THEORETICAL MODELS



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THEORETICAL MODELS

When Ruderman (1975) presented his review of the newly discovered gamma-ray bursts at the Texas Symposium he noted there were more theories than the total number of bursts known at the time. This was a golden era for theorists: almost anything could be proposed. Ruderman noted that among all those speculations one was clearly missing: nobody had yet proposed that the bursts were caused by comets made of antimatter falling into white holes. Almost everything else was. In his recent reviews Nemiroff (1994a,b) compiled a list of over one hundred different theories. One does not have to know much about the subject to realize that if there is one correct theory of the bursts then all but one are wrong. One may continue this reasoning to note that if 99 out of 100 hundred published theories are wrong then most likely all 100 are wrong. In other words, the multitude of proposals is the weakness and not the strength of the field. All theories of gamma-ray bursts ever presented were speculative, yet, they served a useful purpose by exploring so many diverse possibilities.

Over the years people got tired with the original unrestricted freedom and a consensus emerged that gamma-ray bursts were some energetic phenomena on the surfaces of nearby neutron stars. There might have been a rational reason: the discovery of X-ray bursts which had some similarity to gamma-ray bursts. The story of X-ray bursts is one of the most spectacular success stories in modern astrophysics: a reasonable quantitative theory was developed within a year or two of their discovery, and it looks as good now as it did more than a decade ago (Joss & Rappaport 1984). What made that success possible?

First, the sky distribution of X-ray bursts as shown in Fig. 8 instantly reveals their galactic origin and firmly sets their distance scale at about 8 kiloparsecs. Their spectra are thermal, very closely approximated by the Planck curve. The peak luminosity is ergs per second, while the peak temperature is K. According to the last two numbers the radius of the source is kilometers. All this makes sense: 10 km is the radius of a neutron star, and erg/sec is the Eddington luminosity of a neutron star. A simple yet accurate model of a nuclear explosion followed. Also, the optical companion stars were found for many X-ray bursters. These companions provided the source of fresh nuclear fuel for the explosions.

The similarity between the X-ray bursts and the gamma-ray bursts is limited. Both have duration of the order of seconds. Both emit hard photons. So, one might relate them, at least initially. But then, there are mostly differences. The X-ray burst have thermal spectra that peak at about 6 keV. Gamma-ray bursts have very broad non-thermal spectra extending all the way from 1 keV to keV. X-ray bursts show a clear concentration to the galactic center, while gamma-ray bursts have isotropic sky distribution, as shown in Fig. 9. All X-ray bursts have similar intensity variation: fast rise and exponential decay, with a simple correlation between the peak intensity and the burst duration, while there is nothing regular about the intensity variation of gamma-ray bursts. X-ray bursts are known to repeat, while gamma-ray bursts either do not repeat or repeat very rarely.

A fair analogy of the similarities and differences between X-ray and gamma-ray bursts is offered by the similarities and differences between the stars and quasars. The stars and the quasars are unresolved sources of optical radiation, and at least some stars and some quasars are variable. Yet the stars have thermal spectra and are concentrated to the galactic plane and the galactic center, while the quasars have very broad, mostly non-thermal spectra and are distributed isotropically over the sky. Quantitative stellar models exist, and there is not much controversy except for some details. The models of stellar atmospheres are very well described with just a few parameters, the most important being the effective temperature. At this time there are many competing models of quasar emission, none of them really quantitative. Even the geometry of quasar structure is not known, except for rather crude description in terms of the so called ``unified models''. It is generally believed that there are supermassive black holes at the centers of quasars, but no proof exists, and none is in sight. There is no agreement about the origin of quasars, how long they live, and how they die. Recently, it has been found that many of them are not at the centers of galaxies, as it was generally believed just a year ago (Bahcall et al. 1994, 1995).

It is interesting to analogize the star - quasar comparison with the X-ray burst - gamma-ray burst comparison. It is well established that X-ray bursters are ordinary neutron stars emitting thermal spectra with the effective temperature K. It is equally well established that gamma-ray bursts, just like quasars, have very broad non-thermal spectra, and there is no direct evidence they have anything to do with any stars.

There are also three soft gamma repeaters known, and all three are associated with supernova remnants: two in our galaxy, and one in the Large Magellanic Cloud, as shown in Fig. 8 (cf. Kulkarni et al. 1994, Murakami et al. 1994, Vasisht et al. 1994, and references therein). These three objects were suggested to be neutron stars with ultra strong magnetic fields, in the range gauss (Duncan & Thompson 1992). Their peak luminosity is ergs per second (Kouveliotou et al. 1987, and references therein). The spectra look almost thermal, with most energy radiated at keV (Golenetskii et al. 1984, Paczynski 1992c, Fenimore et al. 1994), which is a factor higher than the peak of thermal spectra of X-ray bursts, and completely different than the broad non-thermal spectra of gamma-ray bursts, which extend to GeV energies (Hurley et al. 1994, and references therein). The soft gamma repeaters are super-Eddington events, times more luminous than X-ray bursts. The relation to gamma-ray bursts is unclear. A possible link is provided by the unique March 5, 1979 event (GB790305b) which is related to the repeater SGR 0526-66 in the Large Magellanic Cloud, and which had a peak luminosity in excess of ergs per second (Mazets et al. 1982, Fenimore et al. 1995, and references therein).

As their name implies the soft gamma repeaters repeat. Their intensity variations are very simple: a rapid rise followed by a rapid decline, with no large fluctuations. Their spectra, their intensity variations, their repetition and their sky distribution make them somewhat similar to X-ray bursts, but very different from gamma-ray bursts.

The discovery of X-ray bursts contributed to the popularity of the galactic neutron star hypothesis for gamma-ray bursts, but very soon the latter acquired the life of its own. At any particular time some types of models were fashionable. A few years later the old models were out of fashion, and some new models would be popular. There were common ingredients to most of them: magnetized neutron stars and some source of free energy that was to be released very rapidly. There were starquakes and comets falling onto the surface, phase transition deep under the surface, and nuggets of quark matter. And no consensus ever emerged as to the actual source of energy, or the physical process responsible for the observed emission.

Some spectral features in some bursts were interpreted as cyclotron lines or annihilation lines (Higdon & Lingenfelter 1990, and references therein). There was a lot of excitement when double lines were reported by the GINGA experiment (cf. Murakami et al 1992): two or three gamma-ray bursts had absorption lines at 20 keV and at 40 keV present for a small fraction of the burst's duration. These were interpreted as the fundamental and the first harmonic cyclotron lines in a field of gauss. Sophisticated models were developed to explain the lines in terms of neutron stars located at a distance parsecs, just right for the popular paradigm.

There was also a modest variety of models developed in the past for gamma-ray bursters at cosmological distances, i.e. at Gigaparsec (cf. Higdon & Lingenfelter 1990, Paczynski 1991, 1992, and references therein), and there were even more of those developed following BATSE's discovery of isotropy and inhomogeneity of the distribution (cf. Mészáros et al. 1994, and references therein). Perhaps the colliding neutron stars became the most popular cosmological model. Their main virtue was that they helped many researchers to overcome their prejudice against the cosmological distance scale, but it remains to be seen if they have any relation to the real bursters. I cannot stress more strongly that the validity of the colliding neutron star scenario has nothing to do with the distance scale - if it turns out to be irrelevant for gamma-ray bursters the case for cosmological distance scale will not be affected at all.

A possibility that gamma-ray bursters may be in the extended galactic corona was proposed many times in the past (Fishman et al. 1978, Jennings & White 1980, Jennings 1992, Shklovski & Mitrofanov 1985, Atteia & Hurley 1986). The popularity of the corona was intermediate between the galactic disk and cosmology, pretty much as the distance involved was also intermediate. Until recently no serious attempts were made to build physical models for the corona. Today, those who like the galactic origin relate gamma-ray bursters in the extended corona to the very high velocity neutron stars ejected from the galactic disk (Duncan & Thompson 1992, Li & Dermer 1992, Podsiadlowski et al. 1995). In this scenario the bursters are thought to be at the distance kiloparsecs.

More work was done on models bursting in the galactic disk, i.e. at parsecs, than on all other models combined. However, this distance scale is no longer considered acceptable. Next in number are cosmological models at Gigaparsec. Finally, there are the galactic corona models at kiloparsecs. The relevance, or rather irrelevance of all these models to the determination of the distance scale to real gamma-ray bursters will be discussed in the next section.



next up previous
Next: DISCUSSION Up: HOW FAR AWAY ARE Previous: DISTRIBUTIONS OF VARIOUS



Jerry Bonnell
Tue Jun 6 14:33:23 EDT 1995