There are billions of stars, galaxies and other objects in the sky. There are hundreds of different types of objects known to astronomers. But there are only a few distinctly different types of distributions known. Almost every year a new class of objects is found. But a fundamentally new distribution has not been found in decades.
Figure 2: The distribution of the 1143 galactic planetary nebulae (PN) is shown
in the galactic coordinates. The data was obtained from the CDS in Strasbourg
(V/84) and it is based on A. Acker et al. (1992). Notice the strong
concentration of objects toward the galactic plane, typical for the
distribution of distant stars.
All objects known to exist in the inner solar system are strongly concentrated to the ecliptic: the orbits of all planets, asteroids, zodiacal dust, comets in the Kuiper belt. At larger distances, between our inner solar system and the closest stars, the only known objects are the comets in the Oort cloud. Their distribution is almost spherical, but not exactly: their shape is affected by the tidal disturbances of our galaxy (Clarke et al. 1994). If the bursts came from the Oort cloud, then we should have seen by now the effect of these tidal distortions in the sky distribution of the bursts, and we have not. The Oort cloud comets have yet another property that makes them unacceptable as candidates for gamma-ray bursts: their number density varies with the distance, and it is not uniform anywhere.
Once we get out of the solar system we encounter nearby stars, which are distributed more or less uniformly in space, apart from their tendency to 'cluster' in binaries and multiple systems. The distribution over the sky is almost isotropic, as shown in Fig. 1. Some apparent clustering is due to non-uniformity of the search procedure.
When the more distant stars are placed in the sky map
their tendency to concentrate near the galactic plane becomes apparent:
since Galileo we know that the Milky Way is made of stars.
Among distant objects which are readily detected across the galaxy and
which are related to stars of moderate mass are the planetary nebulae,
the remnants of old red supergiants.
A few thousand years ago the extended envelopes of those former supergiants
flew away from their hosts at 
km/sec, and formed the ring like
nebulae which are named ``planetary''. The ones older than a few thousand
years expanded so much that they are too diffuse to see.
The nuclei of the nebulae, former cores of red supergiants,
are on their way to become white dwarfs. Planetary nebulae are
very bright, and readily discovered out to large distances.
Their concentration to the galactic plane demonstrates that
they belong to the galaxy (cf. Figure 2).
Figure 4: The distribution of the 160 galactic globular clusters (GLOB. CL.)
is shown in the galactic coordinates. The data was obtained from the CDS in
Strasbourg (VII/103) and it is based on R. Monella (1985). Notice the strong
concentration toward the galactic center of these typical galactic halo
objects.
What about the more violent, truly catastrophic stellar deaths known as supernova explosions? These blow huge bubbles in the surrounding interstellar medium forming nebulae known as supernova remnants. Their distribution in the sky is shown in Fig. 3, revealing a striking concentration toward the galactic plane.
There are also galactic halo objects in the astronomical inventory. The most extreme case of halo distribution known to date is offered by globular clusters. These are the oldest components of our galaxy, with nearly spherical distribution, reaching out to tens of kiloparsecs. Figure 4 shows their positions in the sky: a very strong concentration to the galactic center is striking. This is a general property of all known halo objects. Notice, that globular clusters are not distributed spherically around us, but they are almost spherically distributed around the galactic center. As we are 8 kiloparsecs away from the galactic center, we see them concentrated in that direction.
The more exotic objects, low mass X-ray binaries, show the same galactic pattern as shown in Fig. 5. These are neutron stars with solar type companions, and they clearly belong to our galaxy.
All these galactic objects: low mass X-ray binaries, globular clusters, supernova remnants, planetary nebulae and stars, have been detected in the nearby galaxies. This is a general property of all known galactic objects: none of them is specific to our galaxy only, all of them are also found in other galaxies, provided they are luminous enough to be detectable.
The distribution of nearby galaxies is shown in Fig. 6. Their clustering is very strong. In fact, almost all nearby galaxies are members of the Virgo cluster. Looking farther out we find that the more distant galaxies are still clustered but their overall distribution becomes more and more uniform. However, no optical or infrared survey has been deep enough to demonstrate directly that the distribution becomes truly homogeneous and isotropic. This is possible with radio surveys which detect very luminous and very rare radio galaxies and quasars. Because of their enormous radio power these objects are detected at truly cosmological distances, and even the brightest sources show an isotropic and random distribution over the sky, as presented in Fig. 7. Also, a sky map of over 60,000 radio sources is available as a beautiful poster from the National Radio Astronomy Observatory, based on the observations done by Gregory & Condon (1991). The majority of radio sources is distributed isotropically and randomly over the sky, and their distances are cosmological. A subset of radio sources is strongly concentrated to the Milky Way, and these belong to our galaxy.
Figure 6: The distribution of the 276 nearby galaxies in shown in galactic
coordinates. The data were obtained from the CDS in Strasbourg (VII/161)
and it is based on K.-H. Schmidt, T. Boller, & A. Priebe (1993). Notice
the highly irregular distribution concentrated on the nearby Virgo cluster.
Let us summarize our findings. Among the many types of objects there are only two which satisfy the condition that they are random (not clustered) and isotropic: these are the distributions of the nearby stars and the very distant extragalactic objects. Any intermediate distance scale reveals either the galactic structure or the local signature of the large scale structure of the universe. No exception is known! Of course this is nothing new. This was pointed out many times in the past (cf. van den Berg 1983, Paczynski 1991, and references therein). Now we are ready to consider the distribution of gamma-ray bursts.
Prior to the launch of the Compton Gamma Ray Observatory
it was already known that the gamma-ray bursts were distributed isotropically
over the sky (Atteia et al. 1987). Their positions were
measured using the interplanetary network of detectors. It was known that
the isotropic and random distribution in the sky was compatible
with only two distance scales at which other objects have been observed
to have such distribution: one smaller than 
parsecs, and the
other one larger than 
Megaparsecs, but nothing in between.
The radial distribution of the bursters was expected to
be uniform approximately out to the thickness of the galactic disk
in the first case, and approximately out to
the Hubble distance in the second case. These two vastly different
distance scales could be readily distinguished if very weak,
and therefore very distant bursts could be detected. In the galactic
hypothesis the sources more distant than parsecs were expected to
be concentrated to the galactic plane, while in the cosmological hypothesis
arbitrarily distant bursters were expected to remain isotropic.
What was known about the radial distribution of gamma-ray bursters in the pre-BATSE era? Initially there was a terrible confusion about the distribution of burst intensities. For some reason it was customary to present diagrams with the number of bursts as a function of so called ``fluence'', the total energy received from a given burst in all photons over the full duration of the burst. However, the bursts were detected not by measuring their fluence but rather by measuring the maximum count rate of photons in some restricted energy range. Therefore, fluence had very little to do with the burst detectability, and the distribution of the bursts according to their fluence should have never been used to make any inferences about the radial distribution of the bursters. Most unfortunately it was used for just this purpose during a whole decade. As very few bursts had low fluence it seemed that the observed distribution was bounded. One might think that this incorrect use of the observed fluence misled everybody to think that the bursters were at cosmological distances. Amazingly, only very few reached that conclusion, among them were Prilutskii & Usov (1975) and Paczynski (1986).
Figure 8: The distribution of the galactic X-ray bursters (XRB - filled
circles) and the three known soft gamma repeaters (SGR - open circles)
is shown in galactic coordinates. The data were obtained from
J. van Paradijs (1995). Notice the strong concentration
of sources toward the galactic plane and the galactic center.
A few years ago a number of investigators realized that not the fluence but the peak photon count rate should be used to study the space distribution (Mazets 1986, Paczynski & Long 1988, Schmidt et al. 1988). Once the correct measure of burst intensities was adopted it became apparent that there was no clear evidence for the ``edge'' effect in the pre-BATSE data: the bursters were distributed uniformly not only over the whole sky but also in distance. Therefore, there was no way to choose which of the two distance scales was correct, galactic or cosmological. Nevertheless, the galactic origin was favored by almost everybody on the basis of models to be discussed in the next section of this paper.
It was expected that BATSE, with its very high
sensitivity, should resolve the distance puzzle. Its huge detectors were
tested in balloon flights during which 
events should have been
detected if their distribution followed the 
law.
Instead only three were recorded (Meegan et al. 1985). It was clear that
the new detectors were so sensitive that they reached the ``edge''
of burst distribution, but with only three events nothing could be
said about the sky distribution. BATSE was designed to have not only
very high sensitivity, but also to be able to locate the bursts with
a precision of a few degrees. Therefore, it should be very easy for the
BATSE to check if the weak bursts are concentrated to the galactic
plane or are they isotropic, thereby definitely solving the puzzle
of their distance. Or so it seemed.
On September 23, 1991 the first results about the sky distribution
of weak bursts from the BATSE were presented at Annapolis, Maryland.
Their sky distribution was isotropic, yet the distribution of intensities
was approximately 
, a clear indication that the instrument
could see beyond the region filled uniformly with the bursters (Meegan
et al. 1992). At the instant the critical viewgraphs were shown, a large
fraction of the audience accepted them as a clear evidence of the cosmological
distance scale. Many participants
of that historic conference changed their opinion because no concentration
of the weak sources to the galactic plane was apparent in the BATSE data,
even though it was expected by almost all of them.
Nevertheless, some 50% of researchers have not changed their minds.