6 Conclusions

The necessary condition to unequivocally determine position and flux with a multibeam technique is that the source is smaller than the beam sizes. We have developed a method to assess the burst source angular extent which requires data from four beams simultaneously. The qualitative method for three beams provides similar results, except for particular burst positions with respect to the beams. The method is based on the actually observed beams which are the convolution of the source brightness distribution to the beams patterns. The only assumptions made, for simplicity, are that the antenna beam patterns and the sources brightness distribution can be approximated to Gaussian functions. By means of simulations, we have shown that for sources of shape different than axially symmetric Gaussians, the expected error in position made by the inversion method, is of the same order or smaller than the observational uncertainties (about 5 arcsec), for a source of up 1 arcmin long. We also found that a sufficient "a priori'' criterion to compute position is to have a greater than 6% quotient between the lowest and the highest antenna temperatures. Finally, we demonstrate to be negligible any possible side lobe effect for levels as large as 10%.

The method was compared to the previously used approach, for the 48 GHz observation of the solar burst of 30 December 1990, 18:30 UT. This event has three successive major time structures with superimposed finer features. The half power width observed has shown variations with time, and indicated sources' angular extent small or comparable to the HPBW. The positions were then calculated. The difference in position computed by the previous method (Costa et al. 1995) ranges from 5 to 15 arcsec, increasing as the $HPW_{\rm O}$ increases.

The qualitative method to be used when burst data are available only for three beams can provide the angular extent and position determinations. The method is based on the ratio of antenna temperatures for the three beams, the contrast criterion, setting possible conditions for the burst size and position computations. This can be used successfully when the observed contrast is sufficiently high to define unambiguously that the source is small compared with the HPBW. This method was compared to the results obtained using four beams for the 30 December 1990 event.

The use of multiple beam technique for the instantaneous analysis of bursts angular extents and positions is a powerful tool for the investigation of the flaring processes, the locations and time development of different emissions. Assumptions about the physical nature of the radio emissions received might be added to the analysis of the data. For example, in certain cases it may be possible to separate burst emission components due to fast (non-thermal) and to slow (thermal) mechanisms, and multiple beam data analysis done accordingly. However this discussion is beyond the scope of the present paper, and will be the subject of other studies.

The new methods will have important applications in the analysis of the 48 GHz bursts recorded at Itapetinga in the period 1989-1994, most of them obtained only with three beams. A new 48 GHz system is presently being developed, and future observations will greatly benefit with the use of these improved methods. Another important application is directed to the new Solar Submm-wave Telescope, the SST project (Kaufmann et al. 1996) which, at its lower frequency of 210 GHz, will have an array of three beams separated at their 50% levels, and a fourth beam separated at the 10% level from other two beams.

Source equivalent angular extent are derived here just as a tool to check whether or not the sources are small compared to the antenna beams for the purpose of the position determination. However this magnitude might have potential for physical interpretation. This is being studied separately.

Acknowledgements

We wish to thank an anonymous referee whose comments were very helpful for the improvement and the clarity of the present study. We also gratefully acknowledge fruitful comments and suggestions given by A. Magun and K. Arzner from the Institute of Applied Physics (University of Bern, Switzerland).

Partial support for the present work was given by the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP, Brasil) through grants Nos. 93/3321-7, 96/06956-1 and 94/5957-9, and by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brasil) through grant No. 150087/96-9.

CRAAE, Centro de Rádio-Astronomia e Aplicações Espaciais, is a joint center between Mackenzie, INPE, USP and UNICAMP.