Before the launch of CGRO with its BATSE detectors in April, 1991, bursts were thought to originate on local (closer than 200 pc) neutron stars: bursts were explained as magnetospheric activity on such stars, and the absorption lines reported between 15 and 100 keV implied 1012 gauss fields, comparable to the fields observed on pulsars (spinning neutron stars). This hypothesis was built on a variety of arguments which were persuasive but hardly definitive.
The primary observations regarding the gamma-ray burst distance scale have been their spatial and intensity distributions; until recently there had been no definitive signatures in the observations of individual bursts. Because the observed intensity f is proportional to the inverse square of the distance d to the burst, and the volume out to this distance is proportional to the cube of the distance, we expect the number of bursts with an intensity greater than f to be N(>f) proportional to f-3/2 if the burst sources are distributed uniformly in three-dimensional Euclidean space. The argument holds for various types of bursts with different intrinsic intensities since each population contributes a power law distribution N(>f) proportional to f-3/2. Thus as long as the source distribution is uniform, the cumulative intensity distribution will be a -3/2 power law. Note that this argument applies to any intensity measure which varies as d-2; thus f can be the energy or photon fluence (total flux integrated over time) or the maximum energy or photon flux over any particular energy band. Burst detectors trigger on the number of photons detected in a given energy band over one or more accumulation timescales. Therefore the intensity measure most closely related to the detection process is the peak photon flux (ph s-1 cm-2) in this energy band.
The spatial distribution of bursts on the sky reveals the geometry of the source population. For example, a Galactic population is expected to favor the Galactic plane or center when bursts can be seen to distances of more than a few 100 pc, a typical scale height (i.e., the distance over which the density of a given constituent of the Galactic disk decreases perpendicular to the disk). Because it is very difficult to focus gamma-rays into images, other methods must be used to locate bursts. BATSE localizes bursts by comparing the rates in detectors with different orientations. The uncertainty of the resulting localization is typically 5 degrees or more (~2 degrees systematic error and a statistical uncertainty which decreases as the burst intensity increases), which is nonetheless sufficient to determine whether the bursts are isotropic or favor the Galactic plane or center. Strong bursts can be localized to arcminute uncertainties by comparing the arrival times of the burst signal at detectors spread throughout the solar system; thus far three interplanetary networks (IPNs) have operated over the past 25 years. Two detectors localize bursts to an annulus, three detectors to two points mirrored through the plane of the detectors, and four detectors can not only localize the burst to a point but can also set lower limits on the burst's distance. Since bursts were expected to be a Galactic phenomenon, the spatial distribution is typically quantified by moments (primarily dipole and quadrupole) in Galactic coordinates (although other coordinate systems, and coordinate-free moments have been considered).
Before BATSE, bursts were observed to be distributed isotropically, and the intensity distribution was the -3/2 power law expected for a homogeneous source population. This was consistent with the hypothesis that bursts originate on neutron stars in our immediate vicinity; according to this hypothesis detectors before BATSE were detecting bursts only out to distances less than the neutron star population's scale height. Balloon flights with prototype BATSE detectors showed that BATSE would find a cumulative intensity distribution flatter than the -3/2 power law at the faint end. The prediction was that the faint (and therefore distant) bursts would occur preferentially either in the Galactic plane or towards the Galactic center. This is analogous to observing an isotropic sprinkling of stars in the bright night sky above a city, and discovering the Milky Way in the dark countryside sky. What did BATSE actually observe?
The cumulative intensity distribution of the BATSE bursts can be approximated by two power laws, one with an index -3/2 at the bright end, and the other with an index of -0.8 at the faint end; BATSE has definitely seen beyond the region where bursts are distributed uniformly. However, contradicting the hypothesis that bursts originate in the Galactic plane, the spatial distribution is still consistent with isotropy! We are at the center of a bounded spherical source population.
Three explanations were advanced based on possible spheres centered on the earth. A very few scientists suggested bursts are a solar system phenomenon, perhaps occurring in the Oort Cloud. However, some preference for the orbital plane is expected, and no convincing mechanism was ever advanced.
A minority of those studying bursts proposed a population of sources in the Galactic halo. The scale of this halo distribution would have to be large enough to make our offset of 8.5 kpc from the Galactic center unobservable (1 kpc=3.1x1021 cm). Assuming the sources emit isotropically, the halo population cannot be too large or we would observe bursts from nearby galaxies (e.g., the Andromeda Galaxy, M31) which presumably also are surrounded by burst sources. While this hypothesis keeps bursts in the Galaxy, the distance scale is a thousand times greater than for the local disk hypothesis, the energy requirement has increased by a factor of a million, and all the pre-BATSE theories were essentially invalidated.
Finally, the majority of those who were willing to commit themselves placed bursts at cosmological distances. Since the universe is isotropic in the standard cosmology, this explanation automatically results in an isotropic burst distribution. The curvature of space very naturally produces the apparent decrease of burst sources at large distances without invoking an evolving source population (although the population undoubtedly does evolve). The distance scale is now 10 million times greater than for the pre-BATSE theories; the energy is therefore 100 trillion times greater. The required energy is of order 1051 ergs, or somewhat greater, which is about the binding energy of a neutron star. The favored scenario was the merger of two neutron stars, a cataclysmic event which destroys the source.
The burst distribution was shown to be isotropic yet homogenous within about half a year of BATSE's launch. Over the subsequent six years various controversies raged which were surrogates for the debate over the bursts' distance scale. For example, Wang and Lingenfelter (1993,1995) found that five bursts appeared to be clustered in time and space, while Quashnock and Lamb (1993) found an excess of bursts with small spatial separations; these two analyses suggested that bursts repeat. Because the amount of energy required for a cosmological origin almost necessitates a cataclysmic event which destroys the source, it is highly unlikely that cosmological sources would repeat. Also, since the sources are probably in galaxies, it seems implausible that only a small number of sources would be active at any time. Subsequent analysis disputed the significance of the observational evidence for repeaters; an improvement of BATSE's burst localization algorithm revised the burst positions and eliminated the apparent repetition signal.
If bursts are cosmological then their spectra should be redshifted and their lightcurves should undergo time dilation. Faint bursts are presumably further, and therefore should be more affected by these relativistic effects. The difficulty is that burst properties generally vary by orders of magnitude whereas the cosmological signatures are factor of 2 or 3 effects. In addition, intrinsic correlations between burst properties could mimic the cosmological signatures, and at most the observations can be shown to be consistent with the cosmological effect. That faint bursts have softer (lower average photon energy) spectra, consistent with a cosmological redshift, is uncontroversial. The debate has raged over the presence of time dilation, with small and improperly defined samples plaguing the analysis by both those who find an effect and those who do not. Initially Norris et al. (1993) found a strong time dilation signature; Mitrofanov et al. (1996) reported that this signature was absent in their analysis. Fenimore and Bloom (1995) showed that the apparent time dilation of bursts at a given redshift is diminished by spectral redshifting: temporal structure is "narrower" at high energy (i.e., spikes last longer at low energy as a result of spectral evolution), and the observed time dilation is reduced when this narrower structure is redshifted into the observed energy band. Using a variety of techniques, Norris and his colleagues continue to observe time dilation, although the effect is smaller than their initial report. Using a larger sample than before, Mitrofanov and his colleagues also find time dilation. It is currently not clear whether all the studies which find apparent time dilation are consistent.
A great deal of discussion focused on observations which could solve the mystery by testing the predictions of the various hypotheses. If bursts indeed occur outside of the Galactic plane where most of the absorbing gas is found (the K-shells of "metals" such as oxygen in the interstellar medium absorb X-rays below 1 keV), then bursts' X-ray spectra should have a low energy cutoff (assuming the intrinsic spectrum can be estimated). If bursts arise in large Galactic halos, then detectors about an order of magnitude more sensitive than BATSE should detect an excess towards nearby galaxies such as Andromeda. However, the greatest hope was placed in linking bursts with known astrophysical phenomena, primarily by finding a counterpart in another wavelength band. To that end, systems were developed to monitor the sky continuously (e.g., the Explosive Transient Camera---ETC---on Kitt Peak) or to respond rapidly to a burst (e.g., the Gamma-Ray Optical Counterpart Search Experiment---GROCSE---at Lawrence Livermore National Laboratory). These various projects filled in the three-dimensional space of: 1) the time since the burst; 2) the wavelength searched; and 3) the depth of the search. For many years only upper limits were reported. Great hope was placed in the High Energy Transient Explorer (HETE) which had coaligned gamma-ray, X-ray and ultraviolet detectors, the last two with spatial resolution. However, the launch vehicle failed to release HETE, and the mission was lost; the mission is being rebuilt with a soft X-ray detector replacing the ultraviolet camera.