4 Separation of the Galactic and extra-Galactic components

In Figs. A.2 to A.9 we present the power spectrum of the 60 and 100 $\mu$m ISSA maps of our twelve fields (black line). For all these fields, the power spectrum of the noise has been subtracted and the result has been divided by the PSF $\gamma(k)$. At large scale, all the power spectra follow a power law typical of cirrus emission (Gautier et al. 1992). But at $k \sim 0.01$ arcmin^-1 we notice a break in the spectra and an excess from the cirrus power law at small scales. This power excess is observed for all our fields, at 60 and 100 $\mu$m.

4.1 Contribution of strong point sources

The power excess observed at small scales reveals the presence of a component with a flatter power spectrum, like what would be expected from noise or randomly distributed point sources. At this stage, a noise contribution is unlikely as it has been well estimated and removed accordingly. On the other hand, in fields with such low cirrus emission, several extra-galactic point sources were detected. In each of our fields, between 200 and 300 point sources are listed in the IRAS Point Source Catalog (PSC), the vast majority of them being extra-galactic objects. We remove the contribution of all point sources with flux greater than 1 Jy at 100 $\mu$m (and the same sources at 60 $\mu$m). The cut at 1 Jy is chosen such that the PSC above this limit will be nearly complete. This gives a well define separation between the sources contributing to the unresolved CIB and the resolved sources. This is necessary for any quantitative use of our results. We choose this cut in flux as low as possible to remove the contribution of the nearby and resolved galaxies that dominate the power spectrum at scales k > 0.01 arcmin^-1 (for those galaxies, the spatial distribution is indistinguishable from a Poissonian distribution). Moreover, according to recent simulations, the cut of 1 Jy at 100 $\mu$m almost corresponds to the flux where the non-Euclidean part appears in the number counts. To remove the contribution of strong point sources ( $I_{100 ~ \rm\mu m} \geq 1$ Jy) to the power spectrum, they were filtered out from the ISSA map. For each ISSA map, we have extracted the point sources of the IRAS Point Source Catalog with a flux greater or equal to 1 Jy. Then we have applied a median filtering to the ISSA map to estimate the background level and, at each point source position,we have removed the points in a $12\times12$ window that were more than 4 times the noise level ( $\sigma_{\rm issa}$) above the background. Finally, the missing points were replaced by a bilinear interpolation.

The power spectrum of the filtered ISSA maps is the blue line in Figs. A.2 to A.9. A power excess at small scales (k>0.02 arcmin^-1) is still apparent on all power spectra, at 60 and 100 $\mu$m. This excess is likely to be the signature of the unresolved cosmic far-infrared background. To characterize it, the contribution of the cirrus emission has to be removed.

4.2 Contribution of the cirrus emission

As we do not have any independent tracers of the cirrus emission at the IRAS scales for the whole fields, the only way to derive the cirrus contribution is to use the statistical properties of their spatial distribution. Following Gautier et al. (1992) and Miville-Deschênes et al. (2002) the power spectrum of interstellar dust emission is well describe by a power law. To remove this contribution to the power spectrum of the filtered ISSA maps, we have fitted a power law on the large scale part of the power spectrum of the filtered maps. The best compromise between the number of point on which to fit the power law and the contamination from the CIB was to fit on k < 0.02 arcmin^-1. The point corresponding to the largest scale was not used for the fitting as it suffers from a large statistical error. The result of the fitting, and its associated uncertainty, are shown for each ISSA map in Figs. A.2 to A.9. The uncertainty on the slope reflects the dispersion of the points around the fit. The red line in these figures is the result of the subtraction of the cirrus power law from the power spectrum of the filtered map (blue line); it is the signature of the CIB.

Figure 3: CIB contributions to the 60 (left) and 100 $\mu$m (right) power spectra. The black line is the average of the CIB contributions for the 12 fields. The blue lines indicates the uncertainty on the CIB contribution, computed from the uncertainty on the cirrus slope and on the PSF width.

4.3 Contribution of the cosmic far-infrared background

The average of the 12 CIB contributions is shown in Fig. 3 (black lines). The blue lines in this figure indicate the 1$\sigma$ uncertainty on the determination, including the PSF and the estimate of the cirrus contribution errors. The 1$\sigma$ uncertainty is very close to the rms variations of the 12 averaged values. The dispersion between the fields is thus dominated by the PSF and cirrus contribution errors, we do not see any significant variation from field to field. Moreover, it is important to note that the detected excess at small scales is uncorrelated with the cirrus emission (the excess disappears when the cirrus contribution increases). Therefore, our fields being spread over the sky, the excess at small scale is compatible with isotropic properties. This is an other argument in favor of an extra-galactic origin for the excess.

We can note in Figs. A.2-A.9 that the power spectrum of the resolved IRAS sources is varying by factor up to 10 from field to field. The CIB (resolved and unresolved) fluctuations are dominated by the brightest sources in ISSA maps. The number of such sources is quite small, leading to a high cosmic variance, and thus large variation from field to field. On the contrary, for the unresolved CIB fluctuations, as sources above 1 Jy (about 300 per field) are removed, the cosmic variance is lower than 6$\%$, which is negligible with respect to the 1$\sigma$ uncertainty.

The CIB is detected over one decade in scales, from 5 to 50 arcmin. The power spectrum of the CIB at 60 and 100 $\mu$m is compatible with a Poissonian distribution at spatial frequencies between 0.025 and 0.2 arcmin^-1. The fluctuation level is $\sim$ $1.6\times10^{3}$ Jy²/sr and $\sim$ $5.8\times10^{3}$ Jy²/sr at 60 and 100 $\mu$m respectively.