We have considered circle scans that crosses (or not) the region near the galactic centre to check the effects of Galaxy temperature gradients in different situations. For standard PLANCK scanning strategy, a scan circle consists of about 680 integrations at 30 GHz and of about 1700 integrations at 100 GHz. We have carried out simulations that either include or neglect the contribution of the Galaxy for the both frequencies (we have adopted here the scaling law to extrapolate its fluctuations at small angular scales). It results that the Galaxy does not affect the difference between the temperature measured by symmetric and elliptical beams. We have performed our tests using maps at different COBE-CUBE resolution (from 9 to 11) to check the dependence of the result on the resolution of the map.
Figure 2: Difference between the (antenna) temperature observed by asymmetric and symmetric beams for a typical scan circle as function of the scan integration number (top panel) or the corresponding galactic latitude (bottom panel).
Figure 3: Antenna temperature observed by asymmetric (triangles) and symmetric (crosses) beams and differences (circles) between the two measurements for a typical scan circle as function of the scan integration number (top panel) or the corresponding galactic latitude (bottom panel).
Figures 2 and 3 show our results for a test at 30 GHz, the frequency considered here where the emission of the Galaxy and its fluctuations are more important (Toffolatti et al. (1995), Danese et al. (1996)); the distribution of the temperature differences does not depend on the galactic latitude (see Figure 2) and, even where galactic emission coupled to CMB quadrupole large scale waves produces significant increases of the observed antenna temperature, the temperature differences remain practically equal to those obtained in other sky regions (see Figure 3).
Typical results obtained by using maps at COBE-CUBE resolution 11 are tabulated in Table 1 in terms of for different beam FWHM's and distortion parameters . The results do not change significantly by using maps at different resolutions.
These results may be qualitatively interpreted from a geometrical point of view: the contribution of the different parts of the sky observed by beams with different shapes becomes more important and produces a growing effect as the FWHM and/or increases. These two parameters are the most important for what concerns here, whereas the observational frequency is directly not relevant (a part for the obvious relationship between the considered frequency and the beam properties), due to the very small effect of Galaxy fluctuations.
Table 1: value of for different cases.