Figure 1. Sky mask used for template fitting plotted in a Galactic Mollweide projection. Only the green pixels are used in the template fitting analysis.
Figure 2. Mollweide projection in Galactic coordinates of the 108 Nside = 4 regions used to sub-divide the sky and their numerical identifiers. Top panel: region group designations discussed in Section 5.1. Bottom panel: region groups of synchrotron loops discussed in Section 5.2.
Figure 3. Summary of the mean instrumental pixel noise RMS for each data set (points). The black line is the confusion noise model given by equation (10), we fade the line at high frequencies as at these frequencies the steep-spectrum background sources are less relevant. The orange bounded region shows the range of the residual CMB fluctuations for pixels of approximately 1 deg2 (Nside = 64).
optimize the template fitting procedure, we mask regions of the sky that lie along the plane of the Galaxy where components are highly correlated at 1◦ scales or larger and the Hα template suffers from significant extinction, making the separation of components unreliable. The Galactic plane is masked by first median filtering the C-BASS map on 5◦ scales, and then masking the brightest 10 per cent of pixels in the filtered map. The Galactic plane mask is shown as the blue region in Fig. 1.
Point sources can also be problematic for template fitting as they can dominate over the diffuse background emission, resulting in a highly biased estimate of the amplitudes describing the diffuse components. At lower frequencies, we use the source-subtracted 408 MHz and 4.76-GHz C-BASS maps, thus we only mask the very brightest sources or sources that are found to have large residuals after subtraction. Fig. 1 shows bright sources (>10 Jy at 4.76 GHz; Grumitt et al. 2020) masked by a 2° diameter aperture. There are also some fainter point sources (Sν < 10 Jy at 4.76 GHz) that leave residuals in the C-BASS map after subtraction; we mask these using a smaller 1° diameter aperture.
At WMAP and Planck frequencies, the maps are not confusion-limited since the majority of background radio sources have steep spectra and are generally too faint to detect in the WMAP/Planck data. However, there are still a large number of flat-spectrum sources present at high frequencies, and we mask these using the 30-GHz Planck catalogue of compact sources (PCCS) (Planck Collaboration XXVI 2016). We mask 893 PCCS sources in the range 50 < S < 1000 mJy with an aperture of diameter 1°.5, and 628 sources with flux densities S > 1 Jy with a 3° wide aperture. Both the PCCS sources and the C-BASS sources described earlier are shown in Fig. 1 as the orange regions.
4.4 Regions
For this analysis, we divided the sky into equal-sized regions using the Healpix grid (Górski et al. 2005) on the celestial sphere. We chose to use a region size of Nside = 4, which equates to regions with areas of approximately 200 deg2 . There are a total of 108 regions, which are shown in Fig. 2. The maximum number of Nside = 64 pixels within a region is 256, but after masking the number of pixels within each region ranges between 104 and 252 (regions with less than 100 pixels are excluded). The choice of region size is important because regions that are too small have larger spatial correlations between emission types as the template fitting method relies on there being spatial differences between components to work. Whereas larger sized regions become more susceptible to systematics since large scales are generally harder to constrain. Further, larger regions result in less information on the spatial variations across the sky. We found that a region size of Nside = 4 was a good balance between these considerations given the resolution of C-BASS data.
4.5 Noise covariances
As described in Section 4.1, we estimate the uncertainties in the fitted coefficients using bootstrapping, and not the intrinsic noise covariances of each map. However, we still need to calculate the noise covariance to correctly weight each pixel. Fig. 3 provides a summary of all the different contributions to the total noise budget at each frequency. We can see from the figure that the instrumental noise is never the dominant source of noise in the maps – except for the 408-MHz data. At higher frequencies, we have neglected contributions to the noise due to confused infrared galaxies. We give a more detailed description of each contribution below.
MNRAS 513, 5900–5919 (2022)
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