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Astron. Astrophys. 321, 513-518 (1997)

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3. Data analysis and results

During investigations leading to those results already presented by Wielebinski et al. (1993), K96 and X96, we noticed significant variations in the measured flux-densities observed at a particular frequency. The flux-densities varied on time scales of ten to twenty minutes around a stable mean value which itself did not significantly differ between different observing sessions. In order to investigate these modulations further, we studied the time variability of the strongest sources. From eight pulsars detected at mm-wavelengths (K96), only PSRs B0329+54, B0355+54, B1929+10 and B2021+51 exhibited flux-densities large enough to obtain high signal-to-noise ratio measurements during short sub-integrations. Typical examples of observed flux variations are given in Figs. 1 a-d. In all figures each single measurement designated by an open circle corresponds to a sub-integration of five minutes. The plotted value always represents the equivalent continuum flux-density, which is the observed pulse energy averaged over one pulse period. This flux-density would be observed if the pulsar emitted the same amount of energy as a continuum source. Hereafter, quoted flux-densities always refer to this definition. The error for each measurement was derived by taking the calibration procedure into account and was estimated to be about 15 to 20 % of the mean value. The dashed horizontal line marks the average value of the continuum flux-density measured for the corresponding observation. Flux variations of a factor of two or four are clearly seen, which are much stronger than the levels of weak ISS expected at the observing frequencies. Corresponding modulation indices calculated according to Eq. (1) are quoted in Table 2 and plotted versus dispersion measure of the source in Fig. 2.

[FIGURE] Fig. 1a-d. Variations in the flux-density observed for PSRs a B0329+54, b B0355+54, c B1929+10 and d B2021+51 at mm-wavelengths. Each single measurement (open circle) corresponds to five minutes integration. The horizontal dashed line designates the mean value of the flux-density measured for this scan.
[FIGURE] Fig. 2. Observed modulation indices, [FORMULA] (open squares), and expected modulation indices, [FORMULA] (filled triangles), plotted versus dispersion measure. See Table 2 and text for details.

In order to minimize effects due to the measurement of only linearly polarized signals, we concentrated our analysis mainly on total power signals received at 32 GHz. Only for B0355+54, we included observations made with the tunable prime focus receiver. PSR B0355+54, being the strongest source in our sample and, thus, used as a test source, was regularly observed for short time intervals frequently interrupted by pointing and focusing runs. This prohibited a long continuous run as needed for this analysis. For all other pulsars, the analysed data represent total power signals which were obtained after adding left and right hand circularly polarized signals. We used the information provided by the calibration signal to correct for possible gain differences.

The gain stability of the system was monitored by performing the same data analysis simultaneously for on-pulse data and for the calibration signal, present in the first fifty phase bins of the pulse profile. The resulting modulation index of the calibration signal was typically [FORMULA]. The off-pulse power level (baseline) changed smoothly as a function of elevation due to changes in the ground illumination. This variation was subtracted from the data and the remaining calibration signal deflection was found to be stable in time. The inferred gain was found to be stable to 0.3%.

Trying to account other instrumental effects for the observed flux-density modulation, we can also consider pointing problems of the telescope, since inaccurate telescope pointing could have severely altered the measured flux-densities. We examine this effect in detail below. Observing at 32 GHz with a secondary focus receiver at the 100-m Effelsberg telescope, the HPBW becomes [FORMULA]. Monitoring continuum sources prior and after each pulsar observing session resulted in a typical pointing accuracy of about [FORMULA] rms. This confirms results of routine telescope monitoring under good weather conditions (e.g. Altenhoff et al. 1980). The pointing error generally increases if large temperature gradients exist during an observing session. Differential temperature monitoring of the telescope surface, however, revealed only deviations as small as one degree. Assuming that only the largest measured flux-densities represent the "true" on-source measurement, we estimated a typical offset of the Gaussian telescope beam pattern from the actual on-source position, necessary to explain the observed flux-density variations. These calculations imply a tracking inaccuracy of typically [FORMULA] (B0329+54), [FORMULA] (B0355+54), [FORMULA] (B1929+10) or [FORMULA] (B2021+51), respectively. These values are substantially larger than the typical pointing errors derived from measurements of continuum sources. Moreover, even if a large pointing error would exist, i.e. the actual pointing position of the telescope deviates from the requested one, the real tracking accuracy is typically better than [FORMULA] and thus extremely stable. Obviously, we can exclude pointing problems as the reason for the observed flux-density modulations.

As already noted, the weather conditions during the 32 GHz observations in July 1994 were extremely good, suggesting that atmospheric modulations should be negligible. As a check of atmospheric variability we examined the rms variation in the measured flux on the calibration scans, performed typically every one or two hours. Such calibration-scans consisted of cross scans on the calibrator nearest to the pulsars and lasted about two minutes, in total covering elevations between [FORMULA] and [FORMULA]. The rms deviations in observed calibrator flux-densities for the whole 72h observing period (i.e. including day and night time) were no larger than 10-15%. This confirms that the pulsar variations (seen on much shorter time scales and thus for the same atmospheric condition throughout the corresponding scan) at more than 20% are not atmospheric. Additionally, atmospheric effects should be visible in a possible dependence of the derived modulation indices on the elevation of the source during the corresponding observation (column 6 of Table 2). We plot these quantities in Fig. 3. A correlation is obviously not present, confirming that the variations are not atmospheric.

[FIGURE] Fig. 3. Observed modulation indices plotted versus source elevation of the corresponding observation.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998