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Astron. Astrophys. 331, 121-146 (1998)

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6. Conclusions

We conclude that lightning capable of melting a significant fraction of solid material could indeed have occurred in the protosolar nebula. However, this requires some special conditions, which we briefly summarize.

1. We found that global electric fields strong enough to induce lightning could have been generated only if charge transfer processes operated in grain-grain collisions, which were much more effective than grain charging by the Elster-Geitel mechanism and by impact of gas phase ions and electrons on the grains.

2. The gas phase ionization rate has to be much lower than that usually assumed for molecular clouds and is required to be almost as low as that resulting from decay of long-lived radioactive elements trapped in the grains alone. Cosmic ray ionization has to be at most of this same magnitude.

3. Generation of strong electric fields is more likely if local ionization equilibrium did not obtain.

4. Strong electric fields can be generated more easily if precursors of chondrules were compact with a specific mass density not much lower that [FORMULA]. This condition does not necessarily mean that all precursors of chondrules had to be compact but at least a significant fraction of the mm to cm sized grains had to be sufficiently compact in addition to fluffy precursors of the chondrules.

5. For our models corresponding to the protosolar nebula near 1 A.U. the energy released in lightning strokes was found to be large enough to melt solid material. One possibility is that the solid material within a discharge channel melts, if the gas is heated up to the melting temperature of 1800 K (i.e. [FORMULA]) and the turbulent gas velocity is at least 0.5 per cent of the sound velocity. Another possibility is that the energy [FORMULA] released in a lightning stroke is 40 eV per [FORMULA] molecule (in accordance with assumptions by Horanyi et al. (1995)) and the turbulent gas velocity is as large as assumed by our standard parameters.

6. For our models corresponding to 5 A.U. lightning strokes capable of melting chondrules were found e.g. under the assumption that [FORMULA] and the turbulent gas velocity was at least of the order of 10 per cent of the sound velocity.

7. For the dust enriched subdisk we found that for our standard parameters and assuming [FORMULA], the energy released in a lightning stroke was much too low to melt chondrules. Our results indicate that chondrules might have been molten here also in lightning discharges, provided a significant fraction of big grains were cm sized massive particles with a specific density of [FORMULA].

8. If a much lower energy release within the lightning channel was sufficient to melt solid material as could be inferred from the work of Eisenhour & Buseck (1995), then the requirements are less stringent than those mentioned in 5 -7.

9. The occurrence frequency of lightning discharges was found to be large enough to affect a significant amount of material in the protosolar nebula for our models near 1 A.U. and for the dust enriched subdisk if [FORMULA].

10. For our models at 5 A.U. and for corresponding standard parameters only few per cent of the material in the nebula was affected during its lifetime if [FORMULA] is assumed. However, our calculations indicate that here, too, a large fraction of the volume of the nebula might have been heated sufficiently to melt chondrules if a significant fraction of dust consisted of cm sized grains with a specific mass density of order unity.

In the present paper we left out questions concerning time scales for heating and cooling of chondrules and their precursors, respectively, and size distributions of chondrules as expected from flash-heating by lightning discharges and their comparison with petrologic limits. Such questions have been treated by Horanyi et al. (1995) and in context with heating by radiation pulses by Eisenhour & Buseck (1995).

The identification of a sufficiently effective process for charge transfer between grains and a more rigorous justification of the assumption of a low gas phase ionization rate remain as the primary problems in the production of lightning in the protosolar nebula.

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© European Southern Observatory (ESO) 1998

Online publication: February 4, 1998