Astron. Astrophys. 333, 1034-1042 (1998)

2. Observations

New observations of IMD bursts have been made with the very broadband Phoenix spectrometer of ETH Zurich in the 0.1 to 3 GHz range. Details on the instrumentation have been published by Benz et al. (1991). Here we report on the analysis of twelve events that have occurred in the years 1989 to 1993. Their date, time, and frequency of peak IMD activity are listed in Table 1. Since the flare trigger and the channel density were chosen to favor the 1-3 GHz region, all observed IMD bursts occurred above 1 GHz, reaching a maximum frequency of 2.6 GHz (Fig. 2). The frequency-agile spectrometer measured most of the time at 200 channels with a resolution of 10 MHz in frequency and 0.1 s in time. Flux density and circular polarization (Stokes I and V) were recorded. The data has been calibrated and analyed using the standard routines at ETH Zurich (Csillaghy 1997).

Table 1. List of analyzed events with Intermediate Drift fine structures: mean time and frequency of peak IMD activity, shift to peak continuum activity, and average parameters of bursts

2.1. The location of IMD bursts in the spectrogram

The broad bandwidth and the new, high-frequency range of the Phoenix spectrometer allowed for the first time to relate the IMD bursts to the associated type IV continuum event in the spectrogram. A typical example is shown in Fig. 1. In the top part, the total flux density is displayed on a logarithmic scale. The main part of the type IV event is an intense continuum centered at about 1100 MHz. A much weaker continuum extends up to 3000 MHz. It contains weak IMD structure in time and frequency. The IMD bursts in the high-frequency continuum have been enhanced by subtracting a gliding average of 200 MHz bandwidth in frequency and of 5 seconds in time(Fig. 1, bottom).

Fig. 1a and b. Top: Spectrogram of a decimetric type IV burst observed with the Phoenix radio spectrometer of ETH Zurich on March 20, 1993. The preburst background has been subtracted, and the greyscale is logarithmic. Bottom: The intermediate drift bursts have been enhanced by subtracting a gliding average in frequency and time.

The time and frequency of maximum IMD activity in each event is given in Table 1. We have also compared the position in frequency and time of the IMD pattern to the maximum of the continuum. The most significant new result is on the location of IMD burst in the spectrum. There is a significant trend for IMD patterns to occur at higher frequency than the spectral peak of the type IV continuum (positive shift). The maximum displacement was 610 MHz. Only in one of the 12 events the IMD bursts were found at clearly lower frequencies. It is presented in Fig. 2. This case is also the event with the highest frequency IMD bursts, reaching up to 2550 MHz. Furthermore, we confirm earlier reports that the IMD bursts tend to occur after the peak of the type IV bursts by up to 26 s; only two out of twelve IMD groups were before.

Fig. 2a and b. Top: Spectrogram of a decimetric type IV burst observed with the Phoenix radio spectrometer of ETH Zurich on September 1, 1989. The preburst background has been subtracted, and the greyscale is logarithmic. Bottom: The intermediate drift bursts have been enhanced by subtracting a gliding average in frequency and time.

In 3 of the 12 events, BATSE/GRO has reported an associated hard X-ray flare. In all cases both continuum and IMD bursts have occurred during the decay phase of the hard X-ray flare.

2.2. Properties of individual IMD bursts

The recording of a broadband spectrogram makes it possible to thoroughly investigate the drift of IMD bursts, , and the second derivative, . For this purpose, we selected the most suitable time intervals and parts of the spectrum, and subtracted a gliding background both in time and frequency with a scale exceeding the instantaneous duration and bandwidth of the structures. We then investigated individual IMD bursts and determined the drift rate and mean frequency by measuring the time and frequency of the maximum near the start and end of all well-defined single bursts. The result for eight events with the largest number of single bursts and sufficient for a statistical study is shown in Fig. 3.

Fig. 3a-h. The distribution in drift rate of single IMD bursts measured in the eight events with the largest number of bursts. The drift rate has been normalized by the mean frequency between start and end points. The ordinate is in units of .

The drift rate of individual IMD bursts normalized by the mean frequency scatters by up to a factor of two within the same event. IMD groups with different characteristics are presented in the examples of Figs. 1 and 2. Fig. 1 contains IMD bursts with drift rates between s^-1 and -0.090 s^-1. The second derivative changes even more, from s^-2 at high frequencies to s^-2 at low frequencies. The event of Fig. 2 shows much less scatter. The first derivative varies only within 10% around the value from cross-correlation, s^-1 at GHz. The second derivative, correspondingly, scatters only 20% around s^-2. The two events are extreme in the disparity of the ranges in which the parameters of individual IMD bursts vary.

The smallest drift rates of all individual IMD bursts was = -0.0406 s^-1, and the maximum value was found at -0.230 s^-1.

2.3. Average properties of IMD groups

For the the average properties of IMD groups we used the cross-correlation of the most prominent channel in IMD burst activity (mean frequency given in Table 1) with all the other relevant channels. The cross-correlation yields reliable average characteristics if the bursts are not too different in drift rate or peak flux. Fig. 4 is an example, showing a pronounced structure through the center with a peak of 1.0 at zero delay and at 1740 MHz (auto-correlation channel).

Fig. 4. Cross-correlogram of IMD bursts in time. The data of Fig. 1 (bottom, gliding average) has been cross-correlated with the frequency channel 1740 MHz. The correlation coefficients are shown in a linear greyscale and in pseudo-spectrogram representation.

The average drift rate (first derivative of peak frequency in time) was found from the cross-correlogram in the frequency-time plane (e.g. Fig. 4). The peak values were plotted in vs. t diagrams (cf. Fig. 5 left as an example) and fitted by various procedures to reduce the noise: spline, second, third and fourth order polynomials, and gaussian fits. The fitted curve was then derived in time to find the drift rate (Fig. 5 middle). It was fitted again to evaluate the second derivative (Fig. 5 right).

Fig. 5a-c. Left: The peak of the cross-correlation shown in Fig. 4 was marked in each channel and fitted with a third-order polynomial (thin curve). The curve represents the average IMD characteristics of the 93/03/20 1213 UT event. Middle: The drift rate (first derivative) of the fitted curve in the left image was derived vs. time and is shown by crosses. This was again fitted by a third-order polynomial (thin curve). Right: The second derivative, using the fitted first derivative is shown (full curve). Also presented are the results of other fits: dotted for a fourth-order polynomial and dashed for a gaussian fit.

The results of the different fitting methods can be seen in the example of Fig. 5 right. In general, they differ only slightly in the first derivative, but considerably in the second derivative. The largest deviations are at both ends of the frequency range. At the mean frequency, for Fig. 5 right in the middle of the displayed range at 1740 MHz, the values usually converge well. Their range at the mean frequency was taken as indication of the accuracy, which is listed in Table 1. Also listed are the values of the drift rate and the second derivative at the mean frequency using third-order fits.

Note that the average drift rate in different events scatters even more than individual IMD structures of the same event. The average values differ by more than a factor 3, ranging from = -0.167 to -0.046 s^-1. In particular, the IMD bursts of the 93/03/20 events (Fig. 3) drift significantly faster than most others.

Fig. 6 displays graphically the average drift rates listed in Table 1. Indicated by crosses are the mean values at lower frequencies derived by Bernold (1983). They have been extrapolated by a second order (parabolic) fit to higher frequencies, using the following parameters

where is the mean frequency in MHz. Fig. 6 suggests that the extrapolated curve is an acceptable fit also at higher frequencies. However, there is considerable scatter, much larger than the statistical uncertainty.

Fig. 6. The average drift rate of the 12 IMD events vs. frequency is shown with error bars. The average drift rate measured at lower frequency by Bernold (1983, simple crosses) has been fitted by a second order polynomial (dashed curve) and extrapolated to higher frequency for comparison.

No significant correlation was found between the average second derivative and the mean frequency as listed in Table 1. However, Fig. 7 indicates that the second derivative is related to the drift rate. The data has been complemented by low-frequency values derived from the mean drift rates given by Bernold (1983). If those values are again extrapolated by a second-order fit to higher frequencies (dashed), the observed values seem to be well represented. However, the apparent fit is somewhat feigned by the event at -100.5 MHz/s and 37.0 MHz/s² (event 90/06/15 0830) with only 3 IMD bursts, by far the smallest number of all events. The linear regression (first-order fit) is a better representation of the average second derivative. It is given by

where is the drift rate in MHz/s.

Fig. 7. The average drift rates are compared to the average second derivatives of the 12 IMD events. Low-frequency second derivatives have been computed from the frequency dependence of the average drift rates given by Bernold (1983). The average second derivatives have been fitted by a second order polynomial (dashed curve) and a linear regression (first order polynomial, dotted curve).

It is important to note that the second term, proportional to , dominates Eq. (2). It suggests that the drift rate of individual IMD bursts is related to the instantaneous emission frequency such that in the average . This result is also manifest in Fig. 5 middle, where s^-1 over the range from 1450 to 2005 MHz. The dependence of the drift rate on frequency therefore is different whether the average behavior in one event is considered (Fig. 5) or the mean values of different events are compared (Fig. 6).

Finally the ratio k is given in Table 1. It is defined by

The measured ratio has a range of 0.42 to 4.19 at the mean frequency of IMD activity. The values given in Table 1 and gaussian error propagation yield an average accuracy in k of 39% with individual values reaching up to 80%. The mean k value is 1.81, and the median is 1.62. The linear regression above 1 GHz and the values below derived from Bernold (1983) suggest an average k value of 1.3 0.2.

© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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