4 Results and consistency tests

The Archeops power spectrum is presented in Fig. 2 and in Table 1. Two different binnings corresponding to overlapping, shifted window functions (therefore not independent) were used. Archeops provides the highest $\ell$ resolution up to $\ell=200$( $\Delta\ell$ from 7 to 25) and most precise measurement of the angular power spectrum for $15 < \ell < 300$ to date. Sample-variance contributes 50% or more of the total statistical error up to  $\ell\sim 200$.

  

Table 1: The Archeops CMB power spectrum for the best two photometers (third column). Data points given in this table correspond to the red points in Fig. 2. The fourth column shows the power spectrum for the self difference ( SD) of the two photometers as described in Sect. 4. The fifth column shows the power spectrum for the difference (D) between the two photometers.

$$\begin{tabular}{rrr@{~$\pm$~}lr@{~$\pm$}rr@{~$\pm$~}r}\hline\... ...$ 471$ &$ 356$ &$ 323$ &$ -619$ &$ 358$\\ \hline \end{tabular}$$

The Archeops scanning strategy (large circles on the sky) provides a robust test of systematic errors and data analysis procedures: by changing the sign of the filtered TOIs every other circle, a TOI that should not contain any signal is obtained once it is projected on the sky. This TOI has the same noise power spectrum as the original one. This null test is referred to as the self-difference (SD) test. The angular power spectrum of such a dataset should be consistent with zero at all multipoles because successive circles largely overlap. This test has been performed with the two photometers independently. The spectra are consistent with zero at all modes: $\chi^2/{\rm ndf}$ of 21/16 (resp. 27/16) at 143 GHz (resp. 217 GHz). Performed on the two-photometers co-added map, the same test gives a power spectrum consistent with zero, with a $\chi^2/{\rm ndf}$ of 25/16 (see Fig. 2). These results show that there is no significant correlated noise among the two photometers and that the noise model is correct. They limit the magnitude of non-sky-stationary signals to a small fraction of the sky-stationary signal detected in the maps.

A series of Jack-knife tests shows agreement between the first and second halves of the flight (the difference of the power spectra has $\chi^2/{\rm ndf}=21/16$), left and right halves of the map obtained with a cut in Galactic longitude ( $\chi^2/{\rm ndf}=15/16$). Individual power spectra of the two photometers agree once absolute calibration uncertainties are taken into account. The power spectrum measured on the differences (D) between the two photometers is consistent with zero with a $\chi^2/{\rm ndf}$ of 22/16 (Fig. 2) showing that the electromagnetic spectrum of the sky-stationary signal is consistent with that of the CMB. The measured CMB power spectrum depends neither on the Galactic cut (20, 30 and 40 degrees north from the Galactic plane), nor on the resolution of the maps (27, 14 and 7' pixel size) nor on the TOI high-pass filtering frequencies (0.3, 1 and 2 Hz).

Several systematic effects have been estimated and are summarized in Fig. 3, along with the statistical errors (blue triangles). The high frequency photometer (545 GHz) is only sensitive to dust and atmospheric emission, and thus offers a way to estimate the effect of any residual Galactic or atmospheric emission. Extrapolation of its power spectrum using a Rayleigh-Jeans spectrum times a $\nu^2$ emissivity law between 545 and 217 GHz and as $\nu^0$between 217 and 143 GHz gives an upper-limit on the possible contamination by atmosphere (dominant) and dust. The combination of both is assumed to be much less than 50% of the initial contamination after the decorrelation process. The subsequent conservative upper-limit for dust and atmosphere contamination is shown in red crosses in Fig. 3. The contamination appears negligible in all bins but the first one ($\ell=15$ to 22). High frequency spectral leaks in the filters at 143 and 217 GHz were measured to give a contribution less than half of the above contamination. In the region used to estimate the CMB power spectrum there are 651 extragalactic sources in the Parkes-MIT-NRAO catalog. These sources are mainly AGN, and their flux decreases with frequency. We have estimated their contribution to the power spectrum using the WOMBAT tools (Sokasian et al. 2001). At 143 (resp. 217) GHz this is less than 2 (resp. 1) percent of the measured power spectrum at  $\ell\sim 350$. The beam and photometer time constant uncertainties were obtained through a simultaneous fit on Jupiter crossings. Their effect is shown as the dot-dashed blue and green-dashed lines in Fig. 3. The beam uncertainty includes the imperfect knowledge of the beam transfer function for each photometer's elliptical beam. Beam and time constants uncertainties act as a global multiplicative factor, but in the figure we show the $1\sigma$ effect on a theoretical power spectrum that has a good fit to the data. After the coaddition of the two photometers, the absolute calibration uncertainty (not represented in Fig. 3) is estimated as 7% (in CMB temperature units) with Monte-Carlo simulations.

As a final consistency test, the Archeops $C_\ell$ are computed using two additional independent methods. The first is based on noise estimation with an iterative multi-grid method, MAPCUMBA (Doré et al. 2001), simple map-making and $C_\ell$ estimation using SpICE (Szapudi et al. 2001) which corrects for mask effects and noise ponderation through a correlation function analysis. The second is based on MIRAGE iterative map-making (Yvon et al. 2003) followed by multi-component spectral matching (Cardoso et al. 2002; Patanchon et al. 2003; Delabrouille et al. 2002). All methods use a different map-making and $C_\ell$ estimation. Results between the three methods agree within less than one $\sigma$. This gives confidence in both the $C_\ell$ and in the upper-limits for possible systematic errors. Table 1 provides the angular power spectrum which is used for cosmological parameter extraction (Benoît  et al. 2003a).

A comparison of the present results with other recent experiment and COBE/DMR is shown in Fig. 4. There is good agreement with other experiments, given calibration uncertainties, and particularly with the power COBE/DMR measures at low $\ell$ and the location of the first acoustic peak. Work is in progress to improve the intercalibration of the photometers, the accuracy and the $\ell$ range of the power spectrum: the low $\ell$ range will be improved increasing the effective sky area for CMB (which requires an efficient control of dust contamination), the high $\ell$ range will be improved by including more photometer pixels in the analysis.