5 Discussion and conclusion

We have reported here an extensive study of the 1/f noise contamination for different scanning strategies, beam location on the focal plane as well as for different values of the knee frequency. Even in this idealised situation (all other systematics are well under control) we can gain useful information from our study.

First of all from these simulations it seems that moving the spin-axis away from the ecliptic plane does not significantly help the destriping efficiency for typical LFI beam locations and, concerning the 1/f noise alone as source of drifts, it would be preferable to keep the spin-axis always on the Ecliptic plane. This is clear when we compare results as those in the bottom panels of Fig. 2 and Fig. 5 which are practically identical.

Furthermore for most of the LFI beams the choice of $\alpha =90^{\circ }$ would be acceptable: the destriping left only $\,\lower2truept\hbox{${< \atop\hbox{\raise4truept\hbox{$\sim$ }}}$ }\,2\%$ of excess noise with respect to the pure white noise case. On the other hand, some LFI beams are equivalent to on-axis beam which, from the bottom panel of Fig. 6, is clearly a degenerate case. A smaller value of $\alpha$ (namely 85$^{\circ }$) breaks this degeneracy at an acceptable level yielding the usual destriping efficiency. From these two points an indication of a possible choice of the scanning strategy and instrument configuration arises: with $\alpha=85^{\circ}$ and precession of the spin-axis (no thermal drifts) with only 5$^{\circ }$ amplitude (half of what we considered here) appears satisfactory for de-striping performances while preserving full-sky coverage for all channels. This allows data redundancy but introduces irregularities in the integration time distribution, which may be an issue for the data analysis. Without spin axis modulations, a quite complete sky coverage and a smooth integration time distribution at each frequency can be achieved only by assembling data from different receivers, losing redundancy.

The whole set of simulations seems to indicate that there is enough redundancy of observations to remove at acceptable level the contamination due to 1/f noise even if we require a more strict condition of crossings between scan circles. Of course, the performance of this destriping code could be partially optimized in the future by appropriately choosing the number of levels per circle and the crossing condition according to the dominant kind of instrumental noise (the parameters $f_{\rm k}$ and $\beta$), the magnitude of the gradients in the sky emission and our knowledge of other contamination sources. Another point to mention is the possibility of jointly destriping the data from two or more feeds at the same frequency but differently located on the sky field of view: this will enlarge the dimension of the system in Eq. (4) that have to be solved and then RAM requirements. Although feeds in different locations in the focal plane will have different beam shapes and main beam distortions may introduce extra-noise, this is an interesting point particularly with respect "degenerate'' feed positions and will be addressed in a future work.

For what concerns properly the 1/f noise, an important indication comes from the simulation with $f_{\rm k}=0.01$ Hz: the excess of noise before destriping reduces by a factor $\simeq 4\div 5$ with respect to the case $f_{\rm k}=0.05$ Hz, indicating a possible linear relation between the additional rms and knee-frequency. In addition the extra noise level after destriping decreases, at least under these ideal assumptions, by a factor $\simeq 3$. The source of this extra noise after destriping is probably partially due to the 1/f noise on time-scales less than the spin-rate. This can be see when comparing the level of extra noise, after destriping, for the $f_{\rm k}=0.05$ Hz and $f_{\rm k}=0.01$ Hz cases, values larger and smaller than $f_{\rm s}$ respectively.

There are many open issues both astrophysical and instrumental. Regarding the first, the microwave emission model we use, although pessimistic for what concerns galactic emission, can be completed with the inclusion of different foreground contributions. The emission from extragalactic point sources and in particular their variability may decrease our destriping efficiency. We have also not considered here any other source of possible systematic effects such as thermal effects, main beam distortions and stray-light contamination induced by Galaxy emission. These effects may in principle degrade the accuracy in removing 1/f noise stripes, by introducing systematic differences in the temperatures observed in the crossing points used in the destriping algorithm: a preliminary analysis of simulations with an elliptical Gaussian beam (instead of the circular symmetry one considered in this work) with a 1.7 ratio between major and minor axis, indicates a small impact of a such effect on the destriping efficiency. A more comprehensive analysis of the impact of these classes of effects, of their relative weight and of their coupling with the 1/f noise will be presented in a future work (Burigana et al.[1999]).

As proved by the scientific experience in many years of work in physics, in cosmology and astrophysics, efficient data analysis tools can significantly improve the quality of the information extracted from the data, provided that the systematic effects are well understood, but the first and most important step in projecting experiments is to reduce all the contaminations at the lowest possible levels. It is then of great importance to decrease as much as possible the impact of 1/f noise before destriping and $f_{\rm k}=0.01$ Hz is an important goal for instrument studies and prototypes.

Acknowledgements

We gratefully acknowledge stimulating and helpful discussions with L. Danese, J. Delabrouille and M. Seiffert. We also thank the referee for his useful comments which helped to make this paper much more clear and readable.