A METHOD FOR ARC-SECOND D E T E R M I N A T I O N OF SOLAR BURST EMISSION CENTERS W I T H H I G H T I M E R E S O L U T I O N AND SENSITIVITY AT 48 GHz J. E. R. C O S T A , E. C O R R E I A and E K A U F M A N N

Centro de Rddio Astronomia e AplicafOes Espaciais - CRAAE, Escola Polit~cnica - USP,, C.P. 61548, 05424-970, Sglo Paulo (SP), Brazil

and A. MAGUN and R. HERRMANN Institute of Applied Physics, Division of Solar Observations, University of Bern, CH-3012, Switzerland (Received 3 October, 1994; in revised form 17 February, 1995)

Abstract, A 48 GHz five-radiometer front end was installed at the Cassegrain focus of the 13.7-m Itapetinga antenna for the observation of solar bursts. The system works with five beam patterns partly overlapping. The five antenna temperatures are recorded with a temporal resolution of 1 millisecond, including time and antenna position. The ratios of the incoming antenna signals are used to determine the centroid of burst emission. Its coordinates are determined from groups of three receivers by using a least-square fit. In favourable observing conditions we obtain an angular accuracy of about 2 arc sec (r.m.s.), with a time resolution of 1 ms and a sensitivity of 0.05 s.f.u. The accuracy of the antenna tracking, the absolute pointing and the quality of radio seeing at Itapetinga are discussed. A preliminary analysis of an impulsive solar burst event is used to illustrate the capabilities of the method described here.

1. Introduction The microwave spectra of solar bursts are produced by gyro-synchrotron emission, radiated by mildly relativistic to relativistic electrons accelerated during the flare. For many solar events the emission becomes optically thin at shorter ram-waves (i.e., 48 GHz), which makes it very suitable for the investigation of the temporal evolution of the electron population during the impulsive phase. High spatial resolution has been obtained by using interferometers, such as the Very Large Array (VLA). This intefferometer records radio images at centimetric wavelengths with very good spatial resolution (of the order of 1 arc sec) at moderate time resolution (0.2 s) (Bastian et aL, 1994). BIMA (Berkeley-Illinois-Maryland millimeter array) has also been used as a 3-element interferometer to observe solar millimetric bursts with high sensitivity (Kundu et aL, 1994). Although its number of elements was insufficient to form an image and to determine source position, it has been successfully used to estimate the size and complexity of millimetric burst sources around 88 GHz with moderate temporal resolution (N 0.4 s). Solar bursts have shown structures with a duration less than 100 ms at short microwaves (Kaufmann et aL, 1980). Sub-second time structures have also been Solar Physics 159: 157-171, 1995. @ 1995 KluwerAcademic Publishers. Printed in Belgium.

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found at hard X-rays from the HXRBS experiment on SMM (Kiplinger et al., 1983) and have been later confirmed with the higher sensitivity hard X-ray data obtained by BATSE on board the GRO satellite (Machado et al., 1993) and around 100 keV by the PHEBUS experiment on the GRANAT satellite (Vilmer et al., 1994). Structured emission time profiles at microwave frequencies correlated with hard X-rays have been found and investigated (Takakura et al., 1983; Kaufmann et aL, 1985; Correia and Kaufmann, 1987). The complete analysis of the primary energy release and the further energy transport processes during a solar burst require high spatial and high time resolution. For the observation of these fine structures, a five-receiver/feed-horn focal array at 48 GHz was installed at the Cassegrain focus of the 13.7-m Itapetinga antenna, as the result of a cooperative program between the Institute of Applied Physics of Bern University, Switzerland, and the Centro de Rgdio-Astronomia e Aplica~6es Espaciais, Brazil (Georges et al., 1989; Herrmann et al., 1992). The system places five beams in the sky, partially overlapping. Sources smaller than one HPBW can be simultaneously observed by multiple beams and have their positions inferred from the antenna temperatures and knowledge of the beam patterns. In this paper we present a new method to use the multiple beam system for the determination of source positions. The method is based on a technique employed to investigate atmospheric radio seeing with a point source observed at the border of the beam pattern of a single dish (Stephansen, 1981). In order to determine the source position from multibeam observations we use an algorithm that compares the calibrated output intensities of beams pointing to a point source. Thus, it is possible to determine its spatial location with much better resolution than the halfpower beam width (HPBW) of a single beam, by using known beam shapes and converting the ratio of the measured flux densities into a position. A semi-analytical method was used to determine positions of bursting point sources (i.e., source sizes small compared to the half power beam width) in active regions. This method solves analytically a system of equations for gaussian beams. Another method was implemented by Herrmann et al. (1992) with a purely numerical algorithm for beams with arbitrary shapes. This method, although more general regarding the assumption of beam shapes, is by almost two orders of magnitude slower. It is well known that the gaussian beam approximation is adequate when the observed source (smaller than the half-power beam size) is not too far from the main lobe axis (for example, staying within the first nulls). The two methods were compared, and produced consistent results. We also will discuss results from solar limb observation in order to analyze the antenna tracking performance and the influence of atmospheric anomalous refraction.

ARC-SECOND LOCATION OF BURSTING EMISSION CENTERS AT 48 GHz

159

2. Instrumentation The system consists of five radiometers at 48 GHz with the feed-horns placed at the focus of the 13.7-m Itapetinga Cassegrain antenna. The system temperature for the five receivers ranged from 600 to 1000 K. The sensitivity for solar observations is set by the solar background temperature (about 2300 K of uncorrected antenna temperature), providing a sensitivity of about 0.05 s.f.u, at 500 MHz bandwidth and 1 ms time resolution. The use of the large Itapetinga radio telescope for solar observations was described by Kaufmann, Strauss, and Schaal (1982) and a description of the new 48 GHz multibeam system was given by Georges et al. (1989) and Herrmann et al. (1992). The 48 GHz multibeam system became operational late in 1989 and about 70 events have been recorded since then. Several observing campaigns were coordinated with, or coincident to, measurements made at other frequencies and energy ranges (such as the microwave observations by the Bern solar patrol radiotelescopes, image and spectrum by the VLA and OVRO interferometers, and at X-rays by experiments on board the GRO and Yohkoh satellites). The receivers placed at the antenna focus produce beams with a mean angular displacement of a bit more than 2 arc rain. The beams overlap each other partially. Figure l(a) shows the projection of the five beams in the sky. The white circles represent the angular extension of one HPBW (about 2 arc min). The absolute positions of the five beams in the sky are obtained from circular limb fitting of solar maps (Costa et al., 1986). The antenna tracking and pointing parameters have been determined by a procedure similar to that used for the Haystack antenna (Meeks et aL, 1968) by using the center of the Sun determined from best circular fits to the solar limb, at various elevations and azimuth angles. The absolute and relative accuracies are discussed in Section 4.

3. Basic Equations for Multi-Beam Observations 3.1.

DETERMINATION OF THE POSITION OF A POINT SOURCE

Assuming a point source with flux S, the antenna temperature TAj (00, ~0) observed with beam j is given by (e.g., Kraus, 1986)

TAj (0o,

= I;jPn5 (0o,

o)S ,

(1)

where 00 and ~0 are the source coordinates relative to the antenna axis, Pnj, the normalized antenna power pattern, and Kj represents the effective antenna aperture divided by the Boltzman constant. By using quiet-Sun and sky observations for all beams, the proportionality factors KA can be determined. Thus, the determination of the coordinates 00, ~0 can be done by inverting Equation (1):

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Fig. 1. Beam positions and error map. The white circles show the half-power angular extension of the five beams, with about 2 arc rain in diameter, plotted in a box of 4.0 x 3.6 arc rain (a). The gray-scaled maps show the errors of the emission-center positions determined from the difference between a simulated source position and the positions calculated by our method as a function of source flux density relative to the quiet-Sun level (8 s.f.u.). (a) shows the error map for a source with flux density 5 times the measured quiet-Sun flux density at 48 GHz, (b) is for 2.5, (c) is for 1.25 and (d) is for 0.63.

(00, 790) -= nj \

)

with p@l the inverse function of Pnj- Then, combining the antenna temperature of different pairs of beams, the flux S and the constant Kj can be eliminated, resulting in several equations for 00 and 79o. For a system of n b e a m s redundant information on the two variables 00 and 79o is available for n > 3. Thus, the errors involved in the determination of 00 and 79o that are due to uncertainties in TAj can be minimized. In order to use Equation (1) the b e a m patterns, P w , must be known. Scans of the planet Venus showed that the b e a m s are very well approximated b y a gaussian function up to 120 arc sec away f r o m their axis, where the p o w e r drops to about - 1 5 dB ( H e r r m a n n et al., 1992). Therefore, we assume that the antenna b e a m patterns can be approximated by a gaussian function, as follows:

ARC-SECOND LOCATION OF BURSTING EMISSION CENTERS AT 48 GHz

P ~ (00, ~0) = exp[-aj(O0 - AOj) 2 - bj(¢Po - A~j)2] ,

161 (2)

bj are related to the two HPBW of the beams and AOj, Acpj are the relative offsets of the beams in the 0 vs ~ plane. These parameters are well determined from observations of strong point sources such as major planets. Using beam k as a reference we obtain the ratios of TAj/TAx such as

where aj,

{ TAj "] =

In \~Ak J

--aj(O0 -- AOj)2 - bj(¢Po - A p j ) 2 + +ak(Oo - A0~) a + b~(po - A ~ ) 2 •

Since the measured temperatures TAj/TAk have statistical and systematic uncertainties, we minimize the difference between both sides of the above equation by using the least-square method: D } = [ln { T A j ~ + a j ( O 0 - A0j) 2 + b j ( ~ o - A p j ) 2 -

-ak(O0 - A0k) 2 - bk(~o - Acpk) 2] 2, where D j2 is the squared difference attributed to beam j. The total difference may incorporate a weighting function, wj (00, ~0), taking into account the beam pattern gradient at the source coordinates: n-1

D~wj(Oo, ~o) D2

=

j=l n--1

,

(3)

E wj(Oo, ~o) j=l

where the weight wj is defined as

wj(00, ~ 0 ) = - P n j (00, ~0)IVPn~ (0, ~)10=00,~=~,,

(4)

and IVPw (0, qo)[ is the absolute value of the beam pattern gradient. Shifts in angular position produce different amplitude changes depending on the angle with respect to the main lobe axis. For a gaussian beam pattern this dependence is not linear, being maximum where the gradient VP~j (00, ~0) is maximum, and minimum at angles close to the beam axis when the pattern becomes nearly flat. Therefore, a point source observed at the half power of the gaussian beam will allow a better determination of the source position. The first term in Equation (4) is the beam pattern, P~j, that is proportional to the observed receiver

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output, and the second term is its gradient VPnj (0, 7)) that weights the positional accuracy. We note that the gaussian shape of the beam represents only the response to the region within the main lobe. Therefore the weighting function wj decreases to zero for large source displacements from the beam axis due to Pnj. The solution for the minimum of D~ in Equation (3) is found by solving the system of equations

OD2 - - 0 00o '

OD2 - 0 . 07)0

(5)

The above system of two nonlinear equations can be easily solved using a numerical method such as the Newton-Raphson (e.g., Press et al., 1985). To determine the first guess of a position (00, 7)o), we set the weighting function equal to one and repeat the process with the above Equation (5) up to a certain level of convergence. The compact code for the determination of 00 and ~0 was implemented on an IBM-PC. A big advantage of the analytical method presented here is its very small processing time in comparison to the numerical method described by Herrmann et al. (1992). It can be 100 times faster depending on the array sizes set in Herrmann's method. However it cannot be used for arbitrary beam shapes. The two methods have shown that the results obtained are equal, with differences smaller than the predicted errors. The method presented here was tested by simulating a point source passing in front of the array of five beams covering an area of 4.0 × 3.6 arc min in a grid of 19 x 21 points. The time profiles that should be observed from this simulation were calculated with Equation (1) for the five beams. Random noise was added to the antenna temperatures in order to mimic the conditions of 48 GHz receiver outputs during actual solar observations. By using the five time profiles obtained from the simulation we calculated the source positions and compared the results to the original ones. The differences between them produced the spatial error distributions in Figure 1. Figures l(a) to l(d) show the error as a function of the source flux density (5, 2.5, 1.25, and 0.63 times the quiet-Sun level, respectively). The errors are smaller in the regions inside three contiguous beams as shown in the position labeled B in Figure l(a), that we call the baricenter of the 'triplet'. Three similar regions are identified for each 'triplet' as shown by the dark regions in Figures l(b) to l(d). The region labeled A in Figure l(a) presents errors bigger than the regions at the baricenters (like position B) due to the displacement of one of the elements of the 'triplet'. In other words, the region labeled A loses precision in one dimension. Inside the HPBW region of the beams (e.g., position labeled C) the errors increase due to the lower beam gradient and the larger distance of the other beams of the 'triplet'. Figure 2 sumarizes the errors as a function of the source flux density for the source positions labeled A, B, and C in Figure l(a). For flux levels above 5 s.f.u, the errors are smaller than 3 arc sec when the source is located at about the baricenter (position B in Figure l(a)), and errors of about

ARC-SECOND LOCATION OF BURSTING EMISSION CENTERS AT 48 GHz

163

100

~'10 m

o m

C

1

A B

0.]

i

0.1

,

i

i

i

i

iI

i

1 NORMALIZEDFLUX(in quiet sun units)

i

,

f

i

i

r

10

Fig. 2. Error in source position as a function of the burst flux density for the positions A, B and C s h o w n in Figure l(a).

10 arc sec for source position near the pattern maximum of one of the beams (e.g., position C in Figure l(a)). In practice, during the active region tracking previous to a burst, the brightest area is placed at a position nearly equidistant from the three central beam axis, or the baricenter (label B, Figure l(a)), where the beam pattern gradients are larger and provide the best sensitivity for the determination of the source position.

4. Burst Analysis 4.1. D Y N A M I C B U R S T MAP

In Figure 3 the intensity profiles of a solar burst on December 30, 1990, 18:29 UT, are shown as observed by four beams at 48 GHz. The positions of the emission centroids calculated for different times can be represented in what we call a dynamic burst map (Figure 4). The intensity in this map is proportional to the number of occurrences of a source for different positions within a selected time interval. It shows the most likely source position and its dispersion due to receiver noise and real position changes within the time interval of 8 s defined for fluxes above 8 s.f.u. The appearance of at least 2 separate source locations becomes obvious. As the method is based in the assumption of the beam profile convolved with a G-function, it allows us to invert the beam function to recover the coordinates of the bursts, under some limitations. Simple numerical tests of one-dimensional convolution have been done between two gaussian functions, one simulating the beam profile and the other representing a narrow source with variable width, in place of a ~%function. We obtained errors dependent on the source size and position

164

J.E.R. COSTAET AL. ITAPETINGA - 48 GHZ DECEMBER30, 1990 e l ~

1 __

2 0 6 2: ~

channel2

2

.~

.

~

channel3

e¢

5 ~i

c ~ h a n n e l

5,

1828:50 1829:00 1829:10 1829:20

UNIVERSAL TIME Fig. 3.

Time profiles of the December 30, 1990 burst at 18:29 UT measured by four beams at

48 GHz.

in relation to the beam center. Complex artificial situations of multiple large and narrow sources in simulations were tried, leading to inconclusive results. We should remember that the concept of burst position determination using multiple beams was conceived originally for single sources, smaller than one halfpower beamwidth. In practice, in order to avoid the use of our method for large or multiple sources (emitting at the same time) we may control the errors of the inferred positions from different beam triplets. Large disagreements, larger than one rms deviation, are found for large sources and/or multiple sources widely separated as was shown in the analysis of the May 9, 1991 burst by Herrmann et al. (1994b). Thus, the application of the method described here might become doubtful for more complicated situations, such as temporally unresolved multiple emitting sources and sources with angular sizes larger than 20% of the individual beam sizes (about 20 arc sec at 48 GHz). On the other hand, if there are several sources emitting nearly simultaneously in time with a separation of less than 20 arc sec, the method will give the position of the centroid of all sources, weighted by their relative intensities. The resulting emission centroid will stay inside an area delimited by the real positions of all sources.

ARC-SECOND LOCATION OF BURSTING EMISSION CENTERS AT 48 GHz

165

I T A P E T I N G A - 48 G H z 40

30 DECEMBER 1990

2: X ,.A

5

©

0

18:28:50.0 18:29:00.0 18:29:10.0 18:29:20.0 U N I V E R S A L TIME

Flux densities > 8 s.f.u.

f,s.., © Z

© V,< Z

-1

DYNAMIC BURST MAP 20 X 20 ARCSEC RIGHT ASCENSION OFFSETS (arcsee) Fig. 4. The upper plot shows the restored time profile of the event as it would be obtained by a single beam with HPBW much larger than the bursting area. The horizontal line marks the 8 s.f.u. level. The dynamic burst map (bottom) for fluxes above the 8 s.f.u level shows the distribution of the bursting emission centers obtained with a time resolution of 32 ms. The outermost contour is the e -1 level of the maximum in the distribution of source locations.

4.2.

RESTORATION OF THE TIME PROFILE

A s w e a r e t r a c k i n g a b u r s t i n g area, l o c a t e d s o m e w h e r e b e t w e e n the m u l t i p l e b e a m s , apparent movements

o f t h e c e n t r o i d o f e m i s s i o n w i l l l e a d to d i f f e r e n t c h a n g e s in

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J.E.R. COSTA ET AL.

the time profiles from various receiver outputs. Certain applications may require the knowledge of the total burst time profile. It can be restored by calculating the positions of the emission centroid and correcting the changes in the time profiles due to source shifts. The restored burst time profile is then equivalent to an observation carried out with a single beam with a size much larger than the bursting region. For the multlple beam patterns over the bursting area, the restored time profile is then the result of the emission time profiles from one or more sources convolved with the beam patterns. 4.3.

IRREGULAR ATMOSPHERIC TRANSMISSION AND TRACKING ACCURACY

The accuracy of positions of the burst centroids may be affected by irregular atmospheric transmission effects (seeing) and by tracking oscillations of the Itapetinga antenna. The radio seeing at ram-waves may cause important centroid shifts imposing limits on the absolute pointing accuracy (for a review see Stephansen, 1981). Using the Effelsberg telescope for anomalous refraction studies at 23 GHz, Altenhoff et al. ( 1987 ) found apparent source displacements up to 40 arc sec for oscillations with periods up to 30 s on cloudy days, and negligible effects on very clear days. Good tracking accuracy is an intrinsic characteristic of a radomeenclosed antenna like the Itapetinga's. The Itapetinga antenna tracking accuracy and possible atmospheric anomalous angular fluctuations were carefully studied by pointing the antenna to the solar limb. Its temperature gradient is so large that small shifts in positions, of the order of 1 arc sec, are easily measurable. The observations during very fine weather conditions showed that the tracking accuracy is better than 2 arc sec (r.m.s.). These sample data were obtained at 40 ° elevation. No detailed study was done on the fluctuations' dependence on elevation, which doesn't seem significant, based on qualitative evaluation of observations (Figure 5(a)). The anomalous refraction and other less known effects not detected by the encoders have been evaluated after the subtraction of the solar limb tracking fluctuations from the positions measured by the antenna encoders. The net combined angular deviations resulted in shifts with time scales larger than 0.5 s and amplitudes of about 1.3 arc sec r.m.s, for a day without clouds (Figure 5(c)). Since it is nearly impossible to have two or more beams tracking the solar limb at the same time, we cannot be sure whether or not the fluctuations are the same and simultaneous for all five beams. To produce significant different refraction effects on different beams the tropospheric irregularities should be smaller than the angular separation of the beams, possibly too small to be realistic. This is a controversial subject to be investigated separately. The absolute antenna pointing accuracy is determined by fitting the circular solar limb to solar scans as described by Costa, Homor, and Kaufmann (1986). The result is presented in Figure 6. A map is made up of 19 raster scans with a duration of 20 s each covering an area of 36 × 40 are min. The limb fitting method showed a typical rms error of about 5 arc sec for the center of

ARC-SECOND LOCATION OF BURSTING EMISSION CENTERS AT 48 GHz 5I/~

~- _~

167

limb'trackit~k ~

'

(a~

"g 0

0

I0

20

Relative Time (seconds)

Fig. 5. Performance of the Itapetinga antenna tracking: (a) relative position of solar limb as a function of time, (b) antenna position relative to the coordinates of the solar limb, (c) difference between encoder value and position of the solar limb. These data were obtained at 40 ° elevation.

the disc. Figure 6 presents the absolute pointing errors for 32 maps made during 4 days in June 1992. The azimuth pointing errors are comparable to the limb tracking accuracy of about 2 arc sec (Figure 5(c)). The elevation pointing errors include an unavoidable uncertainty in the determination of the effective sky refraction. The procedure to infer the refraction index in our tracking program is similar to that used at Haystack observatory (Meeks et al., 1968) but we noted that for elevation angles smaller than 20 ° the refraction is underestimated by more than about 10 arc sec (see Figure 6(b)). It is known that the tropospheric refraction derived from local humidity, temperature and pressure, may be highly uncertain, but this may be reduced with the development of a more appropriate tropospheric propagation model specific for Itapetinga. Finally, one last source of uncertainty in the position determination is due to the pre-burst background level determined before the onset of the burst for each receiver. They may exhibit a slow time variation throughout the burst duration which affects the absolute positions. 4.4. COMPARISON BETWEEN METHODS We compared the coordinates of burst centroids of emission derived by both methods, the numerical method given by Herrmann et al. (1992) and the present one, for two examples. The event of May 11, 1991 at 13:22 UT withpeak flux density of 70 s.f.u, was observed in the central region of the four beams, and the inferred coordinates were coincident by less than 1 arc sec for both methods. The burst of November 19, 1990 at 13:38 UT is more instructive to analyze the differences

168

J . E . R . C O S T A ET AL. ITAPETINGA

48 GHz

- ABSOLUTE

AZIMUTH ERROR

20

POINTING ELEVATION ERROR

I0 o

J <

0

.

•

•

•

•

•

-/

•

00

•

qDo •

~' -IC

rms = 2.4 arcsec "2C

t

aoo

t

,

t

,

T

3ao

,

+

,

(a) t

I

1

o

t

. . . .

]

3o

+

L

r

r

rms = 4.9 arcsec

,

60

,

ao

,

,

,

T

,

20

A Z I M U T H (degree)

,

(b) ,

,

I

ao

,

,

+

]

T

,

,

,

40

,

50

E L E V A T I O N (degree)

Fig. 6. The scatter diagram for the absolute pointing errors obtained from 32 solar maps during June of 1992; (a) elevation and (b) azimuth. between the two methods. It was observed well within one beam and only marginally by the others (see Figure 7(A)). The peak total flux was about 72 s.f.u. All five receivers (channels labeled 1-5) and the recovered time profile (labeled T) are presented in Figure 7(C). A complete analysis of the same burst was done by Herrmann et al. (1994a). Inspecting the time profiles of the five channels it is possible to note that there was a source displacement because the peaks of channel 3 differ in time from the peaks at the other channels. The arc-second position deviations between the two methods are presented in Figure 7(B) as a function of time. The differences in elevation are negligible and in azimuth they are rippled with a systematic mean difference of 7 arc sec. It can be understood from this figure that the flux density of the two most intense channels, 4 and 2, correspond to two beams almost aligned in azimuth (see Figure 7(A)) but shifted in elevation. However, channel 3 was too weak to allow a better calculation of the azimuth coordinates which produced the larger deviations in these positions (the larger ripple in Figure 7(B)). The mean displacement of about 7 arc sec in azimuth is attributed to the differences between the gaussian and the real beams for large angular distances from the beam center as shown by Herrmann et aL (1992).

5. Concluding R e m a r k s The 48 GHz multibeam solar experiment became operational late in 1989. Solar observations are carried out at Itapetinga, covering 2-3 months each year. The first results have shown that this experiment is a very powerful tool to determine the relative position of burst emission centers with an accuracy better than few

ARC-SECONDLOCATIONOF BURSTINGEMISSIONCENTERSAT 48 GHz

e.,

( ~ @ ( ~

burst site for first peak

~4 arcmin~

169

(A)

Azimuth 15.0

(B)

0.0

7.5 Elevation Difference(arcsec) -7.5

V

×

~hnnnol

(c)

>_ ,.a

Channel3

-

2bann,~k2 f"hnnnel

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f

-

-

-

.

-

~

~ I

1 - - I -

I

. I

.

~

-

13:38

-

&

-

,

I

13:39 UNIVERSAL TIME

Fig. 7. Comparison between methods for the November 19, 1990 solar burst as discussed in the text. (A) shows the five beam disposition in the azimuth and elevation system of coordinates. The asterisk denotes the inferred burst position at the time of the first peak. (B) shows the angular diferences between the two methods in arc sec. (C) shows the flux densities for the five beams indicated in (A). The label T in (C) stands for the recovered time profile as explained in Section 4.2.

arc s e c o n d s at a high time resolution and high sensitivity. T h e m e t h o d d i s c u s s e d to obtain the d y n a m i c burst m a p s p r o v e d to be an essential and fast tool for the analysis o f spatial features o f events at m m - w a v e l e n g t h s , and their t e m p o r a l

170

J.E.R. COSTAET AL.

behaviour. It was shown that the present method produces the same coodinates for the burst's centroid of emission for one example, and a systematic mean angular displacement for another example, compared to the method presented by Herrmann et al. (1992). The results demonstrate the quality of the antenna tracking and negligible effects due to tropospheric propagation anomalies. A complete and detailed analysis of the 30 December, 1990 event, with simultaneous observations made by the V L A and the OVRO intefferometers, will be published in the near future (Costa et aL, 1995).

Acknowledgements The Swiss National Science Foundation provided funds under grant 2 0 - 3 6 4 1 7 . 9 2 for the development of the 5 beam receivers and the fast data acquisition system. We thank R. Hadano for his technical assistance at Itapetinga Radio Observatory, and to J.L.M. do Vale and Eng. R. E. Schaal for the important discussions and help during the Itapetinga antenna tracking accuracy calibrations. FAPESP provided partial financial support for data analysis equipment under contract number 90/4780-7. C R A A E is a joint center formed by agreement between the National Space Institute INPE and the Universities of S. Paulo, Campinas and Mackenzie. We also thank an anonymous referee for his useful suggestions that improved our paper.

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p. 199. Correia, E. and Kaufmann, P.: 1987, Solar Phys. 111, 143. Costa, J. E. R., Homor, J. L., and Kaufmann, E: 1986, in E. Tandberg-Hanssen and H. S. Hudson (eds.), 'Solar Flares and Coronal Physics Using P/OF as a Research Tool', NASA Conf. Publ. 2421, p. 201. Costa, J. E. R., Gary, D., Bastian, T., and Kaufmann, P.: 1995, in preparation. Georges, C. B., Schaal, R. E., Costa, J. E. R., Kaufmann, E, and Magun, A.: 1989, in Proc. 2nd International Microwave Symposium, Rio de Janeiro, p. 447. Herrmann, R., Magun, A., Costa, J. E. R., Correia, E., and Kaufmann, R: 1992, Solar Phys. 142, 157. Herrmann, R., Rolli, E., Correia, E., and Costa, J. E. R.: 1994a, Solar Phys. 149, 155. Herrmann, R., Kaufmann, P., Machado, M. E., Correia, E., Costa, J. E. R., and Fishman, G. J.: 1994b, Astron. Astrophys., submitted. Kaufmann, P., Strauss, F. M., and Schaal, R. E.: 1982, SolarPhys. 78, 389. Kaufmann, P.,Strauss, F. M., Opher, R., and Laporte, C.: 1980,Astron. Astrophys. 87, 58. Kaufmann, P., Correia, E., Costa, J. E. R., Zodi Vaz, A. M., and Dennis, B. R.: 1985, Nature 313, 380. Kiplinger, A. L., Dennis, B. R., Emslie, A. G., Frost, K. J., and Orwig, L. E.: 1983,Astrophys. J. 265, L99. Kraus, J. D.: 1986, Radio Astronomy, McGraw Hill, Inc., New York, 2nd edition, Chapter 3.

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