3. Data analysis
After applying the usual procedures of dark current subtraction, flat fielding and cosmic event corrections, the inaccuracy of the telescope guiding was compensated by shifting the frames: For the time series of coma images, the maxima of the crosscorrelation functions were used; for the tail positions, we recorded coma pictures with a fixed distance from the tail position before and after the observing run, correcting their drift with a linear interpolation. Thus we obtained movies at a fixed position relative to the comet's nucleus. Fig. 3 displays typical single frames of these movies both taken from the coma with the Strömgren v and the Gunn g filter.
In a first step we binned pixels - i.e. - to derive fields of view comparable to those presented two decades ago by Isserstedt & Schlosser (1975). These authors obtained light curves with a photometer aperture of 45 arcsec when observing comet Kohoutek at about the same heliocentric distance as Hale-Bopp had during our observations in April 1997, namely between 0.92 and 0.94 AU (1.38 - 1.48 AU geocentric distance).
Sample light curves from 40" 40" subfields of the comet's coma are shown in Fig. 4. These unprocessed light curves are dominated by long term trends due to changes in the brightness of the sky, the airmass, and the comet's activity during the observations. In order to concentrate on the periods adressed in this study and again, to allow for comparison with the measurements of comet Kohoutek's oscillations, we applied in our data sets the same reduction procedure which was used by Isserstedt & Schlosser, i.e. we subtracted a 5.5 minutes running mean from a 1.5 minutes running mean, reducing the high frequency noise and suppressing all changes on long time scales. Obviously, the processed data has to be treated carefully to avoid misinterpretations due to reduction effects. Some of the processed lightcurves are shown in Fig. 5. The reader should compare these curves with those in Fig. 3 of Isserstedt & Schlosser (1975) which are indeed remarkably similar both in period and amplitude. A first guess to explain this similarity might be to assume that the signal is an artefact either due to the similarity of the applied frequency filter or due to the earth's atmosphere. We will argue below, that neither explanation is satisfactory.
In the next step we calculated the power spectrum for each recorded pixel. In Fig. 6 we display the power corresponding to the lightcurves oscillating with a notable amplitude in Fig. 5, i.e. those observed through the Strömgren v filter and thus representing C3 emission. Both the power of the unprocessed lightcurves and the power of the filtered lightcurves - as shown in Fig. 5 - is displayed. The power around 5 mHz - corresponding to a period of about 3 minutes - is well enhanced by the filter method in particular with respect to lower frequency contributions. The similarity of the peaks in the processed and unprocessed data shows that they are not due to the filter transmission. This excludes the first potential artefact mentioned above.
At any given frequency, one can rearrange the power values taken from all power spectra to form a power map in the spatial domain (Fig. 7). These maps are a tool quite helpful in discussing the power spectra. For calculating the power, the intensity fluctuations were normalized to the mean intensity of the corresponding pixel. Consequently, the noise signal will be reduced with the square root of the intensity. On the left side of Fig. 7(a and c) we show a power map derived from data taken with the Gunn g filter together with a map of the average gradient of the intensity in the same data set. Here, the power is generally reduced with enhanced intensity (see Fig. 3a) and only at the loci of high intensity gradients the power rises again in the inner coma. One can argue straightforward from such a powermap that noise and image motion are the dominant contributors to the oscillations seen through the Gunn g filter 2.
In contrast, the right side of Fig. 7(b and d) shows a power signal that spreads smoothly over the inner coma, gaining amplitude with intensity (see Fig. 3b and Fig. 8), and which apparently is hardly at all influenced by local intensity gradients resulting from the well-known onion peel structure of the coma. Comparing panels b and d with a and c we find that the artefacts made responsible for the power in a will not be the main contributers in b. This excludes the second potential artefact with respect to the oscillations shown in Fig. 5.
© European Southern Observatory (ESO) 1998
Online publication: July 20, 1998