3 Analysis

In this paper, we use data from only a single detector at each of the CMB frequencies, 143 and 217 GHz, with a sensitivity of 90 and 150  $\mu{\rm K_{CMB}.s^{1/2}}$ respectively. To avoid the necessity of detailed modelling of Galactic foregrounds, we restrict the sky coverage to $b > +30\rm ~deg$, giving a total of $\sim$100 000 15 arcmin pixels (HEALPIX nside = 256) covering 12.6% of the sky (see Fig. 1). To extract the CMB power spectrum, we use the MASTER analysis methodology (Hivon et al. 2002), which achieves speed by employing sub-optimal (but unbiased) map-making and spectral determinations.

First, the Fourier noise power spectrum is estimated for each photometer. Signal contamination is avoided by subtracting the data projected onto a map (and then re-read with the scanning strategy) from the initial TOI. This raw noise power spectrum is then corrected for two important effects (Benoît et al. 2003d): (i) pixelisation of the Galactic signal that leads to an overestimate of the noise power spectrum: sub-pixel frequencies of the signal are not subtracted from the inital TOI leaving extra signal at high frequency; (ii) due to the finite number of samples per pixel, noise remains in the map and is subtracted from the initial TOI, inducing an underestimation of the actual noise in the final TOI (Ferreira & Jaffe 2000; Stompor et al. 2002). Simulations, including realistic noise, Galactic dust and CMB anisotropies, indicate that both corrections are independent of the shape of the true noise power spectrum, and thus permit an unbiased estimate of the latter with an accuracy better than 1% at all frequencies. The corresponding uncertainty in the noise power spectrum estimation is included in the error bars of the $C_\ell$ spectrum.

We construct maps by bandpassing the data between 0.3 and 45 Hz, corresponding to about 30 deg and 15 arcmin scales, respectively. The high-pass filter removes remaining atmospheric and galactic contamination, the low-pass filter suppresses non-stationary high frequency noise. The filtering is done in such a way that ringing effects of the signal on bright compact sources (mainly the Galactic plane) are smaller than $\sim$36  $\mu{\rm K}^2$ on the CMB power spectrum in the very first $\ell$-bin, and negligible for larger multipoles. Filtered TOI of each absolutely calibrated detector are co-added on the sky to form detector maps. The bias of the CMB power spectrum due to filtering is accounted for in the MASTER process through the transfer function. The map shown in Fig. 1 is obtained by combining the maps of each of the photometers. A $1/\sigma^2$ weighting of the data was done in each pixel, where $\sigma^2$ is the variance of the data in that pixel. This map shows significant extra variance compared to the difference map on degree angular scales which is attributed to sky-stationary signal.

We estimate the CMB power spectrum in 16 bins ranging from $\ell=15$to $\ell=350$. The window functions derived from the multipole binning and renormalized to equal amplitude for clarity are shown at the bottom of Fig. 3. They are nearly top-hat functions due to the large sky coverage. The bins can therefore be approximated as independent: off-diagonal terms in the covariance matrix are less than $\sim$12%. For the purpose of estimating the power spectrum we made a map that combines the data of the two photometers using two different weighting techniques. Up to $\ell=310$ the data of each photometer has equal weight and at larger $\ell$ values the data is noise weighted. This is valid because the multipole bins are nearly independent. It is also advantageous because it minimizes the overall statistical noise over the entire $\ell$ spectrum; equal weighting gives smaller error bars at small $\ell$ and noise weighting gives smaller error bars at large $\ell$.