Appendix B: Details of the simulations

The results presented in this paper correspond to the "Optimized Configuration'' involving 3 polarimeters and to an angular step of $18^\prime$: the angle between two consecutive samples along a circle is $18^\prime$ and there is one circle every $18^\prime$.

In this case, the number of circles is $n_{\rm {c}}=1200$ and the number of samples on each circle is $n_{\rm {s}}=1195$. The spin axis has a sinusoidal motion around the ecliptic plane with an amplitude of $8^\circ$ and with 8 cycles during the mission. The aperture angle of the circles is $85^\circ$. The simulated noise has ${f_{\rm {knee}}=\eta f_{\rm {spin}}}$ with ${\eta=1 \rm {~and~} 5}$.

The white noise variance is calculated based on the expected sensitivity on Q and U ($3.7~\mu$K/K) of the (arbitrarily selected) 143 GHz polarized channel of the PLANCK mission.

All the maps (CMB, dipole, galaxy, simulation) are HEALPIX maps with 196608 pixels of $27.48^\prime$. Only 12 pixels ($0.006\%$ of the map) are not seen by the mission: their values are set to the average of the map. The signal maps have been smoothed by a gaussian beam with a FWHM set to ${2.5\times 18^\prime}$.

We have run other simulations with "Optimized Configuration'' involving 3 or 4 polarimeters, and with cycloidal, sinusoidal or anti-solar spin axis trajectories (see Bersanelli et al. 1996, and the PLANCK web page for additionnal information about proposed scanning strategies). The aperture angle of the circles have been taken in $[70^\circ,75^\circ,80^\circ,85^\circ,90^\circ]$. In all these cases, the results are similar for ${f_{\rm {knee}}/f_{\rm {spin}}\sim 1}$. For more pessimistic noise cases, the choice of the scanning strategy may have a strong impact on the quality of the final maps. A quantitative study of this point is deffered to a forthcoming publication.