Cosmic gamma-ray bursts

PHYSICS REPORTS (Review Section of Physics Letters) 81, No. 4 (1982) 293—349. North-Holland Publishing Company

COSMIC GAMMA-RAY BURSTS Frances VERTER* Princeton University Observatory, Peyton Hall, Princeton, NJ. 08544, U.S.A. Received June 1981

Contents: Introduction 1. History and instrumentation 2. Properties of gamma-ray bursts 2.1. Temporal properties 2.2. Spectral properties 2.3. Searches for coinciding bursts at other frequencies 3. Spatial distribution of burst sources 3.1. Observations 3.2. Theory 4. The unusual gamma-ray burst of March 5, 1979

295 296 300 300 306 310 315 315 319 320

5. Theories of gamma-ray bursts 5.1. Constraints 5.2. Extragalactic models 5.3. Accretion onto compact objects 5.4. Thermonuclear explosions 5.5. Flare models 5.6. Exotic models 5.7. The gamma-ray burst model voted most likely to succeed References

330 331 333 334 342 343 344 346 347

Abstract: All aspects of cosmic gamma-ray bursts are reviewed. First, instrumentation and experimental technique are briefly covered. Then the observable burst properties are described, and empmcal classification schemes are offered. Searches for coinciding bursts at other frequencies are enumerated. The observed spatial distribution of the burst sources is given, as well as varioustheoretical interpretations. A section is devoted to the unusual gamma-ray burst of March 5, 1979; its features are compared to more typical events and analyzed for insights into burst origins. Theoretical models for gamma-ray bursts are considered in general, and then examined in more detail under the categories of extragalactic models, accretion onto compact objects, thermonuclear explosions, flare models, and exotic models.

S

author is supported in part by a National Science Foundation Fellowship.

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COSMIC GAMMA-RAY BURSTS

Frances VERTER Princeton University Observatory, Peyton Hall, Princeton, N.J. 08544, US.A.

I

NORTH-HOLLAND PUBLISHING COMPANY-AMSTERDAM

F. Verter, Cosmic gamma-ray bursts

295

Introduction This review grew out of a talk which I prepared for a seminar class at Princeton University in the Fall of 1979. I had become interested in gamma-ray bursts during the previous Spring, when I read an article by Strong and Kiebesadel which appeared in a 1976 issue of Scientific American [891.In the past five years, our knowledge of gamma-ray bursts has advanced dramatically, almost entirely through the use of improved instrumentation which has been specifically designed for their study. Although many important questions concerning this phenomenon still remain unanswered, I think that the burgeoning growth of this field has created an urgent need for a comprehensive review that summarizes the present state of gamma-ray burst research. In this article I have attempted to fulfill this need by gathering in one place a fairly up-to-date presentation of both the experimental and observational results on gamma-ray bursts. The first section of this paper begins with the story of how gamma-ray bursts were discovered in 1967, and goes on to briefly describe the equipment and techniques that are used to detect these unpredictable events. The second section summarizes the burst observations. The various behaviors exhibited by these transients can be roughly categorized as either temporal or spectral properties. Section 2.1 is devoted to the former category, including the various structures and timescales seen in gamma-ray bursts, a tentative classification of the bursts’ temporal profiles, the distribution of observed bursts among these classes, the frequency of burst events, and the possibility of recurring bursts. Spectral properties are described in section 2.2, where the surprising uniformity of burst spectra is outlined, although recent observations which suggest that spectral variations occur during the course of a burst event are also presented. This is followed by a discussion of the four gamma-ray transients in which line emission has been observed, and several models are given which may explain the generation of these emission lines. Although the general topic of gamma-ray burst models is taken up in section 5, these line-generating mechanisms could occur in any of a number of different burst scenarios; hence I have chosen to describe them separately, grouped with the observations in this section. Finally, this section closes with a subsection depicting the observational strategies employed to determine if gamma-ray bursts are accompanied by transient events at other frequencies. Section 3 describes the distribution on the sky of the positions that correspond to the arrival directions of gamma-ray bursts. To some extent, this distribution may be used to draw inferences about the nature of the unknown source objects. A number of approaches to the problem are outlined, and some recent results are reported. In section 3.2 a limiting source luminosity is derived on the basis of a reaction in which colliding gamma-rays are converted into electron—positron pairs; caveats which may exempt some burst models from this constraint are also given. The next section may be regarded as a review in itself, as it covers all aspects of a very unusual gamma-ray burst which occurred on March 5, 1979. A description of this event, indicating which characteristics are unusual and why they merit great interest, opens the section. It is followed by a synopsis of the current controversy over the location of the object responsible for this burst. Opponents believe either that the source is a supernova remnant in the Large Magellanic Cloud or a foreground object within our own galaxy. It is also argued that the source of this event is probably a neutron star. Observational limits on the X-ray and optical luminosity of the source are given, and a possible model for this event is sketched. The last section of this paper is the most lengthy, as gamma-ray burst theories are a very diverse topic. By way of introduction, section 5.1 goes over the various constraints which proposed burst models

296

F. Verter, Cosmic gamma-ray bursts

must satisfy. The remainder of section 5 is divided into a series of subsections allocated to different types of models. First, extragalactic models are treated as a class in section 5.2. Then the general scenario of a compact object undergoing accretion is evaluated, and specific examples are considered. These are: Compton scattering in the ergosphere of a black hole [71],accretion of the material ejected by a flare on a binary companion [53],tidal disruption and accretion of a passing comet [37]or asteroid [64], and the sudden infall of material suspended in a “reservoir” above a magnetic polar cap [89], possibly accompanied by amplified electron—positron pair creation [94]. Section 5.4 examines the possibility that a thermonuclear flash on the surface of a neutron star could produce a gamma-ray burst, and section 5.5 evaluates stellar super-flare models. Two exotic ideas are described in section 5.6; they are the explosive evaporation of Zwicky’s nuclear goblins [106]and of primordial black holes [68].After wading through such a potpourri of theoretical astrophysics, the reader will be either delighted or disgusted to find that I have finished this paper with a rather whimsical assessment of the models in section 5.7.

1. History and instrumentation The story of cosmic gamma-ray bursts began with one of those serendipitous discoveries [47] that often results from the development of a new instrument or technique. The field of gamma-ray astronomy has developed only since the means have become available to place instrumentation above the Earth’s atmosphere. Yet it came as a surprise when gamma-ray detectors carried by spacecraft registered brief bursts of gamma radiation of cosmic origin. Because they were not anticipated, for seven years the sole source of burst data continued to be the records from detectors designed for other purposes. As a result, the history of our study of gamma-ray bursts is a history of improvements in the design of signal detection and data storage systems that are flown in spacecraft and balloons [22]. The first instruments to detect cosmic gamma-ray bursts were launched in an array of Earth-orbiting satellites known as the Vela system. The Vela satellites had been designed to monitor the Nuclear Test-Ban Treaty of 1963, which forbade its signatories from exploding nuclear devices in the atmosphere or in outer space. The Los Alamos Scientific Laboratory was assigned to build a satellite capable of detecting the types of radiation and particle fluxes released in a nuclear explosion, including the Xand gamma-rays which would be emitted by either a fission or a fusion device. An identical pair of these satellites was launched to the opposite sides of a circular Earth orbit with a radius of 2.5 x iO~km [89], high enough so that no part of space is shielded by the Earth from observation. A total of six satellite pairs were eventually launched, the later payloads incorporating successively improved instrumentation for detection and signal processing. At the urging of Stirling Colgate, the data records of the early Vela satellites were searched for increasing gamma-ray fluxes near the times at which supernovae appeared. Colgate [23]was the first to propose an astronomical explanation for the bursts, in which the gamma-rays were emitted during the initial stages of a developing supernova.* However, these data searches were unsuccessful. Later, an alteration in the time-base on which Vela data was stored encouraged a more general search. Beginning with Vela 4, the data were processed into a form in which the trigger times of recorded events were * At about this time, Field, Rees and Sciama [301 independently suggested that the processes associated with weber’s gravitational waves could be releasing intense short pulses of gamma-rays that might appear in the records of orbiting gamma-ray detectors. Strong and Klebesadel have never referred to this idea in their accounts of the discovery of gamma-ray bursts, so it appears that they were unaware of it at the time.

F. Verter, Cosmic gamma -ray bursts

297

routinely referred to a common standard, thereby facilitating a comparison of the records of individual spacecraft for responses in near coincidence. The objective of this project was to demonstrate that there was no natural background capable of producing such a stimulus. Instead, three such events were found, a number greater than would have occurred as a result of random probability. Only one of these original events was intense enough to produce distinctive records in the satellites, yet these separate records agreed very well. Thus, cosmic gamma-ray bursts were “discovered” in 1969, but it was not until 1973 that the first published account appeared [471, reporting on 16 bursts detected between July 1969 and July 1972. The slowness with which burst-like events were dredged out of the Vela data records has been attributed to the high performance and longevity of these satellites. As a result, considerably more data were generated than had been expected, and routine data processing fell far behind. For instance, the gamma-ray bursts which were detected in 1969 had occurred in the 1967 Vela 4 records, and by the time the Vela 4 data analysis had been completed, Vela 5 had already been launched bearing similar, but improved, instrumentation. Further delays prevented the resolution of additional gamma-ray bursts prior to the launch of Vela 6. Although the Vela detectors are simplistic in comparison with the instruments incorporated in later spacecraft specifically designed to study the characteristics of gamma-ray bursts, their combination of omnidirectional response with logic and data storage that give nearly continuous time coverage were then unique in observational astronomy. The basic detecting element carried by the Velas is a cesium iodide (CsI) crystal that emits visible light under gamma-ray stimulation. Six such detectors are distributed just beneath the solar arrays on each Vela spacecraft, so as to provide nearly uniform omnidirectional response. Each of the detectors incorporates two level discriminators which define an energy interval. Discrete counts within this range are summed and entered in parallel into a data accumulator and a trigger circuit. This trigger responds to a statistically significant and rapid increase in the summed counting rate by initiating data storage in a sequence of quasi-logarithmically expanding time periods. This design feature was based upon the expectation that the radiation intensity would decrease more or less exponentially with time, and has the annoying consequence that resolution is progressively lost over the course of the event record. Another shortcoming of the Vela network is the lack of recoverable data prior to the trigger. The first instrument to operate in space that was specifically designed to study cosmic gamma-ray bursts was carried by Helios-2. In January of 1976, this satellite was launched into a solar orbit with a perihelion of 0.29 AU and an aphelion of 1 AU that carries it to distances of up to 2 AU from the Earth. The Helios-2 detector was also the first to be placed in interplanetary space for the purpose of obtaining high-resolution burst source locations by using its long baseline for time-of-flight source triangulation. The network of space probes that existed at the time that gamma-ray bursts were discovered possessed only limited capabilities for source location by triangulation. Although the very long baselines between these vehicles are capable of great directional accuracy, most of the earlier designs employed onboard power sources that generated intense background fluxes of gamma-rays. The payload for the solar orbiter Helios-2 provided the first available benign platform. Fortunately, this craft was still under construction in 1973, so it was modified to contain a small piggyback instrument adequate for the detection of gamma-ray bursts of the known intensity, energy spectrum, and frequency of occurrence. The Helios-2 sensor is a CsI crystal with a command-adjustable photon energy threshold set at ~100 keV. In order to accommodate the wide range of rise times encountered in gamma-ray bursts, three command-adjustable trigger modes are provided which can be set in flight at levels that are as .

298

F. Verter, Cosmic gamma-ray bursts

sensitive as is commensurate with tolerable background rates. Following the occurrence of any trigger, both the immediately preceding and the post-trigger time histories are stored in 6 memories on 3 nested time scales, so as to preserve precursor information and to obtain the fastest time structure nearest the trigger time. The temporal scale can be as fine as 4 ms, as compared to 16 ms for the Vela systems. The spacecraft clock time at which the trigger occurred is the crucial element of a burst observation, since the comparison of the times at which the burst arrived at the various spacecraft involved ultimately gives the source direction by wavefront triangulation. These time delays can be checked and verified by artificial trigger commands. But the accuracy of this test is limited by the encoding and decoding delays, which are only known to ~100 ms. This inaccuracy can be completely removed by using an effect referred to as the “roll modulation”. The burst sensor mounting position on the spacecraft endows it with a restricted solid angle of view that is swept past the source as the vehicle spins on its axis. This produces an intensity profile modulation that is maximized for sources near the spin plane of the vehicle. For Helios-2, the spin equator lies in the orbit plane and coincides with the ecliptic. The roll modulation can be used to check the timing of burst profiles to within 60 ms (modulo the 0.99 s spin period). An unavoidable timing error in wavefront arrival comparisons is the inaccuracy that results from corrections that have to be made for different moments of triggering within the burst temporal history by various detectors. We shall see in the section on the spatial distribution of the burst sources that the graph of N(S) vs S is an important tool for distinguishing between various spatial configurations of the sources, such as an isotropic source population or one in the galactic disk, for example. In this graph N represents the number of sources detected down to a limiting total observed energy flux S. The curves predicted by various models diverge for small values of S, making detection of the presumably more numerous bursts of low intensity a prime focus in the design of instrument packages for the detection of gamma-ray bursts. Satellite observations report mainly on bursts of iO~to iO~erg cm2, because of the small sizes and sensitivities of their detectors. But photons of the energies typically observed in gamma-ray bursts can be detected in the Earth’s atmosphere at balloon altitudes. Balloon measurements made with large detecting areas are able to observe net burst fluxes as low as iO~erg cm2. Some balloon flights have used a large area NaI(Tl) detector array whose response and operating characteristics are similar to the crystal scintillation detectors on spacecraft. Other investigators have flown a double Compton scatter gamma-ray telescope belonging to the University of California at Riverside [101]. Due to the differences between the working environments of satellites and balloons, balloon measurements must operate under a different set of constraints. One problem is the phosphorescence produced by cosmic-ray primaries or showers entering the Earth’s atmosphere. This contributes to the background count in low-energy channels, and is eliminated by coincidence circuits between the balloon’s detectors. Another source of unwanted responses is ionospheric or magnetospheric [21] activity involving fluxes of trapped radiation. On the other hand, balloon platforms have the advantage that they are free from trigger criteria; all the data can be telemetered to the ground in real time and searched later with a variety of selection procedures. While balloon flights are limited to timespans on the order of days, the large-area, sensitive detectors that they carry can register weak bursts with might be expected to occur several times a day. To date, no intense gamma-ray bursts have been detected by balloon instruments*, although the measurements have set upper limits on the flux at low intensities that are used to distinguish between source distributions. -~

* Note added in proof: A recent preprint by K. Beurle, A. Bewick, iS. Mills and J.J. Quenby of the Blackett Laboratory at Imperial College, London, reports the detection of a confirmed gamma-ray burst having an energy flux of 3 x 10—6 erg cm2 with a balloon detector.

F. Verter, Cosmic gamma-ray bursts

299

An assessment of the spatial distribution of gamma-ray burst sources can also be aided by an improvement in the accuracy with which burst arrival times at the various detectors are measured. The relative accuracy of the time delay between trigger moments can be improved simply by increasing the baseline between the detectors used to triangulate the source direction. This is currently being done by using sensors onboard interplanetary probes in conjunction with the original Earth-orbiter arrays. The instruments comprising the present interplanetary gamma-ray burst network are summarized in table 1. It is adequate to describe all of the interplanetary network detectors as scintillation or solid state photon counters that are approximately omnidirectional in response, except for spacecraft shadowing. The energy response of these instruments is maximum in the ~100 keV region, but there is some response throughout the range from —30 to —-5000 keV. Each employs accurate timing, in the 1—4 ms range, and each uses an onboard memory capable of describing the entire temporal profile of a gamma-ray burst before and after trigger time with 0.2—16 ms differential timing accuracy. The sizes and consequent sensitivities of all the detectors in the network are roughly similar, although the three Soviet—French units are somewhat larger and have energy responses extending to somewhat lower and higher photon energies. The general uniformity of detectors throughout the network is worth emphasizing, because the observational study of cosmic gamma-ray bursts is often confused by isolated reports of burst-like events and by intercomparisons of results from widely different instruments and search techniques. This network is achieving its purpose of providing the most accurate source field determinations in gamma-ray astronomy, giving —1-arc-minute resolution.

Table 1 Launch date

Vehicle name(s)

1969

4 Vela satellites

1976 1978 1978

Los Alamos Scientific Laboratory Helios-2 Goddard Space Flight Center Pioneer-Venus Los Almos Scientific Orbiter Laboratory International Sun—Earth Goddard Space Flight Explorer-3 = Center ISEE-3 (2 experiments) Los Alamos Scientific Laboratory (1 experiment)

1978

Venera-li

1978

Venera-12

1978

Earth-Orbiter Prognoz-7 Solar Maximum Mission

1980

Experiment designer

Collaborative team: Soviet Academy of Sciences Space Research Institute of Moscow Centre d’Etude Spatiale des Rayonnements of Toulouse University of New Hampshire, Max Planck Institute, Naval Research Laboratory

Current vehicle position Earth orbit (since launch) Solar orbit (since launch) Orbiting Venus since Dec. 1978 Actively maintained in an artificial orbit around the gravitational null point between the Earth and the Sun since Oct. 1978 Solar orbits following Venus gravitational deflections in Dec. 1978

Earth orbit (since launch)

A more comprehensive description of these instruments, with references to detailed articles, can be found in references [20]and [22].

F. Verter, Cosmic gamma-ray bursts

Within the next ten years or so, we can expect to see further improvements in our ability to localize source positions and measure burst spectra. Already the interplanetary network has been augmented by the recent launch of the Solar Maximum Missidn, a satellite which will provide another near-Earth vertex for triangulation. In addition, this spacecraft will perform a high temporal resolution spectroscopic study of any bursts that occur close to the position of the Sun. There are also plans to place gamma-ray sensors onboard the International Solar Polar Mission. In this experiment, two spacecraft will be placed several AU apart, with one above and the other below the ecliptic plane. The spatial resolution expected from this interplanetary network will be up to a factor of ten more accurate than the best resolution that the present network can provide. Lastly, the Gamma Ray Observatory is expected to be launched sometime during this decade. This observatory will house both a large area detector for full-sky viewing, as well as a collimated telescope. Any gamma-ray bursts that happen to lie in the telescope’s comparatively wide field of view can be recorded with a sensitive high-resolution spectrometer that is of “second-generation experiment status” [22].All told, these various experiments promise that, within the immediate future, the data collected on gamma-ray transients will meet or surpass the current standards of quality. Beyond that lies the possibility that the information amassed by these detectors will justify more sophisticated experiments designed to answer specific questions. 2. Properties of gamma-ray bursts 2.1. Temporal properties The time profiles of gamma-ray bursts are very variable; they range from single, very intense spikes to complex structures that begin with one or more precursor pulses. The main burst of a complex transient will consist of a number of sub-bursts which themselves contain pronounced substructure and last about a minute each, often followed by a resurgence of weaker but similar activity occurring a few seconds to a minute later. Table 2 is an attempt to summarize some of the properties of gamma-ray bursts, but it quickly becomes evident that most of them commonly occur over a range of one or more orders of magnitude. Figs. 1—6 show a few burst profiles displaying a variety of possible appearances. Burst variability extends down to structures on timescales of a millisecond. The April 27, 1972 event displayed in fig. 1 is a case in point. It was detected by a gamma-ray spectrometer onboard the manned service module of the Apollo 16 spacecraft, just prior to its re-entry into the Earth’s atmosphere on its return from the Moon. The detector was a large, sensitive instrument flown for the purpose of determining the composition of lunar surface material. The resulting temporal profile is one of the most complex known, probably due at least partially to the high quality of the data rather than to the character of the burst. Associated with periods of relatively intense activity during the event are fluctuations on timescales down to 10—15 ms. Most spectacular of all is a sharp drop in the flux for 25—30 ms during the highest peak, for more than 15 continuous ms of which no count was recorded. The signal abruptly switched off and on again! Another example of a sharp spike of gamma radiation is a burst recorded by Helios-2 on Jan. 23, 1976. While counting gamma-ray photons for consecutive periods of 4 ms, the detector was averaging one photon every other counting period. Then, in one period, 23 photons were counted, with one photon in the preceding period and none at all in the succeeding period. (Perhaps this was the highest peak of a weak burst.) The character of the time structure doesn’t change during the course of an event; rapid variations in intensity persist approximately uniformly throughout the burst history.

F. Verter, Cosmic gamma-ray bursts

301

Table 2 Properties of gamma-ray bursts Parameter

“Typical” values

March 5, 1979 gamma-ray transient

rise time pulse shape duration of high intensity portion duration of total event number of pulses peak flux 2 s’) (erg cm average decay flux (erg cm2 ~‘) total flux (erg cm2) decay shape

2 ms—l s highly structured

<0.25 ms regular

0.1—10s

120 ms

descriptive photon energy spectrum

line emission

recurrence

0(1 s)—O(10 s) l—~l0

**

180

1

5x 10’—Sx iO~

(3.0±0.3)xiO~

below detector thresholds

—lx i05

1 x l0~—1x iO~ unknown

—1 x 10~ monotonic envelope with 50 s decay time modulated by periodic pulsations (p = 8.00 ±0.05 s) with interpulse features

100—200 keV Cline and Desai [16]: N(E) -- exp(—E/150 keV) 100 keVE375 keV N(E) — E2’ 375 keV < E - or Mazets and Golenetskii [60]: dN_E*dE 1.3a~2.5 usually a = 1.5—1.7 few cases (has yet, little spectral data are available) I known case

—50 keV initial pulse: typical decay: N(E) —E’ exp(—E/30 key)

initial pulse: 430 keV FWHM 30—40% decay: none March 6, 1979 April 4, 1979 April 24, 1979

In general, the shortest timescale on which the intensity of a source varies can be used to set an upper limit on the source volume. In order for the emission of the entire volume to change sharply in a time At, the effective diameter of the source cannot exceed the distance light can travel in this time interval. Hence, the narrow width of the peaks seen in typical gamma-ray bursts imply that, if they come from source regions of dimension I that are moving nonrelativistically, then is i0~cm. This is about 3/4 the diameter of the Earth. Exceptions to this rule occur when the observed variation is not due to an effect which requires that emission throughout the entire source volume be coordinated. For instance, the spikes could be produced by a beam of photons sweeping through our line of sight. Another possibility is that different spikes originate in different regions separated by larger distances. A relativistically expanding source can emit radiation that appears to vary over a time interval that is much shorter than the source dimension divided by the speed of light. Consider, for instance, a spherical source. At any instant, a photon that is emitted on the limb will have to travel farther in order

302

F. Verter, Cosmic gamma-ray bursts 1150

I

I

I

I

I 10:58:30.2

EVENT OF APRIL 27, 1972 1050

.

-

950

.

-

OJU

-

C., (~.1 (N

-

‘/,

750-

‘~

650

-

—

U

0~

‘1)

550-

0 -

-

450-~

~

l50~tf~}~ ~

-~

-9

-9

-~

-9’

-9~ -9~

~

UNIVERSAL TIME, hr:mnsec Fig. 1. Time profile of the gamma-ray burst recorded by a NaI (Tl) detector on board the Apollo 16 service module. The data were read out in frames of 327.7 ms duration, with a resolution of 2.56 ms. Error bars represent 1~’levels. This event is a type (b)burst. Taken from Metzger et al. [61].

to reach us than a photon simultaneously emitted from the piece of the surface that is closest to us, and consequently will arrive with a time delay of l/2c, where I is the diameter of the source. Now suppose that the surface of the sphere is expanding with radial velocity v; if v c, the size of the sphere can change so significantly in the time i/c that the apparent expansion will be superluminal [79].Since the observed intensity of a source, for a given surface brightness, is proportional to its apparent size, a relativistically expanding body can exhibit apparent flux changes on timescales much shorter than those on which the source is really changing. The resulting limit on 1 is I s iO~~2 cm, where ‘y = (1— v2Ic2)~”~. A further word is in order concerning the temporal properties of burst events. A number of —

F. Verter, Cosmic gamma-ray bursts

303

500L Venera 12

~.250

0

~-‘----~i—

—

—

—5

0

—

5

10 15 20 25 30 Time relative to the detection time Is)

35

40

45

50

55

Fig. 2. Type (a): a single pulse of medium duration. Time.profile of the November 24, 1978 gamma-ray burst. The time axis is expressed relative to the moment of detection. For this event, the zero point corresponds to 03h 53~ 51’.8 universal time (UT). The individual points that appear prior to this detection time are the prehistory record. The time resolution changes at 34 s after detection from 0.25 s to 1.0 s. A dashed line represents the background level. Taken from Mazets and Golenetskii [60].

investigators think that several classes of burst structure can be discerned amidst the diversity of the observed time profiles. Their schemes were proposed at the 1979 Toulouse Symposium on Cosmic Gamma-Ray Bursts, published in the Feb. 1981 issue of Astrophysics and Space Science. Here, I present a classification scheme suggested by Mazets and Golenetskii [60]in a survey of the gamma-ray burst studies carried out by the Leningrad group in the Konus experiment onboard the Venera 11 and 12 spacecraft. They suggest the existence of at least three typical burst structures, and possibly a fourth whose production mechanism may be linked with that of the unusual event that occurred on March 5, 1979 in the Constellation Dorado. It must be emphasized that the descriptions given are based upon measurements of 85 bursts observed by Konus in the period from Sept. 1978 to May 1979, 50 they are not necessarily characteristic of gamma-ray bursts as a whole. The classification scheme of Mazets and Golenetskii is as follows: (a) Single and double pulses of medium duration. A typical burst of this type is shown in fig. 2. “It is characterized by a relatively slow increase of gamma-radiation intensity (-=2—3 s) with a longer decay, —5—10s. A second pulse a few times weaker in intensity but with the same time constant is frequently found superimposed on the tail of the initial pulse (fig. 3). The total duration of such bursts may add up to 5—15 s. As a rule, the structure does not reveal any details on a finer time scale.” (b) Complex multipulse bursts. Fig. 4 provides one instance, and the April 27, 1972 event that was observed from Apollo 16 may also serve as a typical example of this class. “The number of clearly pronounced peaks in such bursts may amount to 10 or even more. The strongest peak may occur in the middle or even final stage of the burst. The total burst duration may constitute tens of seconds, depending upon the actual number of peaks. The characteristic peak rise and decay times are here, apparently, shorter than those in case (a). The peak time structure may contain fine details lasting a few ms (e.g. the bursts of April 27, 1972 and November 19, 1978). In the short periods between the peaks the radiation intensity may drop down to the background level.” (c) Double bursts. “This term may be used to denote a less representative group of gamma bursts illustrated in fig. 5. A characteristic feature of such events consists in that after the initial phase of the

304

F. Verter, Cosmic gamma-ray bursts

200

Venera 12

100

1~

-~

.~——

0

—

—

—

I

—5

0

—

—

I

5

I

10 15 20 25 30 35 Time relative to the detection time Is)

I

I

40

45

50

Fig. 3. Type (a): a double pulse of medium duration. Time profile of the January 16, 1979 gamma-ray burst. The time axis is defined as in fig. 2 Detection occurred at 08” 59” l4~8universal time. Taken from Mazets and Golenetskii [60].

110: ~

Time relative to the detection time Is) Fig. 4. Type (b): a complex multipulse burst. Time profile of the January 19, 1979 gamma-ray burst, detected at

14h

22” 30~9universal time. The

time axis is defined in the caption of fig. 2. Taken from Mazets and Golenetskii [60].

Time relative to the detection time (sI Fig. 5. Type (c): a double burst. Time profile of the October 25, 1978 gamma-ray burst, detected at 23” 53” 56~0universal time. The time axis is defined in the caption of fig. 2. Taken from Mazets and Golenetskii [601.

F. Verter, Cosmic gamma-ray bursts

305

burst, the radiation decays and reappears in 20—40 s. The second burst phase is comparable to the first one in intensity.” (d) Short bursts. Bursts such as the one displayed in fig. 6 comprise a distinct class. When recorded with 0.25 s resolution, as in this figure, the time profiles of all short bursts look practically the same, differing only in pulse amplitude. These bursts will be discussed further in connection with the unusual gamma-ray burst of March 5, 1979. Again, these classifications are largely conventional. There are many event profiles representing intermediate forms, and quite frequently the structure of weak bursts cannot be determined clearly because of poor statistics. Although the variation in most burst properties appears to be a continuous one, Mazets and Golenetskii [60] have also pointed out that the distribution of burst durations observed for the 85 gamma-ray events in their sample is discrete. Since some of the bursts have long tails, the duration TB was defined to be the time interval within which 80—90% of the measured burst energy fell. While the discontinuities present in their distribution may simply reflect a lack of data, it is of interest to note that these discontinuities roughly correspond with the transitions between categories of their classification scheme. (Recall that the classification archetypes have been defined so that they correlate with event duration; listed in order of increasing average TB they are type (d), (a), (b), (c).) Gamma-ray bursts whose total observed energy fluxes are on the order of iO~erg cm2 occur about 10 times a year. Weaker events can be 10 to 100 times more frequent (refer to fig. 9). Whether or not a given source may produce more than one gamma-ray transient is still an open question. Presuming the bursts are galactic in origin, a simple comparison of the observed burst frequency with the number of available source objects leads to the suspicion that at least some of the sources are repetitive. For example, if Schmidt [83]is correct in placing a limit (to be described in section 3.2) of 2 kpc on the distance to the sources of gamma-ray bursts whose observed total flux is 10~erg cm2, then the few such events which we see each year are produced in a volume that contains only 1/100 of the galaxy’s total mass. Assuming that the burst sources are distributed like the galactic mass, it then follows that there are several hundred bursts per year throughout the galaxy. This event rate is incompatible with the known rates of star formation and death, which are on the order of a few stars per year. The discrepancy is even larger in the case of beamed emission, or for source objects that are 400

C

~ 200 ‘5

.0 ‘5

C

8

_______________

Time relative to the detection time Cs) Fig. 6. Type (d): a short burst. Time profile of a typical short burst, described in the text. The time axis isdefined as in fig. 2. Taken from Mazets and Golenetskii [60].

306

F. Verter, Cosmic gamma-ray bursts

less abundant than typical stars. Another calculation predicting that gamma-ray bursts outnumber their source objects was obtained by Jennings and White [43], who fitted model source distributions to the observational data on N(S). As a result, they obtained a range of allowed values for the number of bursts per year in a unit volume. Combining this model parameter with the number density of source objects yields an estimate of the time required to convert the progenitor objects into gamma-ray bursts. Using their limits on the burst rate density, this lifetime is always much less than the age of the galaxy, even if the entire stellar population contributes to the source density. Hence we are led to believe that if the present epoch is a typical one, then galactic sources of gamma-ray bursts must be repetitive. There are a number of cases where the source regions determined for individual gamma-ray bursts are clustered so closely as to arouse the suspicion that they were all produced by the same object; but the source fields involved are so wide that the odds against this being a chance occurrence are not very large. The only clearly pronounced case of a recurring gamma-ray burst is the March 5, 1979 event, a most atypical example. Burst recurrence has been reliably established in one other instance where a series of three “short” (type (d)) bursts emanated from a single source during a four-day period in early 1979 [60].This is the primary justification for suspecting a link between such bursts and the March 5, 1979 event. Since recurrence is a key criterion for the identification of X-ray bursters, a link with X-ray sources is also conceivable, and this is discussed in sections 2.3 and 3.2 of this paper. It should be emphasized that any conclusions we draw today about burst recurrence must be highly tentative. With data records spanning little more than a decade, and some of them very skimpy at that, the long term behavior of burst sources is completely unknown to us. Only time can fill this gap in our knowledge. 2.2. Spectral properties The Vela detectors provide a minimal amount of spectral information. Vela 5 responds to photons with energies between 150 and 750 keV, whereas Vela 6 is sensitive to the energy range from 300 to 1500 keV. Comparing the photon counts in the two detectors amounts only to a statement of whether the radiation is soft or hard. Cline and Desai [16]used measurements made with the IMP-7 satellite to tentatively conclude that there seemed to be evidence for a single spectrum for all cosmic gamma-ray bursts. IMP-7 was launched in Oct. 1972 into an approximately circular Earth orbit where it collected data on a nearly continuous basis. Its energy resolution was coarse, and the time-averaging so slow that only all-event averages were obtained. Clime and Desai found that, for nine of the bursts detected by IMP-7, the event-average photon number spectra from 100 to 1100 keV are statistically consistent with each having the same shape. Comparisons with other observations have persuaded them that independently reported gammaray burst events are also consistent with the same event-average spectrum. This similarity suggests that the parameters of the emission process(es) producing the bursts should have narrow limits of variability. The arbitrarily constructed spectrum that was found to fit the bursts consists of a 150-keV exponential tangent to a power law of index —2.5 at an energy of about 400 keY. Their spectra are displayed in fig. 7, with the fitted curve superimposed. An extrapolation of the power law tail above a few hundred keV predicts a measurable flux in the range of more than several MeV. Mazets and Golenetskii [60] have extended their analysis of an 85-burst sample of Konus measurements to the question of spectral properties. As usual, it is found that variations in the energy spectra of individual bursts are much less pronounced than their temporal differences, and that for most of the bursts the spectra gradually become steeper with increasing energy. They do disagree with Cline and

F. Verter, Cosmic gamma-ray bursts

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Desai in that they find that the shape of the spectra cannot be represented by one simple law. Many spectra may be roughly described by a power law of index —1.3 to —2.5, the values —1.5 to —1.7 being most common. The second group has more pronounced steepening and is fitted better by an exponential of the form exp(—E/kT), where kT = 100—200 keY. Apparently, any spectral variations that may occur during the course of a burst event do so with a pattern that produces nearly the same event-average spectrum. There is further evidence that for some bursts, not only are the event-average spectra fairly uniform, but the instantaneous spectrum shows little variation over the duration of an event. The Nov. 4, 1978 gamma-ray burst is an example of a transient that showed no spectral variability, to within the statistical uncertainties [25].On the other hand, the burst that occurred on Nov. 19, 1978 exhibits clear evidence of spectral variability that appears to be correlated with the burst structure [25].In the catalogued Konus data, all the burst spectra that are seen to evolve do so by becoming softer and approaching a power law. The presence or absence of line emission in the spectrum of an object emitting gamma-rays places strong constraints on the processes by which the gamma-rays are produced and escape from the source. The pnncipal mechanisms of gamma ray hne production are [74]the decay of excited nuclei formed by

308

F. Verter, Cosmic gamma-ray bursts

radioactive decay or in inelastic collisions [76], positron annihilation, neutron capture, and cyclotron emission in a strong magnetic field. Some examples of common gamma-ray lines are: e~+e-*y+y

(0.51MeV)

n+p-*d+y p+’2C-~13N+y 16*O~16o+ y

(2.2MeV) (4.4MeV) (6.1 MeV).

The particular lines produced, and their relative intensities and widths, are determined by a number of parameters describing the composition and energy spectrum of the particles, as well as the physical conditions in the surrounding medium. Astrophysical sites from which observable gamma-ray line emission is expected [74,76] are solar flares, galactic nuclei, neutron stars [8], black holes, the interstellar medium, and the remnants of novae and supernovae. In recent years, there have been a number of reviews of gamma-ray spectroscopy in astrophysics [59,74, 55]. The majority of gamma-ray transients have no detectable line emission. However, it is only recently that we have begun to routinely take high-resolution spectra of burst events. In August of 1978 a spectrometer was launched onboard the ISEE-3 spacecraft that was specifically designed to provide high-resolution energy spectra of gamma-ray bursts. This instrument has a total resolution of 10 keY at a photon energy of 570 keV, ~5 times better than the best resolution of previous satellite-borne instruments [91].The first results from this spectrometer are just arriving. It may be another year or more before we can say with some certainty whether or not line emission is the norm for gamma-ray bursts. The most notable case of a transient which did contain line emission is the spectacular burst that occurred on March 5, 1979, an atypical event by almost any standard. During the initial spike of this burst, which lasted 0.1—0.2s, a statistically significant line feature appeared at an energy of ~420 keY [60].There are. three other known cases of gamma-ray transients with an emission line in the vicinity of 420 keV, and I have summarized their properties in table 3. If the line that appears near 420 keY in these events is interpreted as a redshifted 511 keV positron annihilation line, then the required redshift is consistent with the gravitational redshift predicted for line emission emanating from the surface of a neutron star. Lingenfelter et al. [58] have used this coincidence as the starting point for a model in which gamma-ray transients are produced when a neutron star undergoes sporadic accretion from a binary companion. This model is very effective at explaining the set of lines seen in the spectrum of the June 10, 1974 gamma-ray transient. The emission lines that appeared at ~0.41 and ~5.95 MeV in this event cannot be identified with any unshifted lines because all the contenders are coupled with stronger companion lines which were not observed. But by applying a redshift of z 0.24—0.28 to the lines at 0.41, 1.79 and 5.95 MeY, they can be interpreted as positron annihilation and neutron capture on hydrogen and 56Fe, respectively. These are the strongest lines predicted when infalling material is gravitationally accelerated and collides inelastically with the surface of a neutron star. The remaining 2.22 MeV line in the spectrum is at the emission wavelength of neutron capture on hydrogen. Presumably this emission arises in the accretion disk or in the companion’s atmosphere where there is no appreciable gravitational redshift. Table 4 summarizes these line identifications, and fig. 8 shows a schematic diagram of this model. The model also predicts other line and continuum emission, but the expected intensities are consistent with the observations of the June 10, 1974 transient. Although we don’t have as much detailed spectral data for comparison, this model is in principle also

F Verter, Cosmic gamma-ray bursts

309

Table 3 Line emission in gamma-ray transients~

Event Mar. 5, 1979 Nov. 19, 1976

Observing instruments ISEE-3, Venera 11 & 12 ISEE-3, Venera 11 & 12

May 10—11, 1976 Balloon-borne gamma-ray telescope targeted on the Crab nebula June 10, 1974

Balloon-borne gamma-ray telescope pointed in the general direction of the galactic anticenter

Line energy (keV)

FWHM (keV)

Flux of total flux

420

130—170

5x 10

420

Broad

4.0 x 10-6 erg cm2

740 400±1

3

2.4 x i05 erg cm2 (2.24±0.65)xi0~ photons cm2 s~

5ergcm2s~

413.2 ±1.8

15

(7.0 ±2.0) X io~ photons cm2 s~

1789.7 ±6.0

95

(3.15 ±0.74)x10—2 photons cm2 s~

2218.6 ±6.3 5946.5 ±3.7

70

(1.51 ±0.49) x 10-2 photons cm2 s~ (1.47±0.46)x10-2 photons cm2 s~

25

% of total burst energy

Comments

Ref.

See table 2 and section 4 of this article Line structure absent in later stages of burst

14 60 14 91

400 keV line was not seen during a scan of the Crab nebula on June 10, 1974: therefore interpreted as a transient Peak flux <1% Unusually long: 20 m of mean back- duration. Source ground flux field of view is >20~:overlaps May 10—11, 1976 source field; includes source field of Jan. 28, 1976 gamma-ray burst

55 56 58

3.3% of initial spike 1.5%

9.2% 3.5cr deviation above continuum

22 42 55 58

applicable to the other three gamma-ray events listed in table 3. By varying the ion temperature, the ratio of positron to neutron production can be made large enough to account for those cases in which only the redshifted 511 keV line is seen at ~420 keY. Teegarden and Cline [91] have pointed out that the 740 keY peak also seen in the spectrum of the Nov. 19, 1978 gamma-ray burst can be explained in this context by redshifting the 847 keV line emitted by the first excited state of iron. If this identification of the 740 keY feature is adopted, then additional lines from higher excited levels of iron should also be present. However, if these high-energy lines are broad enough to blend together, then not only wouldn’t Table 4 Identification of gamma-ray lines observed during the June 10, 1974 transient event Emission process

Emitted line energy (keV)

Mean line energy (key)

Mean redshift

Line energy range

Maximum redshift range

400—420 1740—1860 2180—2260 5935—5960

.28—22 .28—20 .00—.02 .29—28

June 10, 1974 e~+e—~2y 511 ‘H(n,y) 2223 ‘H(n,y) 2223 ‘6Fe(n,y)

413.2±1.8 1789.7±6.0 2218.6±6.3 5946.5±3.7

.237±005 .243±.009 .002±003 .284±001

310

F Verter, Cosmic gamma-ray bursts HOT SPOT T~>IO~° Te<.002

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Fig. 8. On June 10, 1974 a gamma-ray transient was detected by a high spectral resolution gamma-ray telescope operating on board a balloon flight sponsored by JPL [421. The event, which began at about 20:20 UT and lasted —20 minutes, contained four gamma-ray lines of >3cr significance [421. These appeared at 0.41, 1.79, 2.22 and 5.95 MeV [421. Lingenfelter et al. [581have proposed a model in which these lines are produced by material falling Onto the surface of a neutron star. This figure sketches their model, showing the regions from which the different emission lines originate. Taken from Lingenfelter et al. [58].

we detect them, but they would also explain the hard spectrum [91] of the Nov. 19, 1978 burst very nicely. Thus, the basic scenario of neutron star accretion appears to be able to account for the variety of line emission seen in gamma-ray transients. Alternate line interpretations are available. One is to reverse the temporal direction of the accretion process and posit instead that the lines are emitted by material that is thrown upwards by a surface explosion. As before, different line redshifts correspond to emission from matter at different heights above the compact object. Bisnovatyi-Kogan and Chechëtkin [5]advocate this point of view, and they emphasize that the observations of the Nov. 19, 1978 gamma-ray burst are consistent with a model that they have proposed (see section 5.4). The identification of the 740 keY line as an iron line requires slightly less redshift than is needed to shift an annihilation line to 420 keY. This is consistent with a scenario in which the iron line is emitted from a jet ejected by the neutron star. Yet another explanation of the emission lines in the Nov. 19, 1978 burst identifies the line energies with the cyclotron lines of electrons in a strong magnetic field. Apparao and Chitre [2] noted that in a 6.5 x 1013 G magnetic field, the transition from the first excited Landau level to the ground state releases an energy of 420 keY. For the same magnetic field strength, the second excited level is 730 keY above the ground, which is close enough to the observed, 740 keY line to be within the experimental uncertainties. 2.3. Searches for coinciding bursts at other frequencies A discussion of the spectral properties of gamma-ray bursts would not be complete without a review of the searches that have been made for coinciding events occurring outside the energy range (approximately 30—1200 keY) covered by satellite observations. To date, no such events have been discovered, but our attempts to find them have been far from exhaustive. Given the observed rate of —8 intense gamma-ray bursts per year, a thorough search for associated pulses in other wavelength bands

F. Verter, Cosmic gamma-ray bursts

311

would require operation of a worldwide network of full-sky observatories in which there was a significant chance that two or more stations always observed the same region of the sky. Such comprehensive coverage is beyond our present capabilities. As described by Partridge [69], a great deal of the work done in “pulse astronomy” over the past decade was inspired by Weber’s claim to have detected bursts, about a second in duration, of gravitational radiation emanating from the general direction of the galactic center at the rate of one pulse per day. Weber’s results have never been confirmed, even with improved gravitational wave antennas, but for a while observational astronomers eagerly searched for corresponding bursts of electromagnetic waves. Because the interaction of gravitational radiation with matter is 10~° times weaker than that of electromagnetic radiation, Weber’s detections implied enormous energy fluxes: ~ 3 x iO~erg cm2 s Hz’. (This is 1016 times the energy flux of the Sun.) Most of the efforts to find electromagnetic pulses were concentrated in the radio domain, but work was also done at microwave, infrared, optical and X-ray wavelengths. The emphasis in these experiments was on high-sensitivity measurements over a limited solid angle, leaving open the possibility that interesting events were missed because they occurred in parts of the sky away from the galactic center. As history relates, all the observations failed to detect electromagnetic signals corresponding to Weber’s gravitational wave pulses; in fact, with few exceptions, they failed to detect any electromagnetic pulses at all! This still does not rule out the existence of transient events arriving from unexamined parts of the sky or with characteristics outside the range covered by the observations that have been made; more work needs to be done. Although the spectra of the gamma-ray bursts observed so far appear to fall essentially to zero above a few MeY, a number of investigators have published upper limits to the allowed transient fluxes of gamma-rays at energies above 10 GeY. Such photons are sufficiently energetic that they can be detected with ground-based instruments, and two arrays of scintillation detectors are currently gathering independent measurements of high-energy gamma-bursts in India and in Ireland. It is no coincidence that these arrays are also capable of detecting the energetic bursts of gamma-rays predicted by models of evaporating black holes, which are discussed in section 5.6 of this paper. The town of Ootacamund, primarily known for its large radio telescope, is also the home of a mountain laboratory at an atmospheric column density of 800 g cm2. At this site, Indian scientists from the Tata Institute have been collecting data from four liquid scintillation detectors at the corners of a square 11 m on a side since June of 1977. Gamma-rays impinging on the top of the atmosphere initiate electromagnetic cascades that produce many low-energy (0.5—5 MeV) gamma-rays which are able to penetrate to deeper levels, due to their smaller Compton interaction cross-sections. A burst of >10 GeY gamma-ray photons at the top of the atmosphere would yield a burst of photons with energies >0.6 MeY at the mountain altitude. Most of the gamma-ray showers seen by the detectors are the result of fluctuations in small size extensive air showers initiated by cosmic rays. However, a detection of a few gamma-ray showers at closely-spaced time intervals would constitute a candidate for interpretation as a cosmic gamma-ray burst. Investigators from the Tata Institute of Fundamental Research conducted a three-phase experiment in which the upper limits to the coincidence time between detector pulses and the inter-shower time interval were, respectively, 10 ~s and 10 ms; 10 /L5 and 100 ms; 100 ~s and 100 ms. Bhat et al. [4] report that in all phases of the experiment, the frequency of burst events did not exceed the number predicted by random Poisson fluctuations, and consequently the 99% confidence upper limit on the occurrence rate of gamma-ray bursts with energies >10 GeY is 3.8 yr1 sr’. The requirement that the gamma-ray flux be incident in the form of narrow pulses is not inconsistent with the characteristics of the gamma-ray bursts seen by satellite-borne detectors, but Bhat Ct al. calculate

312

F Verger, Cosmic gamma-ray bursts

that if the energy spectrum of the burst is a power law of index —2.6 above 100 keY, then the present experiment requires a total observed flux of ~~3x102 erg cm2 in this energy range in order to register the event as a burst. Since this intensity is a factor of 100 higher than the most energetic gamma-ray bursts seen by satellites, the upper limit they derive does not tell us much about the behavior of the typical burst spectrum at high energies. Still, we can safely conclude that a separate class of very energetic and frequent bursts does not exist. In Ireland, bursts of photons with energies >1013 eY are monitored by a system of four identical cosmic ray air-shower detection systems [28, 29]. Two of these are located near Dublin, at a separation of 550 m, and the other two are located 250 km away near Cork, where they are separated by 3 km. All of these stations, each consisting of three plastic scintillation counters, are operating in absolute time coincidence at an altitude just above sea level. Data collected during a three-year search that terminated in December 1977 yielded the following upper limits, at the 99% confidence level, for transient gamma-ray events in the energy range >2 x 1013 eY that occur over the quoted timescales [29]: Characteristic duration r
Coincidence resolving time ±ls ±ls ±ls

Upper limit rate 0.45/yr 0.9/yr 0.9/yr

In this experiment, the minimum total flux of primary gamma-rays with energies >2 x 1013 eV that is required at the top of the atmosphere to produce a detectable transient coincidence is of the order of i0~erg cm2. Subsequent to the completion of this search, the detection systems have been reorganized to extend their response to timescales of less than 100 ~ s. The stations began recording again in June, 1978; so far, no coincidences have been observed other than would be expected on a purely random basis [62]. Immediately below the energy range at which gamma-ray detectors operate lies the X-ray region of the spectrum. Considerable attention has been given to the similarities between gamma-ray bursts and the recently discovered X-ray burst sources. The operational definition that has been adopted for X-ray bursts consists of three criteria [57]: (1) rise time less than a few seconds, (2) duration from a few seconds to a few minutes, and (3) recurrence. The X-ray burst timescales are suggestive of a gamma-ray burst moving in slow motion. The temporal profiles of X-ray bursts also exhibit a large variety of structures similar to the variability that is characteristic of gamma-ray bursts. Another suggestive comparison can be made between the temporal behavior of the two types of burst spectra. While we have seen that the event-average spectra of gamma-ray bursts show little variation, the evolution of the spec,trum during the course of a gamma-ray burst event has not been well studied. In the previous subsection I quoted the report of Mazets and Golenetskii [60], that in all cases in the Konus data where a burst spectrum exhibited evolution, the burst spectrum softened over the course of the event. In the case of the unusual gamma-ray burst of March 5, 1979, the spectrum was softer during, the long decay phase that followed the initial energetic spike of’emission. This~behavioris

F Verger, Cosmic gamma -ray bursts

313

analogous to the evolution of X-ray bursts, where significant spectral changes are seen in the course of a transient event, typically a softening of the spectrum during burst decay. Spectral hardening during burst rise is also quite common. “Typical” X-ray bursts have been described in terms of two components [57]: (1) an initial pulse which rises and falls sharply in a few seconds and is wider at higher energies, followed by (2) a long decay whose spectrum softens with time as the burst intensity gradually decreases. Although typical gamma-ray bursts have not exhibited these pulse “tails” of decaying intensity, their existence at a level below detection has not been ruled out. (This limitation in sensitivity exists despite the fact that the total flux of a gamma-ray burst is typically —2 orders of magnitude higher than that of an X-ray burst.) In spite of these similarities, one can also point to major differences between gamma-ray and X-ray transients. One of these is the phenomenon of repeating bursts from a single source. Recurring gamma-ray burst sources are a rare species, if they exist at all, whereas recurrence is one of the defining characteristics of X-ray burst sources. Moreover, this recurrence can be very regular, with a period as short as hours or days (excluding one source called “the rapid burster” which produces up to 4000 bursts per day), Although the burst profiles of individual X-ray sources can look very different, repeating bursts from one source usually seem similar. X-ray burst sources differ most dramatically from the sources responsible for gamma-ray bursts in their tendency to be associated with other astronomical phenomena. It is quite common for an X-ray burst source to also emit a persistent, if somewhat variable, flux of X-rays whose time-averaged luminosity varies from <25 to —250 times that of the burst emission (~2for the rapid burster) [57]. However, the galactic distribution of X-ray bursters differs from that of the known X-ray sources with “steady” emission, suggesting that they form a subset of the steady emitters. The coordinate positions of X-ray burst sources are clustered along the galactic equator and concentrated towards the nucleus, a strong tendency towards directional selectivity which gamma-ray bursts do not display. While the origin of gamma-ray bursts still remains a mystery, source objects have been identified for several of the X-ray bursts. At least one is almost certainly associated with a faint blue star, and a very high fraction of the known steady X-ray sources in globular clusters also emit bursts. Thus, closer inspection reveals that the differences between X-ray and gamma-ray bursts outweigh any resemblances in the burst samples. Significantly, we know of no cases in which the same source was responsible for both an X-ray and a gamma-ray burst. This would seem to rule out an interpretation of gamma-ray bursts as the high-energy tails of X-ray burst events, but it does not exclude the possibility that a generic relationship exists between the two types of transient. Theoretical models of each have tended to rely upon the same source objects and/or energy-releasing mechanisms. This leads one to wonder if the two burst classes might be produced by a single burst mechanism operating under different circumstances. The observations of the March 5, 1979 gamma-ray burst lend credence to this hypothesis, as it was an event that seems to bridge the gap between the two classes by possessing features characteristic of each. Below the X-ray domain are the ultraviolet, optical, and infrared regions of the spectrum. There is a paucity of gamma-ray burst research at these wavelengths. The possibility that the bursts coincide with familiar optical transients such as novae or supernovae has been eliminated, but only one general optical search has been performed. In this effort, Grindlay et al. [34]used Prairie Network films to set a limit of m~>5 on the optical emission from two burst events for which there were good exposures of a

314

F. Verter, Cosmic gamma-ray bursts

well-defined arrival direction. To the author’s knowledge there has been no attempt to look for a low-level ultraviolet or infrared variation that coincides with a gamma-ray burst. The possible existence of such emission is made all the more intriguing by the recent discovery [51] of infrared bursts emanating from the “rapid burster” X-ray source MXB 1730-333. The line of sight to this object passes within 6°of the galactic center, and consequently the visual obscuration of the source is high. Infrared photographic plates have been used to identify [49]the seat of the X-ray emissions as a compact globular cluster dubbed Liller I. It has been thought that the X-ray bursts may be emitted near the surface of a compact object in the core of the globular cluster, and that the subsequent disturbance of the surrounding region gives rise to emission at longer wavelengths. This suspicion prompted the observations of Kulkarni et al. [51] which discovered the infrared bursts. The characteristics of these bursts are fairly uniform, and similar to those of Type I X-ray bursts. An explanation of the relationship between these bursts and any others at different wavelengths awaits a satisfactory model of the emission process. As I have said, the observational evidence needed to rule out the occurrence of similar phenomena following gamma-ray bursts is lacking, so their existence is open to speculation. Continuing to lower photon energies brings us to radio wavelengths, where searches for a radio counterpart of gamma-ray bursts have been conducted. A good description of the motivation and history of the search for isolated pulses in the radio-frequency band is given by Inzani et al. [41],and references therein. In order to conduct a systematic search, an automated detection system has been established in Medicina, Italy, which is designed tç discover radio pulses with the following properties [41]: (a) 0.1s~risetimeO (is) (b) lsdurationO (lOs) (c) rate a few events per day (d) random distribution in space and time (e) frequency spectrum extended at least over the VHF (151 MHz) and UHF (408 MHz) bands of the electromagnetic spectrum. The low-resolution aerials of the Medicina station are actually more appropriate for coincident detections of a burst from a celestial source of poorly-determined position than the high-resolution aerials available at most radio observatories. Completed in March, 1977, the three-pronged observational program of the system includes a search for the radio counterpart of X- and gamma-ray bursts, a study of the galactic center and the Cygnus region, and full-sky monitoring. The search for radio pulses coinciding with gamma-ray bursts is carried out a posteriori on stored radio data. Inzani et al. [4] report that of the seven gamma-ray bursts recorded during the year which began in August of 1976, radio records exist for only three. None of these events [85]has a corresponding radio pulse lasting 1 s in the VHF or UHF band, at intensities greater than 10 12 erg cm2 Hz’, that occurs within ±10m of the onset of the gamma-ray burst. Earlier searches [3] also failed to find any cosmic radio bursts that can be matched to the time and position of a gamma-ray transient. None of the searches I have described attempted to find bursts corresponding to gamma-ray transients by intentionally pointing an instrument in the direction of the event and monitoring the post-burst emission. It may prove unfeasible to do this, primarily because the time interval between the occurrence of a burst and the localization of the source region is on the order of months. Whether or not any detectable emission would remain at the end of this time cannot be predicted outside the confines of a specific model, so the question is best settled by observation.

F Verter, Cosmic gamma-ray bursts

315

3. Spatial distribution of burst sources 3.1. Observations Since their discovery, the primary method of determining the celestial coordinates of gamma-ray burst sources has been by triangulation. In this method, the delay between the times at which two detectors respond to a given pulse defines the angle between the normal to the arriving wavefront and the baseline of the detectors. The source may lie anywhere on a cone about the baseline having this opening angle. The difference in arrival time between a third satellite and one of the original two determines another circle on the sky and limits the source position to one of the two intersection points of these two circles; a fourth independent observation would decide the position conclusively. Sometimes strong gamma-ray bursts are registered by satellites which orbit the Earth so closely that only half the sky is visible to them at any one time. These can be used to distinguish between two alternate source positions if only one of them was in the satellite’s field of view at the time the burst occurred. In the early 70’s, the Vela measurements were often supplemented by responses from Uhuru, 060-5, OSO-6, SAS-2, and especially IMP-6 and 7. In practice, the circles that are described on the celestial sphere by the triangulation technique possess a finite width. This thickness is a result of errors in the spacecraft position, the clock calibration, and differences in the moment within the burst temporal profile at which triggering occurred. The best way to reduce the size of the source field defined by intersecting annuli is to obtain redundant solutions from as many spacecraft as possible. An alternate, but less accurate, means of obtaining directional data is to employ gamma-ray detectors of anisotropic angular sensitivity. Then the response of each detector gives the angle of incidence of the wavefront on that detector. Since the standard detecting configuration consists of a cluster of six detectors, the position of a gamma-ray burst source can be determined from the directional cosines of at least three detectors [60]. The accuracy of this calculation is limited by the statistical accuracy of the count rates in the individual detectors, and by the calibration of the angular response function. If the spacecraft housing the detectors is stabilized about only one axis, with the angle of rotation about this axis undefined, then the source field defined by detector response is again spread into a ring on the celestial sphere. So it is still necessary to use more than one spacecraft to localize a burst position, but the advantage of this method is that it is much less time-consuming than triangulation. The Konus experiment designed by the Leningrad group for the Venera 11 and 12 spacecraft uses detector angular response as a supplement to triangulated source positions. For a gamma-ray burst with a total flux of 2 x 10~—2x 10~~ erg cm2 in the range 50—150 keV, the Yenera resolution in this mode is ~0.25° [60]. One of the first tasks that had to be completed before declaring gamma-ray bursts to be of “cosmic” origin was to demonstrate that they could not be produced in the Earth environment or within the solar system. The Yela satellites are well beyond the regions in which the Earth’s trapped radiation is concentrated, but their gamma-ray detectors are susceptible to stimulation by high energy particles. The possibility that the bursts are triggered by energetic particles can be ruled out on a number of grounds. First, it is unlikely that the similar time structure observed by separate Yela satellites could have been produced by a particle signal traversing the geomagnetic field; also, none of the signal times differ by more than the maximum light transit time. Furthermore, the particle detectors carried by the Vela satellites did not respond during gamma-ray bursts. It was also suspected that gamma-ray bursts might .

316

F. Verter, Cosmic gamma-ray bursts

be another type of solar flare activity, but the directional data eliminated our Sun as the seat of the bursts. Other solar system members can also be excluded on this basis. In 1974, Grindlay and Fazio [33] proposed that narrow beams of gamma-rays emitted by relativistic iron grains entering the solar system are responsible for the bursts we see. Since then, widely separated burst sensors have failed to detect the signal differences that would be expected if we were observing beamed emission from a source within the solar system. Once it was concluded that the sources of gamma-ray bursts lie outside our solar system, the question of their distances immediately arose. Are we seeing nearby events, or bursts from throughout the galaxy, and are external galaxies contributing as well? This is equivalent to asking the bolometric luminosity of the objects that are producing the observed energy fluxes. The source distances would also tell us the burst frequency per unit volume. If gamma-ray bursts could be associated with a known class of astronomical objects, we would automatically know both their distances and the nature of the environment in which they are generated. With this hope, the source fields of the bursts have been compared with the catalogued positions of nearby stars, flare stars, white dwarfs, pulsars, globular clusters, supernovae, Seyfert galaxies, quasars, X-ray burst sources, and steady sources of gamma-ray, X-ray, infrared, and radio emission. None of these is found in the error boxes of burst locations derived since the launch of Helios~2;*these fields are thin arcs about 1’ wide and several degrees long. Soon we will have a sample of source positions that is accurate enough, 1’ x 1’ or less, to allow optical searches for candidate objects. The first source region to be accurately located, that of the Nov. 19, 1978 gamma-ray burst, has already been optically scrutinized; only main-sequence stars were seen. The fact that gamma-ray bursts appear to emanate from perfectly ordinary star fields is a form of negative evidence that tells us what the source objects are not. This is a useful constraint on burst models. However, it leaves open the question of source distances. A knowledge of the source distance is necessary in order to choose between candidate objects that are intrinsically faint and those which aren’t visible to us by virtue of their remoteness. Despite the absence of source identifications, a rough indication of the size and shape of the volume in which the observed bursts originate can be obtained from a statistical analysis of burst arrival directions. The overall spatial distribution of matter in the Milky Way, a typical spiral galaxy, can be described for these purposes as a composite of two components: a disk, and a spherical halo. The structure and composition of these components are thoroughly described elsewhere [7]. Our Sun is about 10 kpc from the center of the galaxy, on the edge of one of the spiral arms that lie in the plane of the disk. If one imagines looking out from this vantage point to successively greater distances, then the overall distribution of the astronomical objects that one observes will alter as more and more of the galaxy becomes visible. At large enough distances, one is seeing the distribution of the galaxies themselves, which cluster on a hierarchy of scales from binary systems to superclusters [27].One could hope to deduce the characteristic distance of gamma-ray burst sources by comparing the distribution of their galactic coordinates with the patterns expected at various distances. Unfortunately, there are too few gamma-ray bursts for the proposed comparison to be definitive. The total number of confirmed detections is at present only about a hundred, give or take a few. Many of the early bursts have two alternate source positions, because there weren’t enough detecting satellites to eliminate one of the choices. By a fortuitous circumstance, the orientation of the orbital planes of the Yela satellites is such that the alternate positions are at approximately the same galactic latitude. Hence it is feasible to include these events in an analysis that tests the degree of clustering along the galactic Note added in proof: The Nov. 19, 1978 gamma-ray burst has both an X-ray and a radio source within its error box [15].

F. Verger, Cosmic gamma-ray bursts

317

equator exhibited by burst coordinates. Over the years, the results of such studies have generated considerable controversy. It is now generally agreed that the source distribution appears to be roughly isotropic, although a slight tendency to lie in the galactic plane may exist. If the objects responsible for gamma-ray bursts are mostly located at low galactic latitudes, then we can expect that the weakest events will also tend to lie near the galactic plane. This is true of the Yela data, where Schmidt [84] has found that the average total burst flux is anti-correlated with galactic latitude. Assuming that the intrinsic luminosity of the sources is a constant, and that emission is isotropic, Schmidt has compared the latitude dependence of net burst fluxes with various distributions of material in the galaxy. He finds that when the burst sources are distributed in the same way as the total galactic matter, the weakest events occur 2.3 kpc away and the intrinsic source energy is 1.9 x l0~° erg. For sources distributed like the interstellar hydrogen (ignoring spiral arms), the cut-off distance is 0.65 kpc and the source energy is 1.5 x iO~erg. The most popular method of matching candidate source distributions to burst observations is to plot both on a graph of log N vs log S. Here N is the number of gamma-ray bursts detected per year whose total energy flux exceeds the value S. For idealized models in which the sources are uniformly distributed throughout an infinite array, N(S) takes the form of a power law: N S~.An isotropic distribution results in an a = ~ law, whereas for sources confined to an infinite plane or line a is 1 or respectively. For more realistic source distributions, it may not be possible to express N(S) as an analytic function. In general, any spatial array of burst sources will yield a graph of log N vs log S which can be divided into several regimes that are separated by transition zones which correspond to edges of the confinement region. For example, suppose the source objects all have the same luminosity and are uniformly distributed in a disk population whose half-thickness is z. At heliocentric distances d less than z the source distribution appears approximately isotropic, whereas for z
318

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S(erg cm2) Fig. 9. The frequency, N, of gamma-ray bursts whose total energy flux exceeds S. Superimposed on the data are the power laws N( S) — S~,for the cases a = ~ and ~. All of the observations satisfy the a = ~ law for net fluxes above iO~erg cm2. The Vela and IMP-7 data aren’t very useful below this level because their detector thresholds are too high (--10-’ erg cm2 ~‘) to register weak events. The points and upper limits obtained at lower intensities were measured by the instruments or institutions whose names are associated with their symbols. The references in which these experiments are described can be found in a review by Hurley [401, from which this figure was taken.

ignored is interstellar extinction, since absorpticfn by interstellar matter is negligible at the energies that characterize gamma-ray bursts. It is customary to reduce the parameters influencing N(S) by assuming that the source objects emit isotropically and that the intrinsic burst energy is a constant. If the radiation is actually beamed into a solid angle ~2,the required burst energy would be decreased by a factor of (D/4ir)1, and the number of bursts observed would be only f1/4ir of the total. The assumption of a fixed source energy is not a gross oversimplification, because the N(S) curve is more sensitive to the spatial distribution of the sources than to their intrinsic energy distribution [103,32]. There have been two recent papers, by Fishman [32],’and by Jennings and White [43], in which models confining the burst sources to a disk or halo population of the Milky Way galaxy were tested against the observational constraints on N(S). Both papers conclude that gamma-ray bursts are produced by an old disk population whose scale height z 0 is ?~O.3kpc. The difficulty with halo galaxy

F. Verger, Cosmic gamma-ray bursts

319

models is that the divergence above the a = ~ law which occurs when central concentration is present produces N values that are incompatible with the experimental upper limits at low S. This effect is negligible for models in which the e-folding radius of the source density is ~ 5 kpc [43];but known halo populations typically have characteristic radii of only 2 or 3 kpc. The marginal status of realistic halo models is compatible with the isotropy seen in source positions, which do not cluster the galactic center. In each of these papers the source density of the disk model was taken to have the form n(r, z) = n0 exp[—(r/ro + z/zo)], where cylindrical coordinates apply. Fishman [32]took r0 to be either ~ or 3 kpc, whereas Jennings and White [43] were forced to rule out models with r0 S 5 kpc because of the central concentration effects described above. Fishman [32] found the model fits to be relatively insensitive to the functional form of the z dependence. Values of z0 ~ 0.1 kpc refer to population I objects delineating spiral arms, so models in which the disk sources are restricted to annular “arms” were tested. Because these models require N to fall off at the edge of the local spiral arm, they are more successful than smooth disk models at fitting the low S portion of the log N—log S graph. However, the parameter choice that provides the optimal fit to the observations would require burst luminosities so low that the nearest (isotropically emitting) source objects would be only ~2Opc away. This is not acceptable, because those disk objects for which z0 ~ 0.1 kpc, such as OB stars or cepheids, are not present in the solar neighborhood. Fishman’s [32] successful models predict burst energies ranging from 2 x 10~to 2 x 1041 erg, but Jennings and White [43]place the energy of the sources in their smooth disk models 3. between 1038 and 2 xCombining iO~erg. These correspond to rate presented densities of 6 x iO~and 108 bursts yr~ pc the various arguments in this subsection leads to the following conclusions: Although the identity of the objects producing gamma-ray bursts remains unknown, the isotropy of the burst positions indicates that the sources are either relatively nearby or very distant. Various considerations that render extra-galactic locations of burst sources unfeasible are presented in section 5.2. Given that the bursts are produced within our own galaxy, it is possible to use a graph of the observed frequency of bursts versus their intensity as a criterion for judging source distribution models. The consensus of such evaluations is that the source objects are members of a thick disk population. Jennings and White [43] have used this result as well as other limitations to draw up a list of source candidates they deem acceptable. Their choices are middle and late-type (B5-M) main sequence stars, pulsars, old neutron stars, and pop I accretion binaries whose primaries are distributed like other stars of similar spectral type. Pop I white dwarfs may be acceptable, but little is known about them. 3.2. Theory There is a very general argument which places a limit on the intrinsic luminosity of an object that is emitting gamma radiation. When the density of gamma-ray photons on the surface of a source becomes high enough, the gamma-rays collide with one another and are converted to particle—antiparticle pairs. Hence, an object of fixed size that is postulated to be the source of an observed gamma-ray flux cannot be placed beyond a limiting distance at which the intrinsic luminosity required to supply the observed flux becomes so high that y—y pair production renders the source optically thick. In the case of gamma-ray burst sources, these distance limits are within our own galaxy. The fluxes received from gamma-ray bursts are known, and the characteristic dimension of the source region is limited by the short timescales seen in burst profiles (see p. 301). If an isotropic source cm across is producing a total observed flux of iO~erg cm2, then its optical depth to 1 MeY photons will exceed unity at a distance of ~2 kpc [83]. Since the distance limit scales roughly as ~_1/2, decreasing the total flux to l0_6 erg cm2 would extend the limiting distance to about 20 kpc.

320

F. Verger, Cosmic gamma-ray bursts

This argument is compelling because it does not rely on specific assumptions about particles or fields within the source. However, the same caveats which were applied to the derivation of the maximum source volume are in effect here. For instance, a relativistically expanding object could produce narrow pulses in a larger volume, and therefore the surface photon density would not exceed the y—y pair production limit as easily. Beamed emission would lower the intrinsic luminosity requirement, and hence the surface photon density. Furthermore, when the average angle between emitted photons is reduced by a beaming mechanism, the threshold energy at which an ambient photon undergoes y—y pair production is raised. For example, an opening half angle of 12°corresponds to a 5 MeV threshold, and a i0~erg cm2 source would become optically thick at this frequency if it were more than =6 kpc away. The photon energies being discussed are a bit higher than those characterizing gamma-ray bursts, but MeY photons have been seen in these events [50].Herterich [39]has argued on this basis that compact X-ray sources cannot be the seat of gamma-ray bursts, because gamma-rays above a few MeY will be strongly absorbed before they can leave the source. It would be unwise to interpret these limits too rigorously, as the bulk of the emission observed in gamma-ray bursts is at considerably softer energies, peaking in the vicinity of 100—200 keV. Moreover, there is insufficient information available on the time structure of the high energy emission to ascertain whether the maximum volume of the photon source is the same as that obtained from the burst profiles at lower energies. Still, the limits quoted are fairly generous because large intensity fluctuations occur during bursts, so that momentary fluxes are often much greater than the averages.

4. The unusual gamma-ray burst of March 5, 1979 This particular event warrants a separate section because almost all of its observational properties differ drastically from those of previously observed gamma-ray bursts. This makes it the only event of its kind in more than ten years of essentially continuous operation of the Vela system, which could have detectedother similar bursts. To highlight this comparison, the properties of this burst are listed in a separate column in table 2 and its temporal profile is displayed on various timescales in figs. 10 to 12. The burst began abruptly with a rise time that was too fast to be resolved, <0.25 ms, which is about 2 orders of magnitude shorter than the rise times of previously measured bursts or of previous measurement limits. The burst rose immediately to a maximum intensity more than an order of magnitude greater than the most intense gamma-ray bursts previously seen, despite the fact that the integrated flux from the entire burst is not unusual. Cline et al. [20]illustrated this by plotting the March 5, 1979 event along with the other gamma-ray bursts detected by Helios-2 on a graph of total intensity versus maximum intensity. Their display is repeated in fig. 13. Whereas typical gamma-ray bursts are very structured, a high-resolution profile of the initial pulse of this event reveals little irregularity. The gamma-ray flux remained near the maximum level for about 30 ms, fell to a somewhat lower level for about 70 ms, and then dropped with an ---35 ms decay time to a level several hundred times lower. The overall width of the high-intensity spike, ~l20 ms, is briefer than over 95% of the peaks in previously detected bursts, but similar in width to some short bursts. The rapid fall-off from high intensity was followed by a long decay modulated by periodic oscillations. The monotonic envelope of this decay can be roughly characterized by a decay time of SOs. The penodicity of the oscillations is very sharp; the best estimate of the period, obtained by Fourier analysis, is 8.00 ±0.05 s [92].At least 22 cycles of this oscillation were detected, and from fig. 12 it can be seen that the pulse shape is

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Fig. 14. Curves (i) and (ii) are energy spectra of the March 5, 1979 gamma-ray transient obtained by instruments on board the Venera spacecraft. Eight successive spectra were taken over 4s intervals, starting from the moment at which the gamma-ray detector triggered. Of these, only the spectrum of the first 4 s is significantly different from the rest. Hence, this spectrum hasbeen presented here as curve (i),while the remaining seven spectra were averaged together to give curve (ii). The high-energy tail of the initial spectrum was probably emitted during the brief pulse that began this event; the burst profile recorded by the Pioneer-Venus Orbiter for photon energies above 100—150 keV supports this conclusion. Taken from Cline [14].

fairly uniform. It is of interest to note that the pulse maximum is not synchronized with the initial spike. Because of the obvious interpulse features, a strong second harmonic at 4.0 s appears in the Fourier analysis. There are no other periods significantly above the counting noise level. The existence of the decay phase is one of the most unusual features of this gamma-ray burst. The decay signal is approximately 1% the intensity of the main pulse, which is itself about 100 times as intense as the average gamma-ray burst. Hence it is possible that typical gamma-ray bursts also possess a post-burst decay at a level that is too low to be detected by current instruments. The energy spectrum of this event is also unusual, in that it is softer than the spectra of typical gamma-ray bursts. A descriptive energy would be near 50 keY. It appears that the burst can be divided into two components, the initial peak and the decay phase, which give different contributions to the spectrum. Fig. 14 shows that the energy spectrum of the burst during the first 4s after detection is much harder than the spectrum of the subsequent decay. This is due to the presence of high energy photons which were emitted during the brief initial pulse. The initial spectrum also contains a broad line feature in the neighborhood of 420 keY (see table 3). If it were not for this feature, the initial spectrum would resemble the power law spectra of typical gamma-ray bursts. Mazets and Golenetskii claim [60]that the function E~exp(—EIkT) fits the decay spectrum well when kT = 30 keY. Another unusual property of this burst source is that it is recurrent. Additional bursts (see fig. 15)

F. Verger, Cosmic gamma-ray bursts

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were observed on March 6, April 4 and April 24. Their intensities and event profiles are rather typical, but their spectra (fig. 16) resemble the soft spectrum of the March 5 decay phase. The observational parameters of this gamma-ray transient clearly deviate significantly from the range of values (see table 2) which we have taken to define the “typical” gamma-ray burst. However, this event is not so different as to preclude the possibility that it is an unusual manifestation of the same source mechanism that is responsible for the typical bursts. If we were to concentrate on similarities rather than differences, we would find ample reason to suspect that this is the case. To that end, the decay phase of the March 5, 1979 burst can be ignored, since it may very well be present in all gamma-ray bursts at a level below detection. Then the energy spectrum of the burst would be that of the initial pulse alone, and this is similar to the power law spectra of typical bursts. The presence of the 420 keY emission line is not unique (see section 3.2 of this paper), and further studies of burst spectra may find that this is a common occurrence. As indicated in fig. 13, the net flux observed from the March 5, 1979 transient was typical. Nor is the narrow width of the initial spike without precedent. Among the 90 some odd bursts compiled by the Vela system between 1969 and 1979, there are 3 bursts consisting of brief spikes ~1O0ms wide. Unless these were the most intense portions of weak bursts, they are akin to the event profile seen on March 5, 1979. No spectral data or high-resolution profiles are available for these events. Mazets and Golenetskii [60]found 7 more bursts of this type (type (d), in the terminology of section 2.1) in their Konus sample, with event durations ranging from 0.01 to 0.25 s. Three of these are recurring bursts from the same source. The spectra of both the recurring source and another source

324

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are substantially softer than typical gamma-ray burst spectra, and “close in shape” [60]to the spectra of the repeating bursts emitted by the March 5, 1979 source object. Seen in this context, the March 5, 1979 gamma-ray transient is not unique, but is the most prominent member of a small class of brief gamma-ray bursts that have softer spectra and tend to recur. The connection between these bursts and the more common burst type is completely unknown, but •the observations suggest that they are related. The last unusual property of the March 5, 1979 gamma-ray burst is one that has aroused great controversy among astrophysicists. This is the coincidence of the source position with a known celestial object. The signal arrival times at the various spacecraft of the interplanetary detector network localize the source [24] to a 1’ x 2’ area 40” from the center of the supernova remnant N49 in the Large Magellanic Cloud.* In fig. 17 this error box is superimposed on an X-ray surface brightness contour map of N49 and the accompanying nebulosity (N49). Additional checks on the accuracy of the spacecraft clocks involved will eventually reduce the area of this error box by approximately two orders of magnitude. Some investigators, most notably T.L. Clime at the Goddard Space Flight Center, feel that this positional coincidence is a clear indication that the gamma-ray burst and the supernova remnant are related. Indeed, the chance probability that a source field whose area is 2 x 10-8 times the area of the celestial sphere will fall on a catalogued supernova remnant is very small. The proximity of the March 5, *

The Large and Small Magellanic Clouds are small irregular galaxies that orbit our galaxy at distances of 55 and 70 kpc, respectively.

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1979 source field to the center of N49 corresponds to a random probability of a few times 1O_6 [24].A more relevant statistic is the probability that a source field of this size will be close enough to the center of an SNR that it may contain a compact object formed in the explosion. This is more difficult to estimate, but it seems that in this case the probability is somewhat above iO~[24]. Placing the source of the March 5, 1979 burst in the Large Magellanic Cloud (LMC) would lead to the conclusion that this transient was not a product of the same source mechanism that produces typical gamma-ray bursts. We can arrive at this result by starting from the assumption that both the March 5, 1979 event and common gamma-ray bursts are members of a single luminosity distribution. Then the relative intensities of the fluxes received from various bursts represent the relative distances of their respective source objects. Suppose, for instance, that all bursts have the same or similar luminosities. Then the unusual brightness of the March 5, 1979 event is due to its location in one of our nearest extragalactic neighbors, and gamma-ray bursts of typical intensity are produced by source objects 0.2 to 5 Mpc away. But this causes a contradiction, because there are too few galaxies at these distances to reproduce the observed source distribution. Hence the supposition that the March 5, 1979 event had the same source luminosity as a typical gamma-ray burst is unfeasible. Even if we abandon it in favor of the view that the transient of March 5, 1979 was an extreme example of the intrinsic luminosity distribution, the conclusion still holds. At one extreme, we could consider the March 5, 1979 event to be an unusually faint and nearby example of the gamma-ray bursts that are typically observed in very distant galaxies. This is unfeasible too, because there is no extragalactic distribution of source objects that can satisfy the constraints imposed by the observed spatial distribution of the burst source (refer to section 5.2 of this paper). At the other extreme, we could consider the March 5, 1979 event to be an unusually bright and distant example of the gamma-ray bursts emitted by sources in our own galaxy. This is possible, but contrived. It is more likely that the first unusually bright source detected would be within our galaxy rather than outside it. So the hypothesis that the source of the March 5, 1979 gamma-ray transient is in the LMC leads to the conclusion that the luminosity of this event cannot be attributed to the same mechanism that is responsible for the luminosity distribution of typical gamma-ray bursts. This casts grave doubt upon the belief that the March 5, 1979 transient is related to typical bursts, as the observations suggest.

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Various problems of radiative transfer give further cause to doubt that the March 5, 1979 burst could have occurred at the distance of the LMC. The 0.25 ms rise time of the initial spike implies a source diameter of at most 75 km. A homogeneous, isotropic source of this size could not match the observed flux levels from beyond a distance of ~‘50pc, where its optical depth to y—y pair production would reach unity. A similar limiting distance applies if we impose the Eddington luminosity limit. For a source whose energy generation is powered by accretion, this is the luminosity at which the radiation pressure of the outgoing photons becomes strong enough to prevent further infall. In the case of spherically symmetric accretion onto an object of mass M, the maximum luminosity is LE = 1.3 x 10~(M/M0)erg s~’.Whereas an intrinsic luminosity of 10~erg s~would place the March 5, 1979 1. Models of burstevent 300 pcareaway, thepressed 55 kpc to distance the LMC demands a peak luminosity of iO~~ erg c this sorely explaintosuch a gigantic energy release. On the other hand, counterarguments can be advanced for each of these distance limitations: The Eddington luminosity applies only to an object undergoing steady accretion. There is no guarantee that this is the emission mechanism of the decay phase, and the impulsive part of the burst is not the product of a steady process. A model proposed by Ramaty et al. [75]avoids the y—y pair production opacity by generating the burst in a layer so thin that its width is less than the photon mean free path. Other models can reduce the energy release at the source, either by bringing the object closer, which abandons the LMC hypothesis, or by beaming the photon emission. Focussing the March 5, 1979 burst into a narrow beam would solve several problems at once: the energy output, the y—y pair production threshold, and the rarity of such an intense event. Thus it is possible to get around the limitations proposed, though excessive finagling can make a model seem very contrived. So ends my discussion of the distance to the source of the March 5, 1979 gamma-ray burst. I will not attempt to draw a conclusion to the debate on this subject because I don’t think the arguments in favor of either viewpoint are convincing. I warn the reader that there are those who will disagree with me and claim that any person of reason has to see that the source must/can’t be in the LMC. This may well be one of the most important aspects of this event: astrophysicists who previously had not paid much attention to gamma-ray bursts are now strongly divided on this issue. Those who are proponents of an association with the supernova remnant N49 may be encouraged by the existence of several new models that attempt to explain the March 5, 1979 transient in the context of an LMC origin. Each of these suggestions is rather vague on certain points, and these loopholes will have to be closed before a particular proposal can be seriously adopted. Regardless of the method of burst generation, it is very likely that the source of the March 5, 1979 gamma-ray burst is a neutron star. The regular pulsations superimposed on the burst decay are the strongest piece of evidence in favor of this view. Too short to be an orbital period, the 8s oscillation could correspond to the spin period of a rotating body. In order for a spinning sphere to hold together under such a rapid rotation, its density must be at least 2 x 106 g cm3. From the rise time of the initial spike, it is apparent that the diameter of the burst’s emission region was 75 km. If an entire 1M® body is to fit within this volume, its density would have to be over 9 X 1012 g cm3. Even if 75 km is only the width of a hot spot covering 10% of a larger sphere, the minimum density is still 2 x 1012 g cm3. Only neutron stars and black holes can satisfy this condition. A neutron star would provide the best physical basis for the intensity modulations that have this 8s period. The simplest explanation of such pulsations is that there is a bright spot on the surface of the source which swings in and out of our line of sight as the body rotates. The same effect is observed in pulsating X-ray sources, where the bright spot is attributed to emission from accreted matter falling onto the magnetic pole of a neutron star. This model works best with a neutron star, because a black

F Verger, Cosmic gamma-ray bursts

327

hole would not produce this effect, and strong magnetic fields are not common on white dwarfs. Also, the 8s spin period is consistent with the range of periodicities seen in pulsating X-ray sources [52], though it is longer than typical pulsar periods of ~1 s [80,90]. This could be explained if the 8 s period is actually a precession, and the object’s spin is much faster. The spectrum of the pulsating phase of the March 5, 1979 burst supports an association with a neutron star. Mazets and Golenetskii [60] noted that this spectrum bears more resemblance to the spectra of binary X-ray sources than it does to typical gamma-ray burst spectra. They are so convinced that the source of the March 5, 1979 burst was a “flaring X-ray pulsar”, that they have invented a designation for it: FXPO52O-66. (The numbers give the approximate coordinates of the center of the source field.) Helfand and Long [38] have contributed to this argument by pointing out that a neutron star in the LMC would have just the right luminosity to supply the observed pulsating flux if 10% of its surface were emitting thermal radiation at the observed temperature of 30 keY. Can this be merely a coincidence? A separate line of evidence which hints that a neutron star was responsible for the March 5, 1979 event is the 420 keV emission line in the initial burst spectrum. The gravitational redshift required to shift a 511 keY positron annihilation line to this wavelength can be supplied by a 1M0 body with a radius of 10 km. In other words, the observed redshift is the same as the gravitational redshift at the surface of a neutron star. On purely theoretical grounds, the results of section 5 predispose us to consider neutron stars as source candidates because they participate in most of the gamma-ray burst models that are still viable. So far, none of these arguments has depended upon the distance of the source object. In this light, the superposition of the March 5, 1979 source field on a supernova remnant appears to clinch the identification of the source as a neutron star. The strength of this argument can be evaluated by computing the probability that this superposition is a chance occurrence. Let us accept a value of 3 x 10~pc~[53,66] for the local space density of old neutron stars, and use for their scale height perpendicular to the galactic disk the value of 250 pc [90] that is appropriate for pulsars. The scale height of old, undetectable neutron stars could be larger, but its value is unknown. For the parameters given, a sphere of radius 250 Pc centered on the Sun should contain 2 x 106 old neutron stars. The probability that one of these could fall on the 1’ x 2’ error box of the March 5, 1979 source position is about 0.04. Another test is to compare the estimated ages of the neutron star and the supernova remnant. As pulsars age, they spin down and become fainter. The 8s periodicity in the burst decay is twice the longest known pulsar spin period [90].If this periodicity is interpreted as the spin period of a neutron star, the object must be rather old, and therefore it is not surprising that it is not observed as a pulsar. Unfortunately, its age cannot be judged from its spin alone, so I have simply adopted a typical pulsar age of iO~years as a conservative estimate. In order to estimate the age of N49, I assumed that the supernova remnant is currently in the adiabatic phase of expansion, inHere whichD(pc) case isitsthe diameter is 1(EIn)~5t215. diameter determined by the similarity 4.3 x 10~ of the remnant at Sedov time t(yr), E(erg)solution is the [13]:D energy =release of the initial explosion, and n(cm3) is the ambient density of the interstellar medium. For (Em) I have used the average value 5 X 1051 erg cm3 recommended by Clarke and Caswell [13],and for D I took the —.25 pc diameter given by Helfand and Long [38]. This yields a remnant age of 4 x iO~yr. According to these estimates, the neutron star is vastly older than the supernova remnant with which it is associated, as would be the case if we are observing a chance superposition of a nearby old neutron star on a background object. Are we really seeing a freak coincidence, or are these calculations grossly in error? I decided to check further by computing the average velocity the neutron star would need to travel from the center of N49 to the

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F Verger, Cosmic gamma-ray bursts

center of the source field during the lifetime of the remnant. On the sky, the separation of these two points is 40”, which at the distance of the LMC translates into a trip of 11 pc. The required velocity, 3 x i0~km s1, is a bit high even for a runaway survivor of a supernova, but not unreasonably so if the inaccuracy of the age estimate is taken into account. The final source field for this event will be smaller still, favoring the conclusion that the superposition is not a statistical accident. Any model of the March 5, 1979 gamma-ray burst, regardless of the source distance, faces a severe restriction on its X-ray luminosity. About 8 days before this event, and again —38 days later, N49 and the surrounding region of the LMC were observed as part of a soft X-ray survey conducted with the soft X-ray imaging instruments on board the Einstein observatory. The N49 flux levels measured on these occasions were the same to within <0.8% ~:~t [38].The 4” resolution of the instrument used enables us to set an upper limit on the intensity of any point source lying within the 25’ x 25’ field of view. For N49, the upper flux limit is 2.1 x 10_12 erg cm2 s~,and in the area outside N49 but near the burst source field it is 2.2 x 1013 erg cm2 5_i [38]. These are 3o- confidence limits for the spectral band 0.5—4.6 keY. The limits imply that, independent of distance, the ratio of the source’s steady-state luminosity to the burst luminosity observed at energies above 30 keY is
--.

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——

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F. Verger, Cosmic gamma-ray bursts

329

In the Ramaty et al. [75] model, an unknown energy source releases something like iO~~ erg of internal energy in the form of neutron star vibrations. These vibrations rapidly carry energy to the upper crust and atmosphere, where the oscillations of the magnetic field anchored in the stellar surface accelerate atmospheric particles to temperatures ~ i0~°K.Many electron—positron pairs are created, and the hot, radiation-dominated plasma attempts to expand outward. The resulting compression of the magnetic field leads to rapid cooling by synchrotron radiation, followed by pair annihilation. For magnetic fields ~10h1 G, the particles cool faster than they can be annihilated, and their energy is radiated as photons of tens of keV. The emitted spectrum escapes from a layer whose width is less than the mean free path to photon—photon pair production. (When the magnetic field is ~10h1 G and the pair density is ——2 x 1026 cm3, the width of this transition layer is 0.1 mm [77]!)This spectrum consists of a combination of synchrotron and annihilation radiation. As fig. 18 shows, the predicted spectrum fits the spectrum of the impulsive phase of the March 5, 1979 burst incredibly well. The duration of this emission, which will continue as long as the driving vibrations persist, is also fortuitous. Gravitational radiation should damp the quadrupole and higher mode vibrations on a timescale between 0.1 and lOs [75].If this mechanism was responsible for the ~0.15 s duration of the burst peak, the implied mass of the neutron star is about 1—1.3 M 0 [75]. For a neutron star with this mass and a 10 km radius, the quadrupole vibrational frequency would be about 0.4 ms [75],which is too short to be resolved by the time resolution of present gamma-ray instruments. The authors suggest that the radial vibrations could be damped by the hyperon process, which has a 50 s decay time, the same as the characteristic time of the burst decay. There may be other energy losses, such as neutrino £

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I0~ I 10’ E 1MeV) Fig. 18. The spectrum predicted by the Ramaty et al. [77]emission mechanism is compared to the spectrum observed during the first 4 s of the March 5, 1979 gamma-ray transient. The calculated spectrum results from the synchrotron cooling and subsequent annihilation of e~—e pairs that are injected into a disordered 1011 G magnetic field with an initial kinetic energy of 3MeV [77].Taken from Ramaty et al. [77].

330

F Verger, Cosmic gamma -ray bursts

production, but if the initial energy release is large enough, only a small fraction need be converted into gamma-rays in order to produce the observed fluxes. Certain aspects of this model are a bit vague, requiring clarification. In addition to the identity of the energy source, the nature and efficiency of the vibrational heating are also unspecified. The stability and confinement of the radiating layer, which are essential to the production of the desired spectral shape, should be proved. The 8s pulsations of the burst decay are not explained by this model.

5. Theories of gamma-ray bursts Cosmic gamma-ray bursts are the most enigmatic phenomenon in high-energy astrophysics. To some extent their ability to defy explanation has been a product of experimental difficulties: the bursts are rare, unpredictable, and require special observing equipment. Our sample of burst observations is small, and only now are specialized instruments being brought to bear on this problem. Even if this were not the case, some of the properties of gamma-ray bursts are difficult to reconcile within a single theoretical framework. Perhaps this is why the proposed burst scenarios are so diverse. There have been models that rely upon explosive mechanisms such as supernova shocks, evaporating black holes, and flare eruptions on a variety of stellar bodies. Many models employ a compact object which either undergoes accretion, has a collision, suffers a “glitch”, or a combination of the above. There are even exotic models that involve objects or events which are conceivable but unknown. During the first year following the initial report on gamma-ray bursts, a veritable host of scenarios was brought forth. I use the term “scenario” to describe an idea that is presented as an outline without detailed calculations. Malvin Ruderman [81]gave an excellent review at the 1974 Texas Symposium on Relativistic Astrophysics which not only covered the current ideas but also captured the flavor of the time. This period was followed by a lull of several years in which there was little qualitative improvement in the data and few theoretical papers were written. The latter is not surprising, in light of the fact that almost every possible scenario permutation and/or combination had already been suggested in 1974. What remained to be done was to develop these scenarios to a level where their predictions could be accurately tested. That is not an easy task, as many of the scenarios are based upon inherently complex phenomena which do not readily lend themselves to detailed description. Thus the study of gamma-ray bursts appeared for a while to be at an impasse. Now, two new developments have brought fresh life to this field. One is the use of improved instrumentation with better time and spectral resolution. The other is the occurrence of the March 5, 1979 transient, an event which has done a great deal to revive interest in gamma-ray bursts. The past year or so has seen an upsurge in the number of gamma-ray models appearing in the journals and circulating as preprints. Most of these are geared towards a comparison with the features of the March 5, 1979 transient; special emphasis is given to those aspects of this event which the particular model can reproduce. In this section I briefly review those burst scenarios which still appear to be viable. The overall characteristics of certain model types are evaluated and specific examples are outlined. I have attempted to group these models into natural categories, but in any scheme some borderline cases are bound to appear. (If accretion occurs as the result of a flare, do you call it a flare model or an accretion model?) The first subsection of this section summarizes the criteria that a successful model must satisfy. Following this are five general classes of burst models which are subdivided where necessary. Lastly, I

F Verger, Cosmic gamma-ray bursts

331

have taken the liberty of trying to play bookie at the races*, and have given my odds on the winning gamma-ray burst model. 5.1. Constraints The following is a summary of the observational features that the bursts must reproduce and the theoretical limits on the intrinsic nature of the sources. (1) Burst properties (a) Emission Intensity: Based upon observed peak fluxes of about 10~erg cm2 s~,the source should be capable of producing a total gamma-ray luminosity of L = 1O~(d/pc)2 erg s~’where d is the source distance. (b) Rapid Fluctuations: We have seen that either the energy release mechanism or the emission environment responsible for the burst must be capable of producing strong fluctuations on timescales down to a ms. (c) Event Duration: The energy release should not last longer (or in the case of a relativistically expanding source, should not appear to last longer) than a time on the order of 100 s. (d) Frequency of Occurrence: The bursts must not only be brief and intense, but infrequent. The frequency vs intensity curve can be used as a guideline. It should also be rare to see recurring bursts from a given source within a 10-yr timespan. (e) Energy Spectrum: We expect the energy release as a function of wavelength to show little variation between bursts. The predicted spectrum need not be exactly the Cline and Desai fit, but something similar to it or to the power laws of Mazets and Golenetskii is most likely to be statistically consistent with the data. The characteristic burst energy should fall between 100 and 200 keV. (f) Line Emission: Since typical bursts do not exhibit any line features, either line emission does not escape from the source, or the properties of the lines are such that they cannot be detected by the spectrometers currently being used to study gamma-ray bursts. (2) Source size (a) Upper Bound: The timescales of the observed intensity fluctuations can be used to set an upper bound on the dimension 1 of the emitting region. For an isotropically emitting source, 1 ~ l0~cm

for nonrelativistic internal motions

1

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It is possible to construct situations in which these limits do not apply (p. 301). (b) Lower Bound: It is also sometimes possible to set a lower bound on the size of the emitting region, although in this case the limit is dependent upon other source parameters. The limit applies [81] when the mean energies of the gamma-rays and of the electrons that emit them, when compared in the proper (comoving) frame of the radiator, are roughly equal: is the observed, or laboratory frame, photon energy.) This is generally the case for thermal equilibrium, bremsstrahlung, or (EC)

*

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This analogy is inspired by a similar forecast that concluded Malvin Ruderman’s 1974 review of gamma-ray burst theories [81].

332

F Verger, Cosmic gamma-ray bursts

hot-spot models, and is approximately true in the relativistic shock wave of an expanding supernova. The condition does not hold for synchrotron or curvature radiation, where (Ee> ~ (E,,). When electron and photon energies are comparable, self-absorption limits the maximum gamma-ray luminosity to approximately the value it has for blackbody radiation at a temperature T given by kT (Es). Stefan’s Law can be used to express this limit as L ~ 4ir12a ((E~,,)/ky)4,where I is the radius of the source, and o and k are the Stefan—Boltzmann and Boltzmann constants. Note that the luminosity L is independent of the observer’s reference frame. Since L is unknown, it must be written in terms of the observed flux S and the source distance d. The resulting lower bound on the size of the emitting region is —-.

1 ~ (ykRE,,))2(S/o~)”2dcm. Applied to a nonrelativistic (y 1) source with (E,,) erg cm2 and kpc, •this becomes I ~ io~ S112d cm.

=

150 keY, and taking the units of S and d to be

(3) Spatial distribution of burst sources The celestial coordinates of the source objects should be distributed more or less isotropically. A graph of burst frequency N versus total observed flux S must be proportional to S312 for S ~ iO~erg cm~2,and be compatible with the experimental upper limits at lower intensities. (4) Magnetic fields Typical values of the intrinsic luminosity required for galactic and extragalactic gamma-ray burst sources are 10~and 10~erg s~,respectively [89]. If the energy release is occurring in the form of synchrotron emission, then for a source whose electrons have a Lorentz factor of = 1, the electron energy densities needed to produce this emission are 1011 and 1021 erg cm3. The emitting electrons must be constrained to spiral the field lines; therefore their energy density must be exceeded by the magnetic energy density B2/(8ir), and this implies minimum magnetic field strengths of B = 106 G for galactic sources and B = 1011 G for extragalactic ones. The only known objects with magnetic fields of this magnitude are neutron stars and a subclass of white dwarfs called magnetic white dwarfs. Most pulsar models take the surface magnetic field of a neutron star to be 1012_1013 G [80]. White dwarf radii are about iO~times larger than those of neutron stars, so if the ancestor of a neutron star were compressed only to the densities characterizing white dwarfs, the resulting stellar magnetic field would be 106_107 G, just the range of field strengths that is implied for magnetic white dwarfs. However, only a small fraction, less than 10%, of white dwarfs have measurable (>10~G) magnetic fields [80]. Not only are magnetic white dwarfs rare, but extremely relativistic (y 10~)electrons would be necessary if they are to produce synchrotron radiation at 100 keY. Neutron stars with fields >1012 G could produce sufficiently energetic photons even with nonrelativistic electrons. Hence it appears that neutron stars are the only known objects that could produce the luminosities of cosmic gamma-ray bursts in the form of synchrotron emission. A similar conclusion holds for the field strengths required by flare models of gamma-ray bursts, which convert energy in a stellar magnetic field into electron kinetic energy. Unless the radiation is beamed, thus reducing the amount of energy demanded from the source, the flare magnetic field would have to be ~106G [81].This is discussed in section 5.5. ~‘

——

F Verter, Cosmic gamma-ray bursts

333

5.2. Extragalactic models The farther away a source is placed, the greater the intrinsic luminosity it needs in order to reproduce the observed energy fluxes. Gamma-ray bursts temporarily outshine all other celestial sources of gamma radiation by several orders of magnitude [89].Hence at extragalactic distance scales their energy requirements are enormous. In many models, high luminosities are incompatible with some of the other source requirements imposed by burst observations. By making certain assumptions about the nature of the emitting region, it is possible to set upper and lower bounds upon the size of the source volume. While the upper bound is a fixed limit, the lower bound rises in proportion to the square root of the luminosity of the source 332). For extragalactic objects the two limits are so close that they almost completely eliminate the possibility of observing intense sub-pulses from sources outside our galaxy. In addition, the combination of a small source volume with a high luminosity produces a situation in which the source is likely to be optically thick as a result of photon—photon pair production. All of these arguments are dependent upon the emission mechanism and the geometry of the source. Ramaty et al. [75,77] have shown that, if one is sufficiently clever, it is possible to devise a scenario that avoids all of these pitfalls. It is difficult to reconcile the spatial distribution of extragalactic material with gamma-ray burst observations. Suppose that the density of burst sources, which are assumed to be identical, is proportional to the mass density of galaxies. In order to encompass sufficient mass to reproduce the N(S) S3”2 behavior observed for S ? 5 X iO~erg cm2, it is necessary to place the sources at least a few megaparsecs away. At these distances, the distribution of matter is much too inhomogeneous to produce the nearly isotropic source positions that we observe. Even at distances of tens of megaparsecs, the source directions would be dominated by the Virgo cluster and the flattened geometry of the local supercluster. In fact, it is now suspected that galaxy clustering exists on all scales [27], and that the superclusters themselves form structures separated by immense voids [11].If this is the case, it may be impossible to match the nearly isotropic arrival directions of gamma-ray bursts with any choice of extragalactic sources. Supposing that the large-scale distribution of galaxies is uniform enough to be compatible with the current accuracy of source locations, Usov and Chibisov [95] predict that the resulting N(S) curve is consistent with the upper limits on weak bursts. While N(S) S312 holds for galaxies at distances much smaller than c/H, where H is the Hubble constant, on larger scales relativistic and cosmological effects influence the observations. As a result, N(S) asymptotically approaches a constant value as S goes to zero. The departure from the S312 law occurs at the same flux level in all cosmological models in which the ratio of the mass of the universe to the minimum mass required to reverse its expansion is 1, although the value that N(S) asymptotically approaches varies between models. This conclusion would not be changed by allowing for source evolution. Because of this behavior, it is possible to satisfy the observational constraints on N(S) by choosing the source luminosity so that N(S) turns over below the upper limits set on the frequency of weak bursts. If N(S) is to begin to fall below the ~_3/2 law near S = 10~erg cm2, then the source energy must be 1052 erg [95]. It remains to find a mechanism that is capable of generating the enormous energy fluxes needed to power extragalactic models of typical gamma-ray bursts. If the observed events originate at cosmological distances, then burst sources are exceedingly rare and among the most luminous objects in the universe. The unusual gamma-ray burst of March 5, 1979 appears to have occurred in the Large Magellanic (p.

-~

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334

F Verger, Cosmic gamma-ray bursts

Cloud. If this source identification is correct, the peak of this event corresponds to a luminosity of 10~erg ~ Three other Yela bursts which consisted of very brief spikes are also consistent with the positions of nearby galaxies [15].It is possible that these short bursts constitute a distinct phenomenon which, unlike typical gamma-ray bursts, occur in nearby extragalactic systems. Cline [14] has pointed out that the Gamma Ray Observatory will be sensitive enough to detect events like the March 5, 1979 transient at the distance of the Virgo cluster. Assuming a production rate of one such event per decade per galactic mass, the GRO will detect events from the Virgo region on almost a daily basis [14]. 5.3. Accretion onto compact objects Compact objects are usually formed as end-products of the process of stellar evolution. Depending upon the initial mass of a star, its stellar core will finish its life as either a white dwarf, a neutron star, or a black hole. These compact objects have several properties which predispose them to consideration as gamma-ray burst sources. The temporal variations of gamma-ray bursts impose a 108_109 cm upper limit on the dimensions of the emitting region, a constraint which compact objects easily satisfy. And, because they are so dense, such objects can undergo structural adjustments on short dynamical timescales. The spatial distributions of compact objects seem to be compatible with the data on gamma-ray bursts. Little is known about the distribution of white dwarfs outside the solar neighborhood, and no certain black hole identifications exist to date, but dispersion measures indicate that for the pulsar distribution, the scale height perpendicular to the galactic disk is ~2S0pc [90].For this reason, Jennings and White [43] list pulsars and old neutron stars among the source candidates which are compatible with their models of the galactic distribution of burst sources (refer to section 3.1). These models, which are derived by matching the vs S graph of burst observations, predict burst rate densities ranging from 10_6 to 108 pc3 yr~[43]. Compare this to the number density of compact objects within the emitting volume. The local space density of white dwarfs, based upon a constant birthrate of about 2 x 10_12 yr~over the last 5 x iO~yrs [97],is flWD = 2.5 x 102 pc3. For pulsars, Taylor and Manchester [90] derived a local area density of N~= 90±15 kpc2. (This means that if all the pulsars in a column perpendicular to the galactic plane were projected onto the plane, there would be 90±15 pulsars in an area 1 kpc x 1 kpc centered on the Sun. This result was obtained using (fle) = 0.03 cm3.) More favorable statistics can be obtained by quoting Ostriker et al. [66],who estimated that the number of old, slowly spinning neutron stars which are no longer observable as pulsars is around flNS = 3 x 10_2 pc3 in the solar neighborhood. Adopting this density, and taking the frequency of events with a net flux above l0~erg cm2 to be 10 yr1, we predict an emission rate of 8 x iO~bursts per year per neutron star within 100 pc. This rate is in accord with the observation that almost none of the burst sources detected during the past decade has recurred. Finally, there is growing evidence that emission lines are sometimes present in gamma-ray bursts. The most popular interpretation of a line that has been observed several times near 420 keV (see table 3) is that it is a positron—electron annihilation line that has been redshifted from 511 keV. If the positrons were released near a compact object, this effect could be attributed to the gravitational redshift Vi— 2GM/c2R. Using this formula, the observed redshifts can be reproduced by substituting masses and radii appropriate to surface conditions on a neutron star. Given that the source of the observed gamma-ray bursts is a compact object, there are several reasons to suspect that gravitational accretion is involved in the process of burst generation. Lingenfelter et al. [58]have shown that gravitational accretion is a very efficient means of producing N

F Verger, Cosmic gamma-ray bursts

335

observable gamma-ray lines, because the mean ion energies resulting from this acceleration mechanism are much higher than the mean electron energy. Hence the nuclear line emissivity easily dominates the bremsstrahlung emission. Also, the amount of gravitational energy released by matter falling to the surface of a compact object is appreciable. For the case of a white dwarf, the maximum free fall energy of a nucleon is on the order of 1 MeV, while for a neutron star or black hole it is 100 MeV. On the basis of this energy release estimate and the scale height of the pulsar distribution, one can calculate how much mass must be accreted in order to reproduce the total fluxes observed in gamma-ray bursts. Suppose a compact object 100 pc away releases a iO~erg cm2 burst that lasts 1 s. The required source luminosity, iO~erg s’, can be attained if 1019 g is accreted onto a white dwarf, or if —i0’~g falls onto a neutron star. The simplest case to treat is spherically symmetric accretion, and in this situation both white dwarfs and neutron stars are very efficient at converting gravitational energy into radiation [53]. But in the absence of an accretion disk, black holes perform this conversion with a very low efficiency [53], so considerably more mass would be needed to generate a given luminosity by spherically symmetric accretion onto a black hole. Another incentive for considering accretion as the energy source of gamma-ray bursts is the comparison with compact X-ray sources, which are powered by this mechanism. The source luminosity we are demanding, around 1037_l038 erg is just the value that is observed in these X-ray sources. Section 2.3 of this paper contains a discussion ruling out the association of gamma-ray transients with X-ray burst sources. Still, the possibility remains that the gamma-ray events occur in binary systems where the steady X-ray emission is low enough to satisfy the constraints suggested by the few X-ray observations we have of gamma-ray burst sources [38,99]. The energy spectra of gamma-ray transients are not too different from those of accreting binary X-ray sources [53,60], though their characteristic energies are 3 to 10 times higher. Accretion can be steady or sporadic, fed by mass from a binary companion or gas in the interstellar medium. Isolated neutron stars moving at about 100 km ~ through an ionized gas containing 10_24 g cm3 are likely to accrete matter at the rate of —iO~M®/101°yr [82].This is not adequate to supply the energy needs derived for gamma-ray bursts on compact objects, so an additional source of material is needed. This usually leads to the postulate that the compact object obtains the accreted mass from a companion star in a binary system, although the collision models [37,64] are exceptions to this rule. The companion star may eject mass in a stellar wind, or its outer layers may be pulled off as the star expands beyond its Roche lobe. The latter possibility is the more probable one in a binary system containing a compact object. Even when viewed from its binary companion, the compact object subtends only a fraction of a solid angle, so the primary star would need a very high rate of wind-driven mass loss in order to supply the compact object with enough material to release the energy content of a burst. Mass loss rates of 10_8 M 0yr~[102] are typical for supergiant stars (M ~ 20 M0), but the duration of this mass transfer phase is
—

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336

F Verter, Cosmic gamma-ray bursts

inner structure of the disk. The exact form of this instability is impossible to predict, as the nature of the viscosity acting in accretion disks has long been one of the outstanding puzzles of high-energy astrophysics. Nevertheless, very sharp and luminous X-ray pulses with complex profiles have been observed in the emission from the binary X-ray source Cyg X-1, the leading black hole candidate [81]. Peaks of this type are not observed from more typical X-ray binaries; this is demonstrated in fig. 19 by comparing a temporal profile of Cyg X-1 emission with the output of two other binary X-ray sources. The narrow spikes emitted by Cyg X-i are attributed to turbulence near the inner edge of the accretion disk, where temperatures are hottest and the rotation period is ~s [81]. Tentatively, it seems that we can associate “millisecond variability” [65]with accreting black holes. This is evidence in favor of an accretion model, since rise times on the order of a millisecond are observed in gamma-ray bursts. When a compact object possesses a strong magnetic field, infalling material is channeled along its field lines so that accretion occurs primarily at the magnetic poles. For large mass influxes, the shocked gas piled above the magnetosphere can become Rayleigh—Taylor unstable, dropping suddenly to the surface [65].Other problems develop if non-adiabatic flow is considered. In general, it appears that each complicating effect pertaining to the accretion process can lead to the onset of one or more instabilities [65]. The characteristic timescales of these disturbances are roughly the free fall times from the radii characterizing the various effects. All of the flow conditions that have been investigated so far are unstable for the likely values of the physical parameters [65]. Hence, temporary behaviors of various types may prove to be the norm for systems undergoing accretion. ——

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E

SECON OS

Fig. 19. The X-ray emission from three binary X-ray sources are displayed here on a single time base. Her X-1 and Cyg X-3 are believed to contain neutron stars, but the unseen companion in the Cyg X-1 system is so massive that it is thought to be a black hole. Only Cyg X-1 displays sharp peaks that are well above the noise level. Taken from Ruderman [811.

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Though gamma-ray bursts might be attributed to any one of the many instabilities that afflict steady accretion, there remains the alternative possibility that bursts are generated during episodes of sporadic accretion. In this case, the accreted material will probably fall directly onto the compact object without forming a disk. The relevant burst timescale may then be the free fall time from the accretion radius or the magnetosphere, whichever is less. For example, a point mass falling onto a white dwarf or neutron star would take between 0.1—1 s to travel from the magnetosphere to the surface [53].The sudden mass influx could be caused by a flare on a binary companion [53], or by a collision with a stray body deflected towards the compact object [37,64]. Finally, a gamma-ray burst might be triggered by a change in the compact object itself, rather than in its environment. Specifically, pulsars are known to abruptly and unexpectedly alter their rotation periods by small, but measurable amounts. The fractional change in the rotation rate ~ t~12/fl,is on the order of lObo in old pulsars [67, 81], but changes as large as iO~and 10_6 have been seen in the Crab and Vela pulsars, respectively [80]. The colloquial expression for these frequency jumps is “glitches”. They have yet to be explained by a satisfactory theory, although a number of models have been proposed [80].The most popular idea is that the pulsar experiences a starquake which reduces its moment of inertia, resulting in the observed spin-up. A competing scenario postulates that, due to a magnetospheric instability, some of the plasma that is usually held in corotation by the magnetic field is allowed to shift position. In either case, the magnetic field of the neutron star will be rearranged, giving rise to induced electric fields, Alfvén waves, and particle acceleration. A starquake could also excite acoustic vibrations which carry energy to the surface via a shock [26,75]. The total energy release is model-dependent, but should be at least 10~erg, and possibly much larger [67]. The fact that glitches are rare and unpredictable is also favorable to their association with gamma-ray bursts. Based upon the glitch rate observed in old pulsars [67], and the estimated local space density of old neutron stars [53,66], we can project that about 20 glitches occur each year among the old neutron stars within 20 Pc of the Sun. The distance to the Crab and Yela pulsars are much larger (1700 and 400 pc, respectively [1]), and this may explain why no gamma-ray bursts were observed in coincidence with their large glitches. The reader should by now be convinced that there is a plethora of situations in which accretion onto a compact object may be the cause of a gamma-ray burst. Few of these scenarios have been developed to the level of detailed predictions that can be tested against the observations. Such calculations are inhibited by both the inherent complexity of accretion, as well as the unknown status of certain relevant parameters. The remainder of this subsection is devoted to brief descriptions of those gamma-ray burst models which invoke accretion onto compact objects. Although this survey is intended to be comprehensive, there may be accidental omissions. The author accepts responsibility for this negligence, and also for the intentional exclusion of some models which were deemed too far-fetched. Black hole models The binary X-ray source Cyg X-i contains a compact object which is the leading candidate for identification as a black hole. It is therefore intriguing to note that Cyg X-1 falls within the error boxes of two gamma-ray bursts which occurred on March 15, 1971 and April 12, 1972. In the first case, the determination of the source direction is hampered by a temporary satellite timing error of exactly one second [89].If this error did not exist, the satellite arrival times would define a large source area centered 30 from Cyg X-1. Since Cyg X-1 is in the galactic plane, and the Yela source fields are several degrees across, the number of other possible sources in this field is enormous.

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Nevertheless, the source field is worth noting because this burst occurred during a period when Cyg X-1 was undergoing an unexpected change in its spectrum and intensity [35]. This change, which was basically a transition between two different steady emission states, took place over the course of about a month. However, Cyg X-1 is notorious for the diversity of its variable behaviors, which extended down to timescales of a millisecond, so it is not hard to imagine that a gamma-ray burst could have been superimposed upon this slower alteration. If that was the case, a model of the event should try to explain the relationship between the gamma-ray transient and the new radio source which appeared in Cyg X-i at the end of March, 1971 [35]. The April 12, 1972 burst also had a 6 s duration and a net flux of iO~erg cm2. Only three Yela satellites detected this event, so there are two possible source locations. Each is about 20 square degrees, and they are situated at the same galactic latitude about 40°apart. Cyg X-1 is 10 from the center of one of these source fields. The next gamma-ray burst detected in 1972 had a similar duration and intensity, but its source direction could not be determined. Although these events did not coincide with known changes in the emission of Cyg X-1, since the binary system was not monitored continuously in 1972, it is possible that brief variations were missed [71]. In April of 1975, Cyg X-1 was again undergoing a transition between steady emission states [71]. Two gamma-ray bursts were detected during this period, on April 22 and 26. Once more the duration of each was near 6s and the net flux near iO~erg cm2. Unfortunately, the directions of the burst sources are not known. To produce the fluxes observed in these events, a burst source at the distance of Cyg X-1 (~2.5kpc) would require a luminosity of 10~° erg s~1,or about 100 times the usual luminosity of the X-ray source. As to the burst mechanism, this particular binary system is likely to undergo sporadic accretion episodes, because the primary star fills 98% of its Roche lobe [81]. Hence only a small peturbation is necessary to send matter spilling over the equipotential surface and plunging onto the black hole. The evidence as it stands is purely circumstantial, but it tempts us to associate the X-ray transitions of Cyg X-1 with gamma-ray bursts. If any future gamma-ray bursts occur in Cyg X-1, they will be precisely localized by the interplanetary detector network, leaving no doubt of the source’s identity. Proving that Cyg X-1 is not a burst source would be more difficult, requiring observations over a long period of time. In general, rapidly rotating black holes can generate gamma-ray bursts by a variation of the Penrose Process that employs particle collisions. As first conceived by Penrose [70],the Penrose Process is a way of extracting rotational energy from a black hole by making use of the negative energy states in a region called the ergosphere. The inner boundary of the ergosphere is defined by the event horizon. The outer boundary is a surface called the static limit; observers within this boundary cannot remain stationary with respect to the asymptotically flat space at infinity, but must orbit the hole. (This phenomenon is referred to as the “dragging of inertial frames”.) Penrose devised a thought experiment in which a particle enters the ergosphere of a black hole and splits into two pieces: one piece falls through the horizon, while the other piece escapes back to infinity. In a local reference frame both of these particles will always have positive energy. But to an observer at infinity, it is possible for the swallowed particleto be in a negative energystate. This observer then believes that the escaping particle has gained energy at the expense of the black hole. In practice, Wald [96]has shown that the maximum ratio of energy to rest mass that can be attained by fragments created in this manner is not significantly larger than the maximum ratio available if the same break-up process occurs in flat space. Piran et al. [72]then pointed out that much higher energy gains could be achieved by a “4-body Penrose mechanism” in which two particles inside the ergosphere scatter off of each other. It is this mechanism which is used in the gamma-ray burst model developed by Piran and Shaham [71].

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In their model, collisions occur between radially infalling X-ray photons and plasma electrons rotating deep within the ergosphere. In the local reference frame, these collisions look like ordinary Compton scattering, but to an observer at infinity, the photons gain energy by deflecting the electrons into negative energy orbits. Unlike the idealized cases of isolated scattering, the presence of the rotating plasma prevents the electrons from falling into the black hole. The electromagnetic forces that couple the electrons to the protons in the plasma and to the embedded field will exert a torque that pulls them back into positive energy orbits. Now the same electrons can be scattered again. The net result of this repetitive process is that energy is drained from the plasma, instead of the rotating black hole. The main function of the black hole in this model is to provide a background metric that allows this energy extraction. In order to produce a gamma-ray burst, the optical depth in the ergosphere must be high enough to insure efficient scattering. Piran and Shaham [71]postulate that this condition is satisfied when there is an instability in the accretion disk around a black hole. The exact nature of the instability is not important, provided that material near the inner edge of the disk is sent into highly eccentric orbits with perihelia deep in the ergosphere. This peturbed plasma gradually loses energy and falls into the black hole. When that happens, the plasma is heated to high temperatures and emits bremsstrahlung radiation around a few tens to a few hundred keY. Some of this radiation undergoes the scattering process described and is boosted to energies between a few hundred keY and a few MeV (as measured by a distant observer). The escaping thermal radiation contributes to the lower energy portion of the emission spectrum, while the scattered photons provide a nonthermal high energy tail. The most important feature of the Piran and Shaham model is that the characteristic energy dependence of the predicted spectra is very similar to the observed power laws. The spectra in their paper, which are plotted with error bars representing the statistical errors in their calculations, look just like the gamma-ray burst spectra that are obtained from satellite-borne instruments. In fact, the way in which some of their points at higher energies sometimes fall off the smooth curve formed by the other points is reminiscent of those features in observed burst spectra which have been interpreted as broad emission lines. The Piran and Shaham spectra were calculated with a complicated Monte Carlo computer code devised by the authors. Because the energy of the scattered photons is obtained from the gravitational energy of the infalling plasma, their characteristic energy depends more on the mass of the electron than on the ambient temperature. This explains the relative constancy of spectra derived for different values of the model parameters. Most of the high energy photons escape at angles ~45° from the equatorial plane, so an observer at higher latitudes would only see the thermal emission component of the spectrum. This model also provides an explanation for the temporal structure of gamma-ray bursts. Assuming that a magnetic field is present, the rotating plasma is composed of blobs held together by magnetic forces. The rate at which these blobs fall into the black hole will not be constant. Consequently, the optical depth in the ergosphere, and hence the burst intensity, will fluctuate a great deal. When the optical depth is too low, few high energy photons are produced and the thermal component dominates the emission spectrum. If the optical depth becomes too high, excessive scattering thermalizes the high energy photons as well. Optimal spectra are obtained when the optical depth does not vary far from a value of 3 [71].The timescale of these variations is on the order of the light travel time across a blob of plasma. This can be estimated by using the balance of magnetic and gravitational forces to determine the typical size of a blob. Piran and Shaham [71]figure that most blobs are a few hundred meters across, implying light crossing times on the order of 10_6 s, much smaller than the most rapid fluctuations we have been able to measure. The overall burst duration is given by the time it takes the inner disk to completely collapse and be absorbed by the black hole. This is longer than the free-fall time but shorter

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than the time it would take material to cross this region by steady drift. A more accurate estimate cannot be made without a magnetohydrodynamic model which includes a description of the viscosity mechanism. As a test of their model, Piran and Shaham have used it to calculate the properties of Cyg X-1, comparing their results with the values obtained from the X-ray and optical data. To do this, they assume that the gamma-ray bursts whose source fields contain Cyg X-1 actually originated from that system. They then derive formulas expressing the source distance, the total mass accreted in a burst, and the total energy release as functions of the burst intensity and duration. This involves the approximation of many factors, such as the average scattering cross section, the efficiency of mass-toenergy conversion, the height-to-radius ratio of the inner accretion disk, the anisotropy of emission, etc., etc. Nevertheless, they find that their results are consistent with the parameter values obtained by other means. Neutron star models Lamb et al. [53] have recommended that stellar flares on a close binary companion be considered as a source of material collected during sporadic accretion episodes. There is some uncertainty over the burst rate that one can expect from this scenario. First of all, the fraction of neutron stars which occur in close binaries is open to debate. Secondly, our own Sun is the only star for which we have complete flare statistics. While the energy requirements of a gamma-ray burst demand a flare that would be large by solar standards, it is not reasonable to extrapolate the Sun’s behavior to that of a binary star of a different stellar type which is in close proximity to a compact object. Lastly, although the probability that the flare ejecta will be accreted is a simple geometrical problem, it is dependent upon the expulsion velocity and the binary separation. As a result of these difficulties, the likelihood of observing such an event cannot be predicted with any confidence. Another shortcoming of this scenario is that the authors have not developed a description of the infall history that could yield a prediction of the emission spectrum, so the origin of the 150 keY characteristic energy remains unresolved. A different sporadic accretion model proposed by Harwit and Salpeter [37] attributes gamma-ray bursts to collisions between neutron stars and comets. The wayward comets are thought to be escaped members of the original comet cloud belonging to the stellar progenitor of the neutron star. If most of the comets in this cloud spend the bulk of their lives at large distances from the star, as is the case in our own solar system, then they may not have been affected by the supernova explosion in which the neutron star was formed. Ever so often, a comet is deflected into an orbit with a small perihelion distance. When the inner turning point of this orbit is within the neutrons star’s Roche limit, located at a radius of i0~—iO’° cm [64], the comet will be completely disrupted by tidal forces. The resulting debris enters a set of orbits, some of which plunge directly onto the neutron star, while the remainder fall in after various time delays. This pattern of accretion produces the erratic temporal structure that is observed in gamma-ray bursts. It has been conveniently assumed that the mass of the accreted comet is 1017 g, just the quantity necessary to supply the energy release of a burst. The plausibility of this scenario is suspect; but without better knowledge of the masses and impact frequencies of comets we cannot dismiss the commet collision hypothesis. The idea that neutron stars emit gamma-ray bursts during sporadic encounters with small astronomical bodies has recently been the subject of renewed interest; though collisions with asteroids, rather than comets, are now in vogue. The preference for asteroids is a consequence of a new study on tidal disruption patterns, which showed that an object of high tensile strength, such as an iron asteroid, would produce a more desirable accretion pattern [64]. Depending upon the details of this disruption -~

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process, the duration of the main collision will be on the order of milliseconds to seconds [64]. Subsequent emission from remnant debris falling down the field lines of a magnetic dipole that is not aligned with the spin axis can create a pulsing decay like that seen in the March 5, 1979 burst. Newman and Cox [64]have used a one-dimensional hydrodynamic code including radiation diffusion to simulate a collision between a 1 M0 neutron star and a 1017 g spherical asteroid. They compared models with different parameters, finding that the composition of the asteroid is unimportant, and that initial velocities >iO~km s are needed to insure that the characteristic emission energy is above 20 keY [64]. The predicted luminosities are more than adequate to account for the observed burst fluxes, provided the colliding neutron stars are in the galactic disk. However, one is again faced with the question of how often such neutron stars are likely to collide with a large object. Newman and Cox estimated the space density of interstellar asteroids by assuming that all of the cosmic debris in the solar neighborhood is in the form of 1017 g asteroids. If that is the case, we can expect to see 10 bursts per year from neutron stars within 2 kpc. An interesting feature of this model is the predicted evolution of the burst spectrum. The hottest component of the spectrum is emitted by the central portion of the magnetic pole onto which the falling debris is channelled. During the main part of a burst, a great deal of material is piled above the pole and the central area is obscured. Towards the end of the accretion, the optical depth should become low enough for the central radiation to escape once more. Consequently, the observed spectrum will be harder at the onset of a burst, and perhaps near the end as well. This can easily be checked against the data, which so far do not exhibit a consistent pattern of spectral variation. The burst of Nov. 19, 1978 is a case in point. Two sharp spikes appear about and 8 seconds after the onset of this burst, and in each case the spectrum is softer during the peak [25]. Yet the main peak of this event is accompanied by spectral hardening [25],in direct conflict with the prediction of this model. Sporadic accretion might also be instigated by the sudden rearrangement of the magnetic field that occurs during a rotational glitch. One such circumstance was proposed by Strong and Klebesadel [89],in which a neutron star undergoing steady accretion builds up a “reservoir” of plasma suspended above the magnetic polar caps. This material is presumably held in equilibrium by the combined effects of gravitation, rotation, radiation pressure, and magnetic forces. If the neutron star suffers a glitch, the equilibrium is suddenly destroyed and the suspended material falls onto the stellar surface. In addition to the potential energy thereby released, particles may also be accelerated by the energy release of the glitch itself. For a glitch of relative magnitude ~ 10°, Pacini and Ruderman [67] estimate that particle acceleration along the field lines is insufficient to produce high energy curvature radiation. They do foresee gamma-ray emission from the dissipation of particle motions transverse to the magnetic field lines. Another example of the types of particle acceleration that are possible under these circumstances is the electron—positron “avalanche” described by Tsygan [94]. This phenomenon is a consequence of collisions between plasma falling onto a hot spot and photons rising from below. If a rising photon is scattered backwards by the falling plasma and forwards again by an accelerated electron—positron pair, its energy can be boosted above the pair production threshold. In this manner, a single pair in the vicinity of a spot whose luminosity is —3 x iO~erg can be responsible for the production of iO~ additional pairs [94]. Those pairs and photons which escape constitute the conversion of a significant portion of the plasma energy into gamma radiation. The avalanche mechanism works best when the hot spot has a high luminosity, preferably in excess of the Eddington limit. This is no problem if the accretion process is sporadic, especially if the plasma falls down in the form of optically thick blobs. Such is the case in the glitch scenario envisioned by Strong and Klebesadel [89]. 5

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5.4. Thermonuclear explosions There are a variety of conditions that can lead to a thermonuclear runaway in the surface layers of a neutron star. The resulting explosions have long been considered as possible sources of transient phenomena, particularly of X-ray bursts. In the past few years this suspicion has received strong support from the detailed numerical computations performed by Joss (see [45],and references therein). These calculations seem to indicate that most of the observed X-ray bursts resemble helium-burning flashes on accreting neutron stars: typical rise times, peak luminosities, effective black-body temperatures, decay properties, total emitted energies and recurrence intervals are all in agreement with this model [45]. It remains to consider whether the incorporation of a number of complicating effects that were excluded in J055’ models can alter the explosion parameters sufficiently to produce a gamma-ray burst. Any of the various accretion mechanisms discussed in section 5.3 can add to the mass of a neutron star. In most cases, the accreted material will be mainly hydrogen and helium, with only trace amounts of the heavier elements. (Those models invoking collisions with comets or iron asteroids are exceptions to this rule.) The continued addition of new mass gradually compresses the accreted matter until nuclear reactions can occur. Hence, the neutron core is surrounded by a series of concentric nuclear burning shells. A thermonuclear flash cannot occur in one of these shells unless the temperature and density of the burning layer are in an unstable regime. We are particularly interested in those conditions which will support explosive timescales s 1 s. This is not possible for 3H[82]. burning, but He and C nuclei can react this * High densities alone are not sufficient quickly when they are compressed to densities ~ 10~ g cm to drive explosive burning; the temperature of the burning zone must be high enough to influence the nuclear reaction rates. A minimum temperature of 108 °Kis needed to set off a He flash, and the temperature must be at least 3 times higher to start a C flash [82]. The preignition temperature is related to the accretion rate. This rate cannot be too slow, because even at low temperatures there is a gradual consumption of stored fuel by pycnonuclear burning. No explosion will ever occur unless the average accretion rate overcomes these losses. On the other hand, very high accretion rates would also be undesirable because then the shortened fusion timescale would not allow as much fuel to build up between explosions. The numerical models computed by J 055 accumulate ~..~1021g between explosions [45],using accretion rates of 3 x 1016 to 3 x iO’~g s~[82]. These models rely upon a number of simplifications, such as the use of spherically symmetric accretion, the neglect of all burning shells except the He shell, and the assumption that the core is in thermal equilibrium. Most importantly, the surface magnetic field is ignored. Ruderman [82] has speculated that very strong magnetic fields might have such a great effect upon the explosive behavior of the surface that the escaping photons would resemble a gamma-ray burst. J055 himself discounts this idea, arguing that a magnetic field would tend to stabilize the burning shells against thermonuclear flashes [45].As confirmation, he points to the fact that X-ray pulsars, which are widely believed to be accreting neutron stars with strong magnetic fields, do not exhibit gamma-ray bursts. It has also been suggested that gamma-ray bursts may correspond to thermonuclear explosions in the C burning shells of accreting neutron stars [102].The maximum amount of fuel that can be accumulated on a 1.4M0 neutron star prior to a C flash would release —i0~~ erg, whereas a He flash would produce at most 1038_1040 erg [82].However, more detailed calculations of heat transport in the surface layers of an accreting neutron star now show that a C flash would not emit a burst of high energy photons [45]. *

White dwarfs have been excluded from consideration because these densities are not reached in their Outer layers.

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Most of the work on thermonuclear explosions has been done with accretion models, but there may be other ways to initiate a nuclear runaway in the unburned fuel near the surface of a neutron star. Continued accretion will inevitably cause flashes to recur at intervals of several hours to days, which is a disadvantage to gamma-ray burst models. By contrast, a nuclear explosion which is triggered by a glitch mechanism would have just the right event rate. Bisnovatyi-Kogan and Chechëtkin [5]have provided such a model. The premise of their model is the existence of a nonequilibrium layer having an excess of free neutrons that is formed as the neutron star cools [6]. This layer is found between densities of 1010 and 3, at which the nuclei are in a crystal lattice. An explosion is generated when a starquake 1012 g cm thrusts material from this layer into a region where the density is below io~° g cm3. In fact, the layer in question might even be directly responsible for the starquake, because the inward diffusion of excess neutrons reduces the mass of the layer, and the crystal lattice strains to adjust to this change [6]. In any event, ordinary starquakes induced by the crustal strain of rotational slowdown [80]will do just as well. Once the neutron-rich matter finds itself at lower densities, it rapidly undergoes nuclear fission, throwing out rapid neutrons which initiate fission in other nuclei, and the resulting chain reaction produces an explosion. This in turn sets up a shock wave which propagates to the surface and may eject a cloud of reacting nuclei. The observed spectrum should consist of gamma-rays from this cloud and thermal radiation from the hot spot where it was ejected. Emission lines from excited nuclei will also be present. An interesting consequence of this scenario is that if the ejected cloud falls back onto the neutron star, a second burst will occur. This time, the energy release is primarily due to accretion, and consequently the spectrum should be softer. The authors propose that this is the explanation of those gamma-ray bursts in which the emission fades to the background level and then reappears 20—40 s later. (In section 2.1, I labelled these “double bursts” as type (c), in keeping with the notation devised by Mazets and Golenetskii [60].) This interpretation is worth checking, but at present we only have integrated spectra for such bursts. The spectral condition is fulfilled by the repeating bursts from the direction of the March 5, 1979 source, which are softer than the spectrum of the original event. [5]

5.5. Flare models In the early 1970’s it was noted [9,46, 81, 86] that gamma-ray bursts bear some resemblance to spikes of X-ray emission seen in solar flares, in that they are of the same timescale and similar spectral shape. This prompted the speculation that bursts are produced when nearby stars undergo “superfiares” in which gamma-rays are the predominant emission. Solar flare models postulate that a rearrangement of the surface magnetic field accelerates charged particles and results in radiation from bremsstrahlung, or synchrotron losses, or inverse Compton scattering. For superfiares, the large energy requirement implies a stellar magnetic field about i0~times stronger than that of the Sun, on the order of 106 G. This is much stronger than the field strengths of common late-type main-sequence stars, whose magnetic properties appear similar to those of the Sun. While surface fields as high as iO~G have been measured on magnetic white dwarfs, these objects compose only a small fractjon of the white dwarfs in the solar neighborhood [80]; their space density may not be high enough to account for the observed spatial distribution of gamma-ray burst sources. An additional difficulty is that conventional flare models cannot be directly extrapolated to white dwarfs because these dense stars may not have significant convection zones in their outer layers [81]. It has

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been suggested that the presence of an intense magnetic field might induce a convective instability [10], or that a thermal instability could trigger the annihilation of a neutral magnetic sheet [104]. The magnetic field strength needed to produce a large observed flux could be reduced by collimating the accelerated particles within a magnetic tube analogous to the transient giant coronal streamers seen on the Sun [9]. The energy decrease achieved by beaming the emission would be compensated by a commensurate increase in the rate of flare events per source object. These rates might be so high that repetitive sources would be noticed. Alternatively, strong surface fields would not be necessary if the conversion of magnetic to kinetic energy occurs deeper in the stellar atmosphere [10,46, 104]. None of the flare scenarios developed so far has been able to predict the emission spectrum of a burst, since this relies on detailed knowledge of the particles’ energy spectrum and their coupling to the magnetic field. It is clear, however, that all flare models expect gamma-ray bursts to be accompanied by optical and radio emission. In solar flares, the ratio of the total optical flux to that in hard X-rays is typically >1 [34]. The authors of superfiare models hope that the higher field strengths and particle energies postulated for burst events will increase the fraction of photons emitted as gamma-rays. Still, it will be difficult for these models to satisfy the constraint imposed by unsuccessful attempts to find optical or radio emission from gamma-ray bursts: at least 100 times as much energy must be released in hard X-rays as in optical photons [34]. Finally, a superfiare would probably accelerate protons as well as electrons. The resulting nuclear reactions would produce line emission (at 0.51, 2.2, 4.4 and 6.1 MeY) like that seen in solar flares. 5.6. Exotic models Nuclear goblins In the core of a very massive and dense star, gravitational forces can compress ordinary matter to such high densities that electrons and protons are pushed together, and a sea of neutrons at nuclear densities (~~~1014 g cm3) is formed. Under sufficiently high pressure, these neutrons will not decay. Fritz Zwicky was the first to consider the astronomical scenarios in which such nuclear matter might appear. He conceived of two characteristic configurations that would allow the existence of finite bodies at nuclear densities [105]: The first is a neutron star, a collapsed stellar core whose total internal gravitational energy is sufficient to keep the object bound. Neutron stars appear frequently in astronomical theory. The second configuration Zwicky called a “nuclear goblin” (sic). This is a body of nuclear density, at whose center a neutron is just stable under the gravitational pressure caused by the mass of the goblin. However, the goblin as a whole is only stable under such high external pressures as may be found in the cores of massive and/or very dense stars. The size of a goblin could in principle be as small as a single neutron or as large as a neutron star, but Zwicky predicted [106]that a typical goblin would have a mass of ~~1022 g confined within a diameter of —10 m. If a nuclear goblin in the core of a star is somehow perturbed so that it travels towards the surface, it will explode completely upon reaching a layer of sufficiently low pressure. The goblin travels easily through the stellar interior because it experiences very little viscous drag per unit mass. Since the decay energy of a single neutron is 780 keY, the explosive disintegration of a typical nuclear goblin would release 10~° erg. Hence Zwicky suggested that escaping goblins might be responsible for the outbursts seen on flare stars [105],or for cosmic gamma-ray bursts [106]. Suppose an exploding goblin releases a few percent of its energy content as gamma-rays. Then a gamma-ray burst with a total flux of iO~erg cm2 could be produced by an explosion occurring a few hundred pc away. This distance is compatible with both the observed spatial distribution of burst —

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positions and the space density of possible source objects. Unfortunately, such an event is likely to be observable in visible light as well. Even if the fraction of the energy converted to optical photons is as small as iO~,at a distance of 100 pc the apparent magnitude of this burst would be +10. There are no detailed calculations of the astronomical phenomena that might be produced by small bodies of nuclear matter. Zwicky’s contribution was to hypothesize their existence and compute their gross energetics. An indirect confirmation of his ideas is contained in the study of matter at nuclear densities performed by Hartle et al. [36]. This work examined those modifications to the structure of neutron stars that result from inserting certain corrections in the equation of state for nuclear matter. One of their models predicts that small agglomerations of nuclear matter, about the size of a golf ball, are stable in a high density environment. Given the possibility that “nuclear goblins” may exist, a decisive comparison with gamma-ray burst observations requires a thorough derivation of their behavior during explosive disintegration. A mechanism is needed which will convert the kinetic energy of the neutron decay products into radiation, predicting the spectrum and temporal structure of the resulting emission. Evaporating primordial black holes * A “black” hole of mass M (M is in g) emits a thermal spectrum of particles and radiation that corresponds to a temperature of 1.2 x 1026 M~°K.All species of particle—antiparticle pairs whose rest masses are below the energy corresponding to this temperature will be emitted. As a result of this energy loss, the black hole slowly loses mass, and it will have completely evaporated after a time r on the order of 10_26 M3 s. The only known mechanism for creating small black holes that would presently be in the final stages of explosive evaporation postulates the existence of certain conditions in the early universe; hence these black holes are dubbed primordial. If such primordial black holes exist, those with an original mass s5 x iO’~g have completely evaporated by now, but those of slightly greater initial mass have by now decayed to a mass of around 5 x 1014 g and are radiating energy at the rate of 2.5 x 10’~erg s~with a temperature of 20 MeY. Nine percent of this energy is emitted in a photon spectrum peaked at about 120 MeV. Observations of the isotropic gamma-ray background place an upper limit on the integrated emission of primordial black holes that corresponds to about 1 explosion pc~3 yrt [73].The upper limit on the local number density might be increased by a factor of up to 106 if the black holes are clustered in the halos of galaxies rather than uniformly distributed throughout the universe. Our present understanding of the particle interactions, and hence the energy spectrum of emission, during the final stages of black hole evaporation is vague. The fundamental problem is that the present field theory derivations of particle creation by black holes break down when strong interactions become important. Such interactions may shorten the lifetime of the black hole, relative to the formula r = 10_26 M3 s, for values of M < 1014 g. In any event, one expects that when the hole shrinks to some limiting mass, it will convert itself into a fireball of very heavy hadrons. There are two different approaches to treating these hadrons that are known [98]as nuclear democracy and the quark theory. In the nuclear democracy model, all hadrons are elementary particles that are emitted thermally like non-interacting point particles. The rate of emission would become infinite when the black hole got down to a mass of about 6.6 x 1013 g, corresponding to the “Hagedorn limiting temperature” of about 2 x 1012 °K[98].The resulting fireball would radiate away all its energy in a time of about iO~s, giving a burst of gamma-rays peaked around 250 MeV with a total energy of about 10~ergs. *

Except where otherwise indicated, the reference for this section is Page and Hawking [68].

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In the quark model, the hadrons are regarded as composite bodies made up of elementary particles called quarks, so that black holes smaller than 1014g emit individual quarks as non-interacting point particles. Between 10 and 30 percent of the rest-mass energyof the black holewould emerge as photons at around 500 (M/1014 g)~MeY. When the mass of the black hole got down to 1010 g, a burst of about iO~° photons at around 5 X 106 MeY would be released. Clearly, the gamma-ray bursts predicted by both of these models are far too energetic to be connected with those detected by the Vela satellites and similar instruments. The discovery of heavier elementary particles would not significantly alter these results. The rate of energy loss from a black hole hot enough to emit the heavy species would be increased, and consequently the initial mass of the primordial black holes now exploding could be larger. The final burst of emission would come at some mass intermediate between the Hagedorn mass, 6.6 x 1013 g, and 1010 g. If q is the ratio of the Hagedorn mass to this new limiting mass, then the number of photons emitted would be reduced by a factor of q2 while the energy of these photons is increased by a factor q. 5.7. The gamma-ray burst model voted most likely to succeed More than six years ago, Malvin Ruderman concluded a review of the various models that were then vying to explain gamma-ray bursts with the following odds on the winner [81]: “I would suggest Black Hole ridden by Accretion as the favorite in the race, with Glitch as a dark horse, if only because so many different horses and jockeys are riding under that name.” Today I would say that Neutron Star ridden by Accretion is in the lead by several preprints, and that Glitch is coming in second. If I wanted to hedge my bets, I would favor Black Hole ridden by Accretion as a long shot. The reasons for my prejudices are as follows: I think it is clear from the descriptions in this section that accretion onto a compact object is the most promising of the burst scenarios that have been devised. The accretion mechanisms seem capable of reproducing many of the observed features of gamma-ray bursts without either unduly straining the plausibility of the scenario or leaving important aspects of the burst process unexplained. Furthermore, within the general context of accretion schemes, many options are available. The compact object may be a black hole, a neutron star, or a white dwarf; the gamma-ray burst may be triggered by either an instability in a steady accretion flow, or a sudden episode of sporadic accretion. In the case of a neutron star, either of these trigger conditions may itself be brought on by a glitch. If the number of possible variations on a model is any measure of its feasibility, the accretion scenario is definitely in the lead. By this measure, I would also choose neutron stars as the most versatile of the candidates for the accreting compact object. The strong magnetic fields of these stars produce an environment in which a host of magnetohydrodynamic instabilities are possible, and the magnetic poles serve as natural channels for streaming plasma and radiation. Another advantage that neutron stars have over both black holes and white dwarfs is that the spatial distribution and number of galactic pulsars satisfy the requirements imposed by the N( diagram and the lack of burst recurrence, respectively. The galactic distributions of black holes and white dwarfs are much too uncertain to estimate their compatibility with these constraints. Finally, neutron stars seem the most likely objects to be observed S)

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undergoing accretion, as they are already believed to be responsible for a number of compact X-ray sources. It remains for me to justify my choice of “Accretion” over “Glitch” as the favored jockey of this Neutron Star. Not only are they riding identical horses, but Glitch can be regarded as a close relative to Accretion, since in many gamma-ray burst models the role of the glitch is to trigger an accretion instability. This is not always the case, though, so the two are not equivalent. Personally, I prefer accretion, mainly because it is a more well-understood phenomenon. Also, because I would like to see the galactic volume from which observed gamma-ray bursts emanate extending to a distance of about 2 kpc. This avoids requiring an uncomfortably high space density of source objects, ensuring that neutron stars are compatible with the required distribution. In the glitch model, this may conflict with the fact that no gamma-ray bursts were observed in coincidence with the recent large glitches of the Yela and Crab pulsars, at distances of 0.4 and 1.7 kpc, respectively [1]. Nevertheless, I cannot rule out Black Hole’s chances in this race, since the apparent coincidence of several gamma-ray bursts with X-ray transitions in Cyg X-1 is too intriguing to dismiss. Besides, what could be more appropriate than to have a “dark horse” named Black Hole? Acknowledgements The major debt I owe is to my mother, who typed every draft and two final forms of this paper with arthritic hands. I would also like to thank T.L. Cline, D. ter Haar, G.M. Heiligman, K. Hurley, and S. Margolis for their helpful discussions and invaluable criticisms. To those few who encouraged me in this project I offer my deep gratitude.

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