3 Application to the flare of December 30, 1990

Figure 7: Time profiles of the 48 GHz antenna temperatures during the solar burst of December 30, 1990, as recorded by four beams of the Itapetinga antenna (beam 1, 2, 3 and 5; integration time 8 ms). The horizontal bars labeled by A, B, C indicate the time intervals for which fine time structures are shown in Fig. 4 (a, b, c)

To demonstrate the method developed here we concentrate on the solar burst of December 30, 1990. It is one of the very few events obtained at Itapetinga with more than three beams and it was analyzed in part by Costa et al. (1995). This event was associated with a SN/M1.2 solar flare which started at 18:29 UT at the heliographic position S09 W47 in the active region AR 6624 (SGD 1990). Figure 7 displays the 48 GHz radio emission time profiles, obtained by four beams (1, 2, 3, 5) of the Itapetinga antenna, between 18:28:40 and 18:30:20 UT. We have selected three time periods (A, B and C; see horizontal lines at the bottom) during which major time structures are observed, and for which the inferred convoluted beam angular extent and sources positions will be computed using the analytical solution of the system of Eqs. (8).

Figure 8: 48 GHz radio emission time profiles (top) as recorded by beam 5 and temporal evolution of the estimated values of the $HPW_{\rm O}$ (bottom) for time intervals A, B and C, shown in Fig. 7. The values of the $HPW_{\rm O}$ have been calculated assuming symmetrical Gaussian brightness distribution

Figure 9: Mean positions of the sources for the peaks labeled from 1 to 21 in Figs. 8 (a, b, c). The mean value is obtained by averaging the data during 400 ms around each peak. The size of the crosses correspond to two times the standard deviation. Peak 15 position was not determined because some antenna temperatures are bellow the 6% level

Figure 8 shows detailed antenna temperature time profiles for the periods A, B and C observed by the beam 5 (top). The values of the observed convolved beam, $HPW_{\rm O}$ (bottom) are calculated with the data of four beams as described in Sect. 2. Data plotted was taken with 8 ms time resolution except for the beginning of the event (up to 58 sec after 18:28:00 UT) where the time resolution was 32 ms. The "noise" patterns in the plots of $HPW_{\rm O}$ are the result of the system temperature fluctuations, which become more pronounced for small burst signal levels, at least in one of the four beams. We note that the variations in $HPW_{\rm O}$are considerably more pronounced than the noise, suggesting a genuine variation with time of the source (or source complex) angular extension. Due to the beamshape uncertainty a point source convolved with our beams might produce a $HPW_{\rm O}$ in the range from 102 to 136 arcsec. All the structures, except 15, seen in the event have $HPW_{\rm O}$ between 130 and 140 arcsec, which indicates that sources are small compared with our beams and then their positions can be determined unequivocally.

Figure 9 shows the calculated positions for peaks labeled in Fig. 8 (top). The size of the crosses corresponds to two times the standard deviation of positions determined within 400 ms intervals around the peaks. The positions of the peaks lay in a NE-SW strip, about 10 arcsec wide, 40 arcsec long, with peaks from structure A (Figs. 7, 8a) located eastwards. Position of peak 15 cannot be estimated because some of the antenna temperatures are below the limit of the 6% level respect to the maximum observed temperature.