic time scale of neutron stars, which is of the order of milliseconds. Even if a glitch does occur rapidly enough, could much of its energy be converted into electromagnetic energy in a fraction of a second? Such rapid energy conversion is plausible, but not certain. If a glitch is generated by the sudden braking of a rotating superfluid, it will predominately excite toroidal modes that have no radial displacement. The toroidal oscillations do not emit gravitational radiation as copiously as the spheroidal ones do. The toroidal oscillations can, nevertheless, excite electromagnetic radiation by "shaking" magnetic field lines frozen in the surface of the star. The power radiated by this process is proportional to the square of the surface amplitude of the oscillation and at least the fourth power of the oscillation frequency [56, 68]. Previous estimates for the damping rate of torsional oscillations by emission of electromagnetic radiation gave time scales of several days to several years for typical neutron star parameters [68, 69]. Amazingly, there are additional effects, not previously considered, that may reduce the time scale to fractions of a second. First, the earlier estimates neglected the effects of the neutron superfluid on the oscillation modes. Since the neutron superfluid couples only weakly to the solid crust, the oscillation frequencies are higher and, for a given energy, the amplitudes are larger [70]. Second, resonant, mode-mode coupling may efficiently funnel from the lower-frequency modes to the higher-frequency ones, which then are quickly damped by electromagnetic radiation [71].
5. The gamma-ray burster as an adolescent neutron star
This report has so far focused on the physical issues of gamma-ray bursters; let us now consider them in an astronomical context, In a glitch model, gamma-ray bursters are relatively young, single neutron stars, many or most of which are born in supernova explosions. Soon after the explosion they have large translational velocities (~100 km s -1) and strong surface magnetic fields (-1012 G) and produce pulsed radio emission [72]. While the neutron stars are radiating as pulsars, they experience glitches, but apparently do not produce gamma-ray bursts. Searches for gamma-ray bursts coincident with several glitches from the Vela pulsar failed to discover any events above - 3 × 10 -6 erg cm -2 s -1 [73]. This lack of correlation between observed glitches and gamma-ray bursts can be rationalized by postulating that the physical conditions required for the production of pulsed radio emission are incompatible with the generation of gamma-ray bursts. This is plausible because a neutron star that is an active pulsar produces an electron-positron pair plasma that generates radio emission [74]. A sudden impulse of energy during a glitch may simply increase the number of pairs but not generate highly relativistic particles that could radiate gamma rays. In some models of pulsars the pair plasma responsible for the radio emission is generated by gamma rays interacting with a strong magnetic field near the surface of a
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neutron star [74-76]. Pulsed radio emission terminates ~107 years after the neutron star is formed [77], possibly due to decay of the strength of the surface magnetic field of the neutron star. Magnetic field evolution might explain the absence of gamma-ray bursts when pulsars glitch and the difference between the soft repeating bursters and the classical bursters. In active pulsars the magnetic field may be so strong that photons with energies even slightly above the pair rest mass are converted to an electron-positron plasma, which absorbs the lower-energy gamma radiation. Gamma-ray bursters could correspond to extinguished pulsars with weaker magnetic fields; in fields below ~1011 G radiation above - 3 MeV could escape freely. Furthermore, recently deceased pulsars are good candidates for the repeating gamma-ray bursters. They would be the youngest gamma-ray bursters and hence the most active with the fastest repetition rates. Because of their youth (--10 7 yr) they would be found near the galactic plane. Laros et al. noted [22] that the repeaters are located within 30° of the galactic plane, whereas the overall distribution of gamma-ray bursts is isotropic on the sky. This is suggestive, even if statistics based on three objects is not overwhelming. The detectable bursts from the young bursters should be soft, since if even a small fraction of their energy were above an MeV, the radiation would interact with the magnetic field and produce an opaque pair plasma. The classical bursters are presumably older neutron stars (~>108yr) with weaker surface fields (~<101°G). They glitch only occasionally, but perhaps very violently. The older neutron stars travel - 5 kpc into the halo, and if the intrinsic luminosities of their bursts are less than ~10 37 erg s-1, the events they produce would appear fairly isotropic for fluxes greater than several times 10 -7 erg s -1
6. Outlook
In the next few years data from several new gamma-ray burst instruments on the Gamma-Ray Observatory satellite (scheduled for 1990), the Japanese satellite Ginga (formerly ASTRO-C, it has been in orbit since February 1987) and P86-2 (an Air Force satellite scheduled for the early 1990s) should resolve some of the important questions about gamma-ray bursters. If all goes well, the reality of the cyclotron lines and the pair annihilation lines will be decided, and the anisotropy of the burst arrival directions will be measured. The Gamma-Ray Burst Detector on Ginga, which is sensitive down to - 2 keV, may be able to discover soft, repeating bursts and determine whether the repeating bursters are confined to regions near the galactic disk. The low-energy capabilities may also enable Ginga to detect thermal emission from the surface of a neutron star and thus prove the neutron star origin of the bursts. Finding accurate positions for several repeating bursters would improve the prospects for discovering optical or soft X-ray emission that is radiated simultaneously with a gamma-ray burst and during quiescence between bursts. These data could well resolve whether bursters are single stars or in binary systems and whether they accrete matter steadily between bursts. The glitch interpretation of gamma-ray bursters would be strengthened if it is found that (1) gamma-ray bursters are single, nonaccreting, neutron stars, that (2) the classical sources are contained in a thick spheroidal volume and that (3) repeaters lie near the disk. Since gamma-ray bursters would be an older population of neutron stars than those that are observed as radio emitting pulsars, their spatial distribution and X-ray and ~/-ray spectra would provide a measure of the birth rate of neutron stars and the evolution of the surface magnetic field strengths over time scales of 108 years or more. An improved understanding of the instability that produces glitches and its temperature dependence might give a measure of the thickness of the crust of a neutron star, its interior temperature and its dependence on stellar age. The temperature evolution provides a handle on the properties of matter at
R.I. Epstein, Gamma-ray bursts and glitching neutron stars
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supernuclear densities because the cooling rates and the equation of state of dense matter are intimately interconnected. For example, the existence of pion or kaon condensates at several times nuclear density would dramatically increase the neutron star cooling rate and would also soften the equation of state. It is a measure of the unity of various areas of astrophysics that one of the much discussed questions in supernova theory, the equation of state at supernuclear densities, may be an important ingredient in the theory of gamma-ray bursters.
Acknowledgment This work was carried out under the auspices of the US Department of Energy. The author thanks Gordon Baym, France Cordova, Diane Roussel-Dupre, Bill Feldman, Ed Fenimore, Ray Klebesadel, John Laros, Bill Priedhorsky, and Wojciech Zurek for discussing the material in this report.
References [1] R.W. Klebesadel, I.B. Strong and R.A. Olson, Astrophys. J. (Lett.) 182 (1973) L85. [2] A.B. Migdal, Zh. Eksp. Teor. Fiz. 61 (1971) 2210 [Soy. Phys.-JETP 36 (1973) 1052]. [3] R.F. Sawyer, Phys. Rev. Lett. 29 (1972) 382. [4] D.J. Scalapino, Phys. Rev. Lett. 29 (1972) 386. [5] G. Baym and D.K. Campbell, in: Mesons in Nuclei, Vol. 3, eds M. Rho and D. Wilkinson (North-Holland, Amsterdam, 1979). [6] D.B. Kaplan and A.E. Nelson, Phys. Lett. B 175 (1986) 57. [7] V.R. Pandharipande, D. Pines and R.A. Smith, Astrophys. J. 208 (1976) 550. [8] K.A. Van Riper and D.Q. Lamb, Astrophys. J. (Lctt.) 244 (1981) L13. [9] M.B. Richardson, H.M. Van Horn, K.F. Ratcliff and R.C. Malone, Astrophys. J. 255 (1982) 624. [10] S. Tsuruta, Phys. Rep. 56 (1979) 237. [11] R.E. Linganfelter, H.S. Hudson and D.M. Worral, eds, Gamma Ray Transients and Related Astrophysical Phenomena (Am. Inst. Phys., New York, 1982). [12] M.L. Burns, A.K. Harding and R. Ramaty, eds, Positron Electron Pairs in Astrophysics (Am. Inst. Phys., New York, 1983). [13] S. Woosley, ed., High Energy Transients in Astrophysics (Am. Inst. Phys., New York, 1984). [14] E.E Liang and V. Petrosiau, eds, Gamma-Ray Bursts (Am. Inst. Phys., New York, 1986). [15] R.I. Epstein, in: Radiation Hydrodynamics, IAU Coll. No. 89, eds K. Winkler and D. Mihalas (Springer, Berlin, 1986) p. 305. [16] E.E Mazets and S.V. Golenetskii, Soy. Sci. Rev., Sect. E 1 (1981) 205. [17] G. Vedrenne and G. Chambon, Space Sci. Rev. 36 (1983) 319. [18] M.J. Rees, in: Accreting Neutron Stars, eds W. Brinkmann and J. Triimper, MPE Report No. 177 (Max-Planck Institute for Extraterrestrial Physics, Garching, 1982) p. 179. [19] D.Q. Lamb, Ann. NY Acad. Sci. 422 (1983) 237. [20] F. Verter, Phys. Rep. 81 (1982) 295. [21] E.E Mazets, S.V. Golenetskii and Yu.A. Gur'yan, Soy. Astron. Lett. 5 (1979) 343. [22] J.G. Laros et al., Astrophys. J. (Lett.) 320 (1987) Ll11; and presentation at the Los Alamos Workshop on Gamma-Ray Stars (1986). [23] Ref. [14], Ch. 1, Section II. [24] R.W. Klebesadel, J.G. Laros and E.E. Fenimore, Bull. Am. Astron. Soc. 16 (1984) 1016. [25] J.L. Atteia et al., Astrophys. J. Suppl. 64 (1987) 305. [26] E.E Mazets, S.V. Golenetskii, Yu.A. Gur'yan and V.N. Ilyinskii, Astrophys. Space Sci. 84 (1982) 173; see also: S.V. Golenetskii et al., Soy. Astron. Lett. (May/June 1987). [27] E.P. Mazets, S.V. Golenetskii and Yu.A. Gur'yan, Soy. Astrou. Lett. 5 (1979) 343. [28] W. Lewin and P.C. Joss, Space Sci. Rev. 28 (1981) 3. [29] T.L. Cline et al., Astrophys. J. (Lett.) 237 (1980) L1. [30] J.G. Laros et al., Nature 322 (1986) 152. [31] J.N. Imamura and R.I. Epstein, Astrophys. J. 313 (1987) 711. [32] E.P. Mazets et al., Astrophys. Space Sci. 80 (1981) 3, 85, 119. [33] G.J. Heuter, in: High Energy Transients in Astrophysics, ed. S. Woosley (Am. Inst. Phys., New York, 1984) p. 373.
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[34] G.H. Share, S.M. Matz, D.C. Messina, EL. Nolan, E.L. Chupp, D.J. Forrest and J.F. Cooper, Adv. Space Res. 6 (1986) 15. [35] J.H. Swank, R.H. Becker, E.A. Boldt, S.S. Holt, S.H. Pravdo and P.J. Serlemitsos, Astrophys. J. (Le,It.) 212 (1977) 173. [36] F.K. Knight, in: Positron Electron Pairs in Astrophysics,eds M.L. Burns. A.K. Harding and R. Ramaty (Am. Inst. Phys., New York, 1983) p. 141. [37] E.P. Liang and P.L. Nolan, Space Sci. Rev. 38 (1984) 353. [38] N.E. White, J.L. Kaluzienskiand J.H. Swank, in: High Energy Transients in Astrophysics,ed. S. Woosley(Am. Inst. Phys., New York, 1984) p. 31. [39] T.L. Cline et al., Astrophys. J. (Lett.) 255 (1982) IA5. [40] C. Alcock, E. Farhi and A. Olinto, Phys. Rev. Lett. 57 (1986) 2088. [41] S.V. Golenetskii, V.N. Ilyinskii and E.P. Mazets, Nature 307 (1983) 41. [42] E.P. Mazets and S.V. Golenetskii, Astrophys. Space Sci. 75 (1981) 47. [43] E.P. Mazets, S.V. Golenetskii, R.L. Aptekar, Yu.A. Gur'yan and V.N. Ilinskii, Nature 290 (1981) 378. [44] E.P. Mazets, S.V. Golenetskii, V.N. Ilinskii, Yu.A. Gur'yan, R.L. Aptekar, V.N. Panov, I.A. Sokolov, Z.Ya. Sokolova and T.V. Kharitonova, Astrophys. Space Sci. 82 (1982) 261. [45] Ref. [14], Ch. 2, Section IID. [46] R.E. Lingenfelter and G.J. Hueter, in: High Energy Transients in Astrophysics, ed. S. Woosley (Am. Inst. Phys., New York, 1984) p. 558. [47] J.G. Laros, W.D. Evans, E.E. Fenimore, R.W. Klebesadel, S. Shulman and G. Fritz, Astrophys. J. 286 (1984) 681. [48] S.M. Matz, D.J. Forrest, W.T. Vestrand, E.L. Chupp, G.H. Share and E. Rieger, Astrophys. J. (Lett.) 288 (1985) L37. [49] R.I. Epstein, Astrophys. J. 297 (1985) 555. [50] A.A. Zdziarski and D.Q. Lamb, Astrophys. J. (Lett.) 309 (1986) L79. [51] K.S. Cheng, C. Ho and M. Ruderman, Astrophys. J. 300 (1986) 500. [52] F. Pacini and M. Ruderman, Nature 251 (1974) 399. [53] A.I. Tsygan, Astron. Astrophys. 44 (1975) 21. [54] A.C. Fabian, V. Icke and J.E. Pringle, Astrophys. Space Sci. 42 (1976) 77. [55] I.G. Mitrofonov, Astrophys. Space Sci. 105 (1984) 245. [56] A.G. Muslimovand A.I. Tsygan, Astrophys. Space Sci. 120 (1986) 27. [57] G. Baym and C.J. Pethick, Annu. Rev. Nucl. Sci. 25 (1975) 27. [58] G. Baym and D. Pines, Ann. Phys. 66 (1971) 816. [59] E. Lohsen, Astron. Astrophys. Suppl. 44 (1981) 1. [60] G.S. Downs, Astrophys. J. 249 (1981) 687. [61] P.W. Anderson and N. Itoh, Nature 256 (1975) 25. [62] D. Pines, J. Shaham, M.A. Alpar and P.W. Anderson, Prog. Theor. Phys. Suppl. 69 (1980) 376. [63] M. Ruderman, Astrophys. J. 203 (1976) 213. [64] W.E. Caner and D.S. Robertson, Sci. Am. 255 (1986) 46. [65] J.T. Tough, in" Progress in Low Temperature Physics, Vol. VIII, ed. D.F. Brewer (Noah-Holland, Amsterdam, 1982) p. 133. [66] R.P. Feynman, in: Progress in Low Temperature Physics, Vol. I, ed. C.J. Goner (North-Holland, Amsterdam, 1955) p. 17. [67] P.J. Feibelman, Phys. Rev. D 4 (1971) 1589. [68] P.N. McDermott, M.P. Savedoff, H.M. Van Horn, E.G. Zweibel and C.J. Hansen, Astrophys. J. 281 (1984) 746. [69] B.W. Carroll, E.G. Zweibel, C.J. Hansen, P.N. McDermott, M.P. Savedoff, J.H. Thomas and H.M. Van Horn, Astrophys. J. 305 (1986) 767. [70] R.I. Epstein, Astrophys. J., in press. [71] I. Wasserman, R. Nelson and R.I. Epstein, in preparation. [72] B. Anderson and A.G. Lyne, Nature 303 (1983) 597. [73] R.W. Klebesadel, private communication. [74] P.A. Sturrock, Astrophys. J. 164 (1971) 529. [75] M.A. Ruderman and P.G. Sutherland, Astrophys. J. 196 (1975) 57. [76] J. Arons and E.T. Scharleman, Astrophys. J. 231 (1979) 854. [77] A.G. Lyne, in: Supernovae: A Survey of Current Research, eds M.J. Rees and R.J. Stoneham (Reidel, Dordrecht, 1982) p. 405. [78] R.I. Epstein and G. Baym, Astrophys. J., in press. [79] L.B. Idsten and R.I. Epstein, in preparation.
GAMMA-RAY BURSTS AND GLITCHING NEUTRON STARS Richard I. EPSTEIN Space Astronomy and Astrophysics Group, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Abstract: Gamma-ray bursts, short flashes of nonthermal radiation, may shed light on the structure and formation rate of neutron stars. At least one and possibly all gamma-ray bursts originate from neutron stars, and the study of the mechanisms for generating bursts may elucidate the internal structure of these stars and, hence, the properties of high-density matter. This report summarizes salient observations of gamma-ray bursts and considers whether there is more than one class of gamma-ray burster and in what ways other astronomical systems have observed properties that resemble gamma-ray bursts. It then examines physical constraints on neutron star models of gamma-ray bursters and explores a particular model in which crustal glitches in neutron stars produce gamma-ray bursts.
I. Introduction
Above a few tens of keV the sky is "dark"; a satellite borne gamma-ray detector typically measures a total flux of less than 10 -7 ergcm -2 s -~ (this radiation does not penetrate the earth's atmosphere). A few hundred times each year, however, the darkness is pierced for several seconds or less by a gamma-ray burst which appears much brighter than the sum of all other sources in the sky. The brightest of these bursts exceed 10 -5 erg cm -2 s -~. The origin and nature of gamma-ray bursts has been an outstanding mystery in astrophysics since the announcement of their discovery in 1973 [1]. This report summarizes the observed properties of the bursts, some general physical constraints which are largely model independent, and one approach to modeling gamma-ray bursters. Gamma-ray bursts, fascinating and perplexing phenomena in their own right, hold out the possibility of augmenting our understanding of supernovae. First, there is good reason to believe they originate from neutron stars which are the products of supernova explosions. Thus, the statistics of gamma-ray bursters reveal the rate and distribution of supernovae. Second, the physics of dense matter, crucial in understanding supernovae during the core collapse phase, is manifest in the structure and evolution of neutron stars and possibly in gamma-ray bursts. In particular the stiffness of dense matter and the presence of pion or kaon condensates [2-6] directly affect the size of the neutron star crust and the stellar cooling rate [7-10]. In some gamma-ray burster models that involve neutron star glitches, the crustal thickness and the stellar temperature play crucial roles.
2. What if anything is a gamma-ray burster?
In discussing the observations of gamma-ray bursts, one must consider whether there is such a thing as a gamma-ray burster. That is, does one unique class of events produce gamma-ray bursts or are gamma-ray bursts the products of several diverse and possibly unrelated phenomena? If the former possibility were true, then all the reliable burst observations should be used to constrain and construct 0 370-1573/88/$4.20 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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burster models. In the latter case it would be as unrealistic to try to develop one physical model to explain all the observed gamma-ray bursts as it would be to invent a single model to explain all apparently star-like objects such as main-sequence stars and quasars. In the fourteen years since the discovery of gamma-ray bursts were reported, researchers have amassed a rich collection of data on several hundred events. Readers may consult the proceedings of several workshops [11-14] and some recent review articles [15-20] for detailed discussions of the data and attempts to model them. Here we will only mention observations which are new, which bear on the question of the uniqueness of the gamma-ray bursters, or which clearly constrain theoretical models. Some researchers have suggested that there are at least two types of gamma-ray burst sources: the "classical" bursters, which include the vast majority of the observed events, and the "repeating" bursters, which include three sources which are known repeaters and perhaps other sources with similar spectra and durations [21, 22]. The classical bursters typically emit most of their energy above 300 keV in bursts that are observable for the order of one second, though some are detected for less than 100 ms and one was followed for over 1000 s [23, 24]. The gamma-ray intensity during a classical burst often fluctuates widely with significant variations on the minimum resolvable time scales of a few ms [23]. The classical bursts have not been seen to repeat; there is no strong indication that any two of the - 9 0 well-localized gamma-ray bursts originated from the same source. This lack of observed repetitions has been used to establish a minimum recurrence interval of - 8 years for classical bursts brighter than --10 -6 ergcm -2 s -~ [25]. The three known repeating sources are the 1979, March 5 source, which has been reported to have repeated 16 times [26], the 1979, March 24 source with three detected recurrences [27], and the 1979, January 7 source, the most recent addition to this class, which appears to be the most prolific repeater (searches of archival records from the ISEE/ICE satellite have turned up 111 recurrences of the 1979, January 7 source between August 1978 and June 1986 [22]). The intervals between bursts from the 1979, January 7 source range from I s to over one year, and they show no obvious correlations with burst intensity, in contrast to the X-ray "Rapid Burster" [28]. The bursts from all three of the repeating sources are softer and shorter than the average classical burst; most of the energy from a repeating burst is emitted around 50 keV and persists for - 0 . 1 - 0 . 4 s. The phenomenally intense 1979, March 5 event, however, was detected above 1 MeV, and produced faint, but measurable, radiation for >~180 s [29]. Even though an intriguing case can be made that the classical and the repeating bursters are distinct types of sources, the argument is not compelling. There is no clear division between the classical bursts and the repeaters. The spectra of the various bursts span a broad range with the repeaters at the soft end of this range. However, the repeaters are not necessarily the softest of the gamma-ray bursts nor are they grossly different from many other bursts. The range of the distribution of gamma-ray burst spectra is illustrated in fig. 1, which gives schematic spectra of the 1979, January 7 burst and four other bursts in terms of P, the power per logarithmic energy interval, and E, the photon energy. All the gamma-ray burst spectra rise steeply at low energies and then decline gradually. At energies well below the peak the spectral index a (defined by P ~ E ~) is greater than 1, and in some events exceeds 2 [31]. Above the peak the spectral indices are often less steep than - 1 ; the high-energy portions of the spectra above - 1 MeV do not terminate abruptly. The spectra of the repeating sources peak at - 5 0 keV, whereas most of the other bursters peak above 200 keV; nevertheless, spectral considerations by themselves do not allow one to separate gamma-ray bursts into two groups. In the KONUS catalog of gamma-ray bursts [32] we find that - 1 5 % of all spectra peak near or below 100 keV and - 2 5 % have their maximum values of P below 150 keV. Given the continuity of spectral properties that are found for gamma-ray bursters, the repeaters need not be
R.I. Epstein, Gamma-ray bursts and glitching neutron stars
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treated as a separate class. The more appropriate conclusion to draw is that the softer sources burst more frequently.
3. Bursting neutron stars After the initial flurry of unbridled speculation following the discovery of gamma-ray bursts [1], most theoretical work has focussed on neutron star models of gamma-ray bursts. Direct observations provide compelling evidence that at least one gamma-ray burst source is a neutron star. This evidence is the periodic intensity variations in the long tail of emission from the 1979, March 5 event. Following an intense initial spike, the gamma-ray flux varied periodically for at least 22 eight-second cycles [29]. Periodicity of this sort is a signature of rotation or pulsations of a compact star (a neutron star or a white dwarf, but not a black hole), and the rapid rise of the initial spike of radiation (<0.25 ms) and the hard X-ray emission for the 1979, March 5 event [29] rule out a white dwarf. The case for all gamma-ray bursts originating from neutron stars would be stronger if the 1979, March 5 burst were not such a peculiar event. It is a soft, repeating source, and it was the most intense and rapidly rising burst yet seen. Because it occurred at a propitious time when the full interplanetary network of satellites was functional, its position is known to -0.1 arcmin 2 and is consistent with that of the - 2 arcmin 2 supernova remnant N49 in the Large Magellanic Cloud (LMC) [39]. If this source actually is in the LMC, it is - 5 5 kpc from the Earth, the luminosity of the March 5 burst would have exceeded 10 44 erg s -1, and the subsequent bursts would have been in the range 1041-42 erg s -1. The task of plausibly explaining repeating bursts of these intensities in terms of neutron star events has stifled
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Theory of supernovae
theorists, though it has been suggested that these events may originate on a sister of a neutron star, a "strange star" [40]. Perhaps the simplest hypothesis is that, despite the small sizes of the positional error box and the supernova remnant, the superposition of the two is coincidental, and the 1979, March 5 burster is located in our galaxy [41]. The reported existence of spectral features in a significant fraction of the gamma-ray burst spectra suggests that the bursts originate from the surfaces of neutron stars. Mazets et al. [42-44] report that - 7 % of the spectra they measured have bumps or wiggles near 400 keV and that about a fourth of them have similar deviations from a smooth continuum at 50-100 keV. The former features have been interpreted as 511 keV electron-positron annihilation lines redshifted in the gravitational field of a neutron star and the latter as emission or absorption lines from cyclotron resonances in magnetic fields of several times 1012 G. If either of these interpretations were correct, it would essentially prove that many gamma-ray bursts arise from near the surface of neutron stars. However, the experimental evidence for the spectral features is inconclusive [45], and their theoretical interpretations are not without difficulties. Several attempts to confirm the KONUS observations of the 400 keV features with other instruments have been negative or ambiguous [45]. In the case of the lower-energy features, the observations appear to be more secure, but the interpretation in terms of cyclotron resonances is suspect. The UCSD HEAO-1 observations of the 1978, March 25 event found an absorption feature near 55 keV which, if interpreted as a cyclotron absorption, implies a field of - 5 x 1012 G [33]. On the other hand, much of the power from this source escapes at energies above 1 MeV (see fig. 1), and these high-energy photons would have been destroyed if they encountered transverse magnetic fields of greater than 3 × 1011 G. One might suppose that this apparent contradiction could be reconciled by assuming a two-component model in which the emission near -60 keV is generated in a region close to the star where the magnetic field is - 5 × 1012 G and high-energy emission is generated in a larger region with weaker magnetic field far from the star [46]. However, to be consistent with the "cyclotron" absorption line this model must be more elaborate. Since the radiation from the high-energy emitting region cannot have a -55 keV cyclotron absorption feature, the two-component model must explain why the radiation from the larger region does not swamp the radiation from the region near the star. Some physical mechanism is needed that would allow the large region to dominate the spectrum at ~>1 MeV but not at ~<100keV; none has been proposed. If neutron stars actually make gamma-ray bursts, what can be deduced about the morphology of the source, its power, and the emission mechanisms? The shape of the burst continuum, which often exhibits a deficiency of X-ray emission below the peak and an abundance of photons above 1 MeV, supplies much information about these questions. To understand the issues involved, consider the schematic bursting neutron star model shown in fig. 2. In this model an isotropic source of gamma rays of characteristic dimension - h is located a distance - h above the surface of neutron star. The dimensions and luminosity of the source region are seriously constrained by considering two processes which degrade the gamma radiation. First, some of the radiation impinges on the star and heats the stellar surface. The surface reradiates the energy as lower-energy photons in the X-ray or UV range. Since the observed spectra fall off rapidly at the X-ray energies below the peak in P, the re-emitted radiation from the neutron star surface cannot be too large. Laros et al. [47] made a careful study of the X-ray emission from four bursts and found that the emission in the 3-10 keV band was - 2 % of the emission above 30 keV. Requiring that the thermal emission from the stellar surface obeys this bound, restricts the luminosity and the dimension h in the schematic model to the region to the right of the band marked "L x > 0.02Lv" in fig.
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3 [31]. (If the surface becomes hotter than the "Eddington temperature" TE, radiation pressure drives a wind so that energy that would otherwise emerge as electromagnetic energy is transformed to kinetic energy of mass motion. The region in fig. 3 where this occurs is to the left of the line marked T~rf> TE.) Second, the highest-energy photons leaving the source can interact with each other to produce electron-positron pairs. The observations that the burst spectra do not cut off above a few MeV [48] indicate that few high-energy gamma rays are eliminated by photon-photon pair production. (Gammarays can regenerate by the reverse process but the energy of these gamma rays is on the average lower
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because positrons tend to annihilate with the more abundant lower-energy electrons.) The condition that the high-energy spectrum above - 2 MeV does not suffer appreciable degradation due to photonphoton interactions, restricts acceptable models to the region to the right of the band labeled ~ + ~ / ~ e + + e - [49]. Figure 3 illustrates that the characteristic dimension of a gamma-ray producing region must be larger than or comparable to the stellar radius. Even though this constraint was derived for the geometry of fig. 2, in which the source region is on one side of the neutron star, other geometries, such as a source region that surrounds the neutron star should give similar results. If the emission is collimated rather than isotropic, the emission region could be, in principle, much smaller since high-energy photons would not necessarily intersect at large enough angles to produce pairs and the gamma radiation could be beamed away from the surface of the neutron star. Nevertheless, if the emission were from a small region near the neutron star surface, the beaming and collimation would have to be very precise to satisfy the constraints indicated in fig. 3. On the other hand, if the source region is located far from the stellar surface, it is difficult to understand how the putative cyclotron or annihilation features could arise. As an approach to modeling gamma-ray bursters, one can try to draw analogies with other high-energy sources while bearing in mind the specific constraints implied by the gamma-ray burst spectra. The lower part of fig. 1 shows sketches of the spectra for a number of different types of sources: XB1724-30, an X-ray burster; Vela X-I, an accretion-powered pulsar; the low state of Cyg X-l, which is probably an accreting black hole; and the rotation-powered pulsar in the Crab Nebula. All of these high-energy sources have higher ratios of X-ray to ~/-ray emission than the typical gamma-ray burst. This is not necessarily a problem for making an analogy with gamma-ray bursters. For example, Zdziarski and Lamb [50] have studied a gamma-ray burster model that has common features with the accretion-powered sources. They invoke a large cloud of plasma containing hot electrons which engulfs a neutron star and has an outer dimension which is at least several stellar radii (this model is consistent with the constraints of fig. 3). The predicted spectra are in agreement with the typical gamma-ray burst spectrum below 500 keV, but the origin and energization of the electron cloud has not yet been elucidated. Rotation-powered pulsars are attractive prototypes of very nonthermal gamma-ray sources. Their gamma rays are thought to originate from "outer gap" regions which are at ~ 1 0 3 stellar radii [51], in agreement with the constraints of fig. 3. The gamma-ray emission from these objects is not necessarily intimately related to the X-ray emission, so it may be possible to devise a gamma-ray burster model that is similar to a rotation-powered pulsar with the X-ray emitting regions "turned off". The analogy between rotation-powered pulsars and gamma-ray bursts will be examined in more detail in what follows.
4. Glitching neutron stars
In a rotation-powered pulsar the braking of the rotation of the neutron star by the magnetic field frozen into the stellar surface powers the observable electromagnetic radiation. This process produces a fairly continuous stream of radiation, which appears pulsed because the star is rotating. The striking difference between pulsars and gamma-ray bursters is that gamma-ray bursters appear to lie dormant for years, radiate intensely for a few seconds, and then return to dormancy. The key to developing a pulsar-like model for gamma-ray bursters is understanding how the energy source is turned on for such
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brief intervals. Observations of the period changes of pulsars provide a clue: the periods occasionally undergo glitches, which are sudden decreases that must be due to violent readjustments in the internal structure of the neutron star. One approach to modeling gamma-ray bursters is to hypothesize that the energy released in a glitch is somehow transferred to gamma radiation [52-56]. Most of these models posit that glitches excite oscillations which jiggle the stellar surface. The motion of the magnetic field that is frozen in the surface then produces low-frequency electromagnetic radiation which damps the oscillations and accelerates high-energy particles which in turn produce gamma rays. To assess the possibility that glitches produce gamma-ray bursts, one must first examine mechanisms for known glitches in radio emitting pulsars. The glitch, a sudden decrease in the pulse period, is universally interpreted as an abrupt increase in the rotational velocity of the crust of the neutron star. The stellar crust contains nuclei in a Coulomb lattice. The "inner crust", the denser part of the curst extending from densities of - 4 x 1011 to - 2 x 1014 g cm -3, contains a free neutron gas that coexists with the nuclei [57]. Several hypotheses have been put forward to explain glitching. An initially popular interpretation was that star quakes produce glitches [58]. As the rotation rate of a neutron star slows due to magnetic braking, its equatorial bulge would decrease if the crust were not solid. Instead, stresses build in the solid crust until it cracks. The cracking or star quake decreases the crustal moment of intertia and, by conservation of angular momentum, spins up the crust. This was an attractive theory when the only known repeating glitches were from the Crab pulsar with small relative changes in the angular velocity, A/2/O = 10 -8 [59]. The subsequent discoveries of ~>100 times larger glitches from the Vela pulsar recurring on time scales of years [60] dealt a death blow to this model; the required strains could not be built up in a neutron star crust between glitches. Even though neutron star quakes should occur, they cannot explain the most outstanding glitches. Recent efforts to understand glitches have focused on mechanisms for transferring angular momentum from the free neutron gas in the inner crust of the neutron star to the solid crust [61-63]. An analogous process perturbs the earth's rotation period; angular momentum is exchanged between the solid earth and the atmosphere. Relative shifts in the earth's rotation rate of the order of AO/I2 = 10 -7.5 are compensated by changes in the atmospheric jet stream velocity [64]. In a neutron star the only component which may be sufficiently decoupled from the rest of the star to be able to play the role of the "neutron star jet stream" is the free neutron gas in the inner crust. Throughout much of the inner crust the free neutrons pair to create a superfluid which moves through the nuclear lattice with very little dissipation. The superfluid can impart momentum to the crust if it has an angular velocity Osr which is larger than that of the crust Ocr. This differential motion is possible because the rotating superfluid contains vortices which interact with the crustal nuclei. Even though superfluid flow is irrotational, i.e., the curl of its velocity is zero, its circulation, the line integral of the velocity around a closed loop, need not be zero. The circulation can equal NK, where N is an integer and K = h / m is the quantum of circulation (h is Planck's constant and m is the mass of a Cooper pair, which is twice the neutron mass). For each quantum of circulation there is a small region, a vortex core, in which the superfiuidity vanishes. At small distances r from each core the azimuthal velocity of the superfluid around the core varies as K/(2~rr). Since a vortex core contains a normal neutron gas rather than a superfluid, pairing energy is expended in forming a core. On the other hand, the kinetic energy density of the superfluid flow increases as 1/r 2 near the vortex core. Minimization of the total kinetic plus condensation energy determines the size of the vortex core; it is of the order of 10 fm in the neutron star crust. The energy of the vortex core can be further decreased if the vortex core is positioned to take advantage of the inhomogeneities created by the nuclei. Depending on the superfluid and nuclear parameters in the
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different layers of the star, the energy of a core is lowered by either threading through the nuclei or by avoiding the nuclei. By finding a minimum energy path through or between the nuclei, a vortex line pins itself to the nuclear lattice [78]. In the regions of the star where vortex lines are pinned, the motion of the superfluid can be decoupled from that of the crust. This may sound paradoxical, but pinning the vortex lines to the crust is far different from coupling the superfluid flow to the crust. In fact, the distribution of the quantized vortex lines determines the rotation rate of the superfluid throughout the star. When the neutron star crust rotation slows due to magnetic braking, the superfluid rotation in the inner crust is largely unchanged because the pinned vortex lines cannot be easily moved. The velocity difference between the crustal nuclei and the neutron superfluid thus grows. Current models of neutron star glitches exploit the excess angular momentum and free energy of the rotating superfluid. How does the superfluid lose angular momentum during a glitch? One possibility is that the angular velocity of the superfluid decreases due to the displacement of some vortex lines away from the rotation axis. A proposed mechanism of this type invokes catastrophic unpinning of vortex lines when the differential velocity between the crust and the superfluid approaches a critical value [61, 62]. An alternative explanation is that the stresses on the crust from the pinned vortex lines crack the crust, thereby displacing the lines without unpinning them [63]. Another possibility is that the distribution of vortex lines and the superfluid velocity do not change during a glitch, but rather the mass of the superfluid decreases. An analogous phenomenon would occur in the laboratory if rapidly rotating superfluid He II in a slowly rotating bucket is heated to the critical h-temperature. As the ratio of superfluid to normal helium decreases, angular momentum would be transferred from the superfluid to the normal matter, and the bucket would rotate more quickly. A neutron star glitch similarly can be "thermally driven" if a sudden energy input - perhaps from a crust . . .neutron . superflmd . .to above ~ts crlucal temperature, - 1 0 9-1o K. The q u a k e - heats rapidly rotating normal (nonsuperfluid) neutron gas quickly grinds to a halt relative to the crustal material and the excess angular momentum is imparted to the crust. In such a thermally driven glitch the energy for destroying the superfluidity is supplied by a separate mechanism such as a crust quake; the rapidly rotating superfluid in the inner crust is merely a passive reservoir of angular momentum. A perhaps more attractive model is a "velocity-dissipation" glitch mechanism. In this model the relative velocity between the superfluid and the crust provides both the angular momentum and the energy for a glitch. When the relative velocity difference between a superfluid and the crustal nuclei exceeds a critical velocity, the flow of the neutron gas around and through the nuclei becomes dissipative. The dissipation can be due to the emission of excitations somewhat analogous to rotons or to the generation of superfluid turbulence [65]. The critical velocity for roton emission can be estimated by scaling from the conditions in He II to be - - 1 0 9 c m s -~ [66], and the critical velocity for the onset of superfluid turbulence could be many orders of magnitude smaller [65]. Several of the above glitch mechanisms (the vortex-unpinning model, the crust-cracking model, and the velocity-dissipation model) are induced when the differential velocity between the superfluid and the crust attains a critical value, but only the one with the lowest threshold velocity can actually occur. Hybrid models are also possible. For example, crust cracking (due to changing stellar figure or to vortex-pinning stresses) could nucleate the onset of superfluid turbulence. If this were so, then seismically quiet stars might have fairly evenly spaced glitches whereas crust-quake prone stars might have numerous quakes that trigger many glitches. The glitches observed in radio pulsars speed up the crust on time scales shorter than one day. If glitches power gamma-ray bursts, the glitches must be excited on time scales considerably shorter than a
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day, typical gamma-ray burst time scales are a fraction of a second. This time scale is a significant constraint on glitch models for gamma-ray bursts. In the vortex line unpinning model the glitch time scale is set by the rate at which vortex lines unpin and impart angular momentum to the crust. Angular momentum may be transferred by electron scattering from vortex cores. If the electrons are scattered only by the neutron magnetic moments [67], the glitch time scale is ~years, which is not adequate to explain the radio pulsar data and is totally unacceptable for gamma-ray bursters [79]. Inclusion of other dissipation processes may significantly shorten this time scale. For example, since the vortex lines tend to attract or repel nuclei (depending on the neutron gas density), they are charged so that Coulomb scattering of electrons is significant [79]. The other glitch mechanisms discussed above (crust-cracking and velocity-dissipation glitches) function on the characteristic dynamic time scale of neutron stars, which is of the order of milliseconds. Even if a glitch does occur rapidly enough, could much of its energy be converted into electromagnetic energy in a fraction of a second? Such rapid energy conversion is plausible, but not certain. If a glitch is generated by the sudden braking of a rotating superfluid, it will predominately excite toroidal modes that have no radial displacement. The toroidal oscillations do not emit gravitational radiation as copiously as the spheroidal ones do. The toroidal oscillations can, nevertheless, excite electromagnetic radiation by "shaking" magnetic field lines frozen in the surface of the star. The power radiated by this process is proportional to the square of the surface amplitude of the oscillation and at least the fourth power of the oscillation frequency [56, 68]. Previous estimates for the damping rate of torsional oscillations by emission of electromagnetic radiation gave time scales of several days to several years for typical neutron star parameters [68, 69]. Amazingly, there are additional effects, not previously considered, that may reduce the time scale to fractions of a second. First, the earlier estimates neglected the effects of the neutron superfluid on the oscillation modes. Since the neutron superfluid couples only weakly to the solid crust, the oscillation frequencies are higher and, for a given energy, the amplitudes are larger [70]. Second, resonant, mode-mode coupling may efficiently funnel from the lower-frequency modes to the higher-frequency ones, which then are quickly damped by electromagnetic radiation [71].
5. The gamma-ray burster as an adolescent neutron star
This report has so far focused on the physical issues of gamma-ray bursters; let us now consider them in an astronomical context, In a glitch model, gamma-ray bursters are relatively young, single neutron stars, many or most of which are born in supernova explosions. Soon after the explosion they have large translational velocities (~100 km s -1) and strong surface magnetic fields (-1012 G) and produce pulsed radio emission [72]. While the neutron stars are radiating as pulsars, they experience glitches, but apparently do not produce gamma-ray bursts. Searches for gamma-ray bursts coincident with several glitches from the Vela pulsar failed to discover any events above - 3 × 10 -6 erg cm -2 s -1 [73]. This lack of correlation between observed glitches and gamma-ray bursts can be rationalized by postulating that the physical conditions required for the production of pulsed radio emission are incompatible with the generation of gamma-ray bursts. This is plausible because a neutron star that is an active pulsar produces an electron-positron pair plasma that generates radio emission [74]. A sudden impulse of energy during a glitch may simply increase the number of pairs but not generate highly relativistic particles that could radiate gamma rays. In some models of pulsars the pair plasma responsible for the radio emission is generated by gamma rays interacting with a strong magnetic field near the surface of a
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neutron star [74-76]. Pulsed radio emission terminates ~107 years after the neutron star is formed [77], possibly due to decay of the strength of the surface magnetic field of the neutron star. Magnetic field evolution might explain the absence of gamma-ray bursts when pulsars glitch and the difference between the soft repeating bursters and the classical bursters. In active pulsars the magnetic field may be so strong that photons with energies even slightly above the pair rest mass are converted to an electron-positron plasma, which absorbs the lower-energy gamma radiation. Gamma-ray bursters could correspond to extinguished pulsars with weaker magnetic fields; in fields below ~1011 G radiation above - 3 MeV could escape freely. Furthermore, recently deceased pulsars are good candidates for the repeating gamma-ray bursters. They would be the youngest gamma-ray bursters and hence the most active with the fastest repetition rates. Because of their youth (--10 7 yr) they would be found near the galactic plane. Laros et al. noted [22] that the repeaters are located within 30° of the galactic plane, whereas the overall distribution of gamma-ray bursts is isotropic on the sky. This is suggestive, even if statistics based on three objects is not overwhelming. The detectable bursts from the young bursters should be soft, since if even a small fraction of their energy were above an MeV, the radiation would interact with the magnetic field and produce an opaque pair plasma. The classical bursters are presumably older neutron stars (~>108yr) with weaker surface fields (~<101°G). They glitch only occasionally, but perhaps very violently. The older neutron stars travel - 5 kpc into the halo, and if the intrinsic luminosities of their bursts are less than ~10 37 erg s-1, the events they produce would appear fairly isotropic for fluxes greater than several times 10 -7 erg s -1
6. Outlook
In the next few years data from several new gamma-ray burst instruments on the Gamma-Ray Observatory satellite (scheduled for 1990), the Japanese satellite Ginga (formerly ASTRO-C, it has been in orbit since February 1987) and P86-2 (an Air Force satellite scheduled for the early 1990s) should resolve some of the important questions about gamma-ray bursters. If all goes well, the reality of the cyclotron lines and the pair annihilation lines will be decided, and the anisotropy of the burst arrival directions will be measured. The Gamma-Ray Burst Detector on Ginga, which is sensitive down to - 2 keV, may be able to discover soft, repeating bursts and determine whether the repeating bursters are confined to regions near the galactic disk. The low-energy capabilities may also enable Ginga to detect thermal emission from the surface of a neutron star and thus prove the neutron star origin of the bursts. Finding accurate positions for several repeating bursters would improve the prospects for discovering optical or soft X-ray emission that is radiated simultaneously with a gamma-ray burst and during quiescence between bursts. These data could well resolve whether bursters are single stars or in binary systems and whether they accrete matter steadily between bursts. The glitch interpretation of gamma-ray bursters would be strengthened if it is found that (1) gamma-ray bursters are single, nonaccreting, neutron stars, that (2) the classical sources are contained in a thick spheroidal volume and that (3) repeaters lie near the disk. Since gamma-ray bursters would be an older population of neutron stars than those that are observed as radio emitting pulsars, their spatial distribution and X-ray and ~/-ray spectra would provide a measure of the birth rate of neutron stars and the evolution of the surface magnetic field strengths over time scales of 108 years or more. An improved understanding of the instability that produces glitches and its temperature dependence might give a measure of the thickness of the crust of a neutron star, its interior temperature and its dependence on stellar age. The temperature evolution provides a handle on the properties of matter at
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supernuclear densities because the cooling rates and the equation of state of dense matter are intimately interconnected. For example, the existence of pion or kaon condensates at several times nuclear density would dramatically increase the neutron star cooling rate and would also soften the equation of state. It is a measure of the unity of various areas of astrophysics that one of the much discussed questions in supernova theory, the equation of state at supernuclear densities, may be an important ingredient in the theory of gamma-ray bursters.
Acknowledgment This work was carried out under the auspices of the US Department of Energy. The author thanks Gordon Baym, France Cordova, Diane Roussel-Dupre, Bill Feldman, Ed Fenimore, Ray Klebesadel, John Laros, Bill Priedhorsky, and Wojciech Zurek for discussing the material in this report.
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