DISCUSSION

Following the BATSE's discovery the old galactic disk paradigm was practically eliminated as it was in a direct conflict with the observed distribution. The two competing distance scales emerged: one was the galactic corona and the other was cosmological. The nature of the arguments leading to these two possibilities was (and still is) very different.

There is no evidence in the BATSE (or any other) data which would point to the galactic corona as the site of gamma-ray bursters. The proposed distribution is unprecedented in that there is no other observed population of sources in that region. It requires the bursters to have constant space density out to a distance of at least 30 kiloparsecs away from the center, so that our 8 kiloparsec offset from the center would not be noticed. A typical burster is now supposed to be at kiloparsecs, a factor of 1,000 farther away than in the old galactic disk paradigm, and therefore it has to be times as luminous. All models ever developed for the disk paradigm are useless, including the models that so nicely explained the spectral lines reported by the GINGA team. The main problem faced with all coronal models is the need to explain their distribution, or more precisely how gamma-ray bursters come to be in an area where nothing else is. It is paradoxical that the galactic distribution proposed for the bursters is designed so as to erase any trace of the galactic origin in the observed distribution.

Ever since the extended corona was first proposed as the site for gamma-ray bursters the emphasis was on the radial extent and sphericity, hence the popularity of the very high velocity neutron stars which can go out as far as we please. But the really difficult problem with the coronal idea is not its outer extent, but the size of its inner core, the region over which the number density of the bursters has to be uniform, independent of location (Paczynski 1991, Hakkila et al. 1994, and references therein). In order not to see our 8 kiloparsec offset from the galactic center that core must be at least 30 kiloparsec in radius. In spite of the many papers written about the coronal models I am not aware of a satisfactory explanation of the extent of this uniform density region. The observed isotropy of the strong bursts (Atteia et al. 1987) combined with the observed radial uniformity of the PVO bursts (Fenimore et al. 1992, 1993, and references therein) demands that there is a region around us which has a constant number density of gamma-ray bursters. If that region is in our galaxy it must be at least 60 kiloparsecs in diameter. This is the most serious problem faced by any galactic corona model.

The nature of the problem is twofold. First, there is nothing else observed to have so extended constant density volume. Second, the galactic mass is concentrated to its center and this makes it very difficult, perhaps impossible, to design a theoretical distribution which could be made and kept uniform within such a big sphere.

The observed distribution is automatically satisfied if we adopt cosmological distance scale: all objects detectable at cosmological distances are distributed isotropically in the sky, and the number density of all of them appears to decrease at sufficiently large distances as a consequence of the redshift. The uniform density region in almost any cosmological scenario is a few Gigaparsec in extent. The observed distribution is the most important argument for the cosmological distance scale to gamma-ray bursters.

There are plenty of models, or rather very schematic scenarios for either distance scale. As the sources are clearly non-thermal the diversity of models is limited only by the skill and imagination of theoreticians. This is not a unique situation. To the contrary: this is a typical situation. It is pretty much the same with all other non-thermal sources, like radio pulsars or quasars, even though we know the distance to those objects. Once we have to abandon the constraints of thermal equilibrium and feel free to add magnetic fields, turbulence, relativistic particles, and other ``high energy'' ingredients, it is next to impossible to come up with a unique and highly quantitative description of what is going on. This is not to say that we should not try to invent new non-thermal models. In the process we find a large variety of interesting possibilities, and perhaps at some point we shall find a testable model which will turn out to be correct. I do not expect this to happen as long as we do not know for sure how far away the bursters are, and therefore we do not know what the energy requirements are. I am not aware of a single case in the history of astrophysics in which a distance to any non-thermal source was reliably established using any non-thermal emission models. Unfortunately, even when the distance is known it is still difficult or impossible to decide which non-thermal model is correct.

The distribution of radio pulsars in the sky, as well as the effect of the interstellar medium on the propagation of pulsar emission, revealed their distance almost instantly. Yet, we still do not have a quantitative model for their radio and gamma-ray emission. The distance to quasars was found when their emission line spectra revealed their redshifts, and some of them were found at the centers of galaxies. However, even though there is no longer a significant dispute over their distance, we still do not have a quantitative model of their non-thermal emission which extends from long wave radio to GeV gamma-rays. Of course there are plenty of models of radio pulsar and quasar emission, but none of them is generally accepted, and no consensus is in sight after three decades of hard work.

Perhaps the most devastating argument against using models to determine the distance scale is the history of gamma-ray bursts. As far as I can see the galactic disk origin with its distance scale of parsecs has been practically abandoned in spite of the fact that most theoreticians used to be convinced it was correct. More models were developed, and more theoretical papers were written for the distance of parsecs, than for all other distances combined. Yet, those models developed over almost two decades had to be abandoned because of the BATSE observations. In spite of so many very diverse possibilities no bursts were convincingly found to be at parsecs. I do not think the quality of models developed for the distance of kiloparsecs or Gigaparsec is any higher than was the quality of the disk models: none is nearly good enough to be really trusted. I am not aware of any reason why the physics of the new models is superior to the physics of the old models. My conclusion is that the models of gamma-ray bursters as currently available are useless for distance determination. Each model is designed to work at some particular distance, be it 100 parsecs, 100 kiloparsecs, or 1 Gigaparsec. In fact there are many competing models for every possible distance. Even when the distance is finally established by model independent means we still shall not know which model, if any, is correct, as is still the case for quasars.

How can one determine the distance if one does not know what it is that one tries to determine the distance to? In fact, this is how astronomy usually works. The stars were known for millenia and they were used for variety of purposes, from navigation to astrology, while nobody knew what they were, or even how far away they were. About 150 years ago the distance to the first star, 61 Cygni, was measured using the Earth's motion around the sun (Bessel 1838). Gradually, not only many stars had their distances measured, but also the size of the Galaxy was estimated. Still, it was not known what makes the stars shine, and no quantitative stellar models existed. Finally, some 60 years ago the energy of the stars was explained in terms of thermonuclear reactions and the first quantitative stellar models were built, often refining the distance.

When a new class of objects is discovered it is a standard procedure to estimate the distance from the observed distribution. It is always clear that if the sources are concentrated to the galactic plane or the galactic center then their distances must not be very different from a kiloparsec. If the distribution is isotropic then they must be either very close, at parsecs, or very far, more than Megaparsecs away. Often new types of objects, or even a diffuse background which may not be resolved into sources, are separated into galactic and extragalactic components on the basis of their sky distribution. The same procedure can be applied to gamma-ray bursts. And the verdict is: the distance scale seems to be cosmological. Has this been proven? Certainly not. Gamma-ray bursts are so enigmatic that in fact they may be a manifestation of an entirely unknown phenomenon, they may be events on an unknown and unprecedented type of objects, with a new and unprecedented distribution in space. We must have a truly firm determination of their distance before we may hope to understand what they are and how they burst.

What can be done to to prove the distance scale? Some steps have already been taken. The cosmological distance scale is suggested by the fact that the observed distribution is not only isotropic but also appears to be bounded. The latter effect comes about because the distant sources are supposed to be redshifted. If they are redshifted we should look for additional observational consequences, of which at least two are promising. First, the redshift affects not only the wavelength of every photon but also the apparent duration of every burst (Paczynski 1992, Piran 1992). Second, the spectra are not strict power laws, they are somewhat curved. Therefore, a redshifted spectrum should appear somewhat softer (Paczynski 1992). The time dilation effect was apparent in some correlations, but the possibility of the redshift interpretation was not noticed for a while (Kouveliotou et al. 1992, Paciesas et al 1992). Recently, both effects were reported to be present in the data (Lestrade et al 1992, Norris et al. 1994, 1995, Nemiroff et al. 1994, Wijers & Paczynski 1994) at approximately 4 level. Some doubts remain (Mitrofanov et al. 1994, Band 1994b, Fenimore & Bloom 1994) and it will take some time until the consensus is reached on the presence or absence of the effect, and on its interpretation. At this time the case for the presence of the cosmological redshift effect in the weak BATSE bursts looks promising, but it is not proven yet. The case for cosmological redshift will be stronger when the two methods, the time dilation and the spectral softening, are shown to agree.

What about a variety of arguments advanced against the cosmological distance scale? Let me list some of the more common. The lines reported by the GINGA experiment, and previously claimed by the KONUS as well as some other experiments, are a common objection to the cosmological distances. I think the reality of the lines is far from proven. Only two fully algorithmic searches were done for the lines: one for the SMM data (Messina & Share 1992), the other for the BATSE data (Palmer et al. 1994), and no line was found in either of the searches. All lines ever claimed were found using subjective human judgement, and at best a posteriori statistical analysis was performed.

Let us suppose the lines turn out to be real. There is no unique way to interpret them. For example, at least three papers were written pointing to gravitational femtolensing as a possible cause if the bursters are at cosmological distances (Gould 1992, Stanek et al. 1993, Ulmer & Goodman 1995). This explanation was never pushed very hard because the confidence in the reality of the lines is not very high. Why spend time explaining something which may not exist? In any case, the only models explaining the lines in terms of cyclotron absorption required the bursters to be at parsecs (cf. Lamb 1992, and references therein). None of those models can be adapted to work at either galactic corona or cosmological distance scales, as the bursting material is expected to expand relativistically in either of those two cases. If the lines are proven to exist a new explanation and new models have to be developed for any of the two distance scales currently under consideration. The lines, even if they exist, will not resolve the galactic corona vs cosmology controversy.

Huge energies required by cosmological gamma-ray bursts are often pointed out as a problem. This argument was often used in the past against the extragalactic distance to M31 and the cosmological distance to quasars. A term ``supernova'' was even invented many decades ago to ridicule the possibility that a stellar explosion observed in M31 as S Andromedae might be as powerful as required by the supposedly extragalactic origin. Today we know that supernovae are indeed very powerful, that M31 is another galaxy, outside of our own, and cosmological distances to the quasars are no longer seriously disputed.

I think it might be useful to point out that in astronomy ``large'' is not less plausible than ``small''. In fact, many types of objects and events are known to be possible only if they are ``astronomically large''. For example, it is well established that thermonuclear burning of hydrogen may be sustained in a self-gravitating object only if its mass is larger than grams. The only known neutrino bursts, those from supernovae, are on a scale of ergs, all released within seconds. Everything we know in our universe is very low on energy compared with the Big Bang. Incidentally, the term ``Big Bang'' was also invented to ridicule the concept. Therefore, the energetics of gamma-ray bursts is not a distance indicator and cannot be used against them being at cosmological distances.

The repetition is well established for the X-ray bursts and for the soft gamma repeaters (all three of them) but it is a controversial issue for gamma-ray bursts (cf. Band 1994a, and references therein). The repetition, if established, will be very important for the understanding of gamma-ray bursts, but it has no relation to the distance scale as long as we do not know what the gamma-ray bursters really are. For example, Ostriker (1992) thinks the bursters are at cosmological distances and he expects them to repeat.

A common feature of all anti-cosmological arguments is that all of them are model dependent. The author(s) always have some specific model in mind when a claim is made that the model could not possibly give rise to a burst at a distance of a few Gigaparsecs. And usually the argument is correct, but only for that particular model, or for a particular set of models. There never was a proof that no model could possibly produce a burst at any specific distance scale. Also, there never was a model that could quantitatively demonstrate that it must produce a burst. Notice, that even though so many sophisticated models were developed for the distance scale of parsecs, we have no observational evidence that there are any events of the type described with those models. My conclusion is: we have to admit we do not know what gamma-ray bursters are and we do not know what makes them burst. Therefore, if we want to determine their distance we must use a model independent method. And this is perfectly normal: this is how distances are established in astronomy.

There is a complication with the cosmological distance scale which should be mentioned here. All types of objects observed at cosmological distances, quasars, galaxies, and clusters of galaxies, are known to evolve: their typical luminosity and their number density observed at large redshifts are different than local. The population of gamma-ray bursters may also evolve. If there were no bursters in the early universe, then the observed distribution appears bounded because there are no bursters at large distances, and not because the redshift made the distant bursters very dim, and pushed them below the detection threshold. In this case the weakest BATSE events could be relatively nearby, and their redshifts may be too small to measure. What is interpreted as a redshift might instead be a consequence of evolution. This is a rather ugly possibility, but unfortunately it cannot be ruled out as long as we do not understand gamma-ray bursters. The case for cosmological redshift will be stronger when the time dilation and the spectral softening are found to be consistent with each other.