5 The effect of Galaxy fluctuations

The results presented above hold in absence of significant Galaxy contamination. On the other hand we expect that main beam distortions may be more sensitive to the larger temperature gradients due to diffuse Galaxy emission. We have then carried out simulations for circle scans crossing the Galaxy plane in two regions near the galactic centre and far from the galactic centre to check the impact of Galaxy temperature gradients in different situations (see Fig. 5). Again we have considered two frequencies, 30 GHz, where the emission of the Galaxy and its fluctuations are significant, and 100 GHz, where they are much smaller than the CMB ones (Toffolatti et al. 1995; Danese et al. 1996), and two scaling laws, $C_l \propto l^{-2}$ and $C_l \propto l^{-3}$, to extrapolate its fluctuations at small angular scales ($\,\lower2truept\hbox{${< \atop\hbox{\raise4truept\hbox{$\sim$}}}$}\,0.5^{\circ}-1^{\circ}$). Figure 6 (top panel) shows the difference between the temperature measured by symmetric and elliptical beams as function of the anisotropy temperature for a case corresponding to the test 2 of Table 1, but including the Galaxy contribution. The temperature differences typically increase with the signal; in this case for the whole scan circle we find ${\rm rms_{th}}=2.49 \,\mu {\rm K}$, not significantly higher than the value found for the test 2. On the other hand, by averaging only over the points with a signal larger than $200 \,\mu{\rm K}$,i.e. where the galactic emission dominates, we find ${\rm rms_{th}}=3.22 \,\mu{\rm K}$.

  

Figure 5: Thermodynamic temperature observed by asymmetric (triangles) and symmetric (crosses) beams for a typical scan circle as function of the scan integration number along the circle (top panel) or the corresponding galactic latitude (bottom panel). The higher and lower peaks reflect the crossings with the Galactic plane near and far from the galactic centre respectively, whereas the other slow variations are essentially generated by the CMB quadrupole large scale waves. The figure refers to a test analogous to the test 2 in Table 1, but including Galaxy emission with small scales fluctuations extrapolated assuming $\beta=2$

  

Figure 6: Absolute (top panel) and relative (bottom panel) difference between the thermodynamic temperature observed by asymmetric and symmetric beams for the case of Fig. 5 as function of the temperature measured by the symmetric beam. The increase of the beam distortion effect at high galactic signal is evident (top panel), but the relative error remains small (bottom panel). (The high relative error at small signals is of course not relevant)

For the same case considered in Figs. 5 and 6, the solid line in Fig. 7 shows the value of $\rm rms_{th}$ as function of the galactic latitude when we bin the temperature differences in steps of $3.5^\circ$. The beam distortion effect does not increase significantly in the regions far from the galactic plane but it can be 2-3 times larger at galactic latitudes less than about $5^\circ$. We find essentially the same result by adopting a different scaling law, $C_l \propto l^{-3}$, for Galaxy fluctuations (dashed line). A similar effect does not appear at 100 GHz (dotted line) where the impact of Galaxy emission is negligible; we find indeed the same results found in the test 5 in Table 1. Although the difference between the temperature measured by symmetric and elliptical beams can increase by a factor 2 or 3 at 30 GHz due to the Galaxy contamination, the relative error in CMB anisotropy plus Galaxy temperature measurements does not increase significantly where the galactic signal is high (see Fig. 6, bottom panel) and remains always less than few per cent. Then, in those sky regions where high galactic emission prevents an accurate determination of CMB fluctuations, an accurate determination of Galaxy emission in not significantly affected by main beam distortions.

  

Figure 7: Values of $\rm rms_{th}$ from the observed temperature differences between asymmetric and symmetric beams as a function of galactic latitude binned in steps of $3.5^\circ$.Different lines refer to two tests at 30 GHz with of a slope $\beta=2$ for the Galaxy angular power spectrum (solid line) and a slope 3 (dashed line) and to a test at 100 GHz with a slope 2 (dotted lines). For all the cases we have adopted a CDM model for CMB fluctuations and a beam distortion parameter r=1.3