Planck 2013 results. XVI. Cosmological parameters
- Ade, P.A.R. et al
- arXiv:1303.5076CERN-PH-TH-2013-129
 | \planck\ foreground-subtracted temperature power spectrum (with foreground and other ``nuisance'' parameters fixed to their best-fit values for the base \lcdm\ model). The power spectrum at low multipoles ($\ell=2$--$49$, plotted on a logarithmic multipole scale) is determined by the {\tt Commander} algorithm applied to the \planck\ maps in the frequency range $30$--$353$\,GHz over 91\% of the sky. This is used to construct a low-multipole temperature likelihood using a Blackwell-Rao estimator, as described in~\citet{planck2013-p08}. The asymmetric error bars show 68\% confidence limits and include the contribution from uncertainties in foreground subtraction. At multipoles $50 \le \ell \le 2500$ (plotted on a linear multipole scale) we show the best-fit The CMB spectrum computed from the {\tt CamSpec} likelihood (see~\citealt{planck2013-p08}) after removal of unresolved foreground components. \referee{This spectrum is averaged over the frequency range $100$--$217\,{\rm GHz}$ using frequency-dependent diffuse sky cuts (retaining 58\% of the sky at 100 GHz and 37\% of the sky at $143$ and $217\,{\rm GHz}$) and is sample-variance limited to $\ell \sim 1600$.} The light grey points show the power spectrum multipole-by-multipole. The blue points show averages in bands of width $\Delta \ell \approx 31$ together with $1\,\sigma$ errors computed from the diagonal components of the band-averaged covariance matrix (which includes contributions from beam and foreground uncertainties). The red line shows the temperature spectrum for the best-fit base \lcdm\ cosmology. The lower panel shows the power spectrum residuals with respect to this theoretical model. The green lines show the $\pm 1\,\sigma$ errors on the individual power spectrum estimates at high multipoles computed from the {\tt CamSpec} covariance matrix. Note the change in vertical scale in the lower panel at $\ell=50$. |
 | \planck\ foreground-subtracted temperature power spectrum (with foreground and other ``nuisance'' parameters fixed to their best-fit values for the base \lcdm\ model). The power spectrum at low multipoles ($\ell=2$--$49$, plotted on a logarithmic multipole scale) is determined by the {\tt Commander} algorithm applied to the \planck\ maps in the frequency range $30$--$353$\,GHz over 91\% of the sky. This is used to construct a low-multipole temperature likelihood using a Blackwell-Rao estimator, as described in~\citet{planck2013-p08}. The asymmetric error bars show 68\% confidence limits and include the contribution from uncertainties in foreground subtraction. At multipoles $50 \le \ell \le 2500$ (plotted on a linear multipole scale) we show the best-fit The CMB spectrum computed from the {\tt CamSpec} likelihood (see~\citealt{planck2013-p08}) after removal of unresolved foreground components. \referee{This spectrum is averaged over the frequency range $100$--$217\,{\rm GHz}$ using frequency-dependent diffuse sky cuts (retaining 58\% of the sky at 100 GHz and 37\% of the sky at $143$ and $217\,{\rm GHz}$) and is sample-variance limited to $\ell \sim 1600$.} The light grey points show the power spectrum multipole-by-multipole. The blue points show averages in bands of width $\Delta \ell \approx 31$ together with $1\,\sigma$ errors computed from the diagonal components of the band-averaged covariance matrix (which includes contributions from beam and foreground uncertainties). The red line shows the temperature spectrum for the best-fit base \lcdm\ cosmology. The lower panel shows the power spectrum residuals with respect to this theoretical model. The green lines show the $\pm 1\,\sigma$ errors on the individual power spectrum estimates at high multipoles computed from the {\tt CamSpec} covariance matrix. Note the change in vertical scale in the lower panel at $\ell=50$. |
 | Comparison of the base \LCDM\ model parameters for \plancklensing\ only (colour-coded samples), and the 68\% and 95\% constraint contours adding \WMAP\ low-$\ell$ polarization (\WP; red contours), compared to \WMAP-9 (\citealt{bennett2012}; grey contours). |
 | Comparison of the base \LCDM\ model parameters for \plancklensing\ only (colour-coded samples), and the 68\% and 95\% constraint contours adding \WMAP\ low-$\ell$ polarization (\WP; red contours), compared to \WMAP-9 (\citealt{bennett2012}; grey contours). |
 | Comparison of the base \LCDM\ model parameters for \plancklensing\ only (colour-coded samples), and the 68\% and 95\% constraint contours adding \WMAP\ low-$\ell$ polarization (\WP; red contours), compared to \WMAP-9 (\citealt{bennett2012}; grey contours). |
 | Constraints in the $\Omega_{\rm m}$--$H_0$ plane. Points show samples from the \Planck-only posterior, coloured by the corresponding value of the spectral index $\ns$. The contours (68\% and 95\%) show the improved constraint from \plancklensing+\WP. The degeneracy direction is significantly shortened by including \WP, but the well-constrained direction of constant $\Omm h^3$ (set by the acoustic scale), is determined almost equally accurately from \planck\ alone. |
 | Constraints in the $\Omega_{\rm m}$--$H_0$ plane. Points show samples from the \Planck-only posterior, coloured by the corresponding value of the spectral index $\ns$. The contours (68\% and 95\%) show the improved constraint from \plancklensing+\WP. The degeneracy direction is significantly shortened by including \WP, but the well-constrained direction of constant $\Omm h^3$ (set by the acoustic scale), is determined almost equally accurately from \planck\ alone. |
 | Marginalized constraints on parameters of the base \LCDM\ model for various data combinations. |
 | Marginalized constraints on parameters of the base \LCDM\ model for various data combinations. |
 | noimgSummary of the CMB temperature data sets used in this analysis. |
 | \textit{Top}: \planck\ spectra at $100$, $143$ and $217\,\mathrm{GHz}$ without subtraction of foregrounds. \textit{Middle}: SPT spectra from R12 at 95, 150 and $220\,\mathrm{GHz}$, recalibrated to \planck\ using the best-fit calibration, as discussed in the text. The S12 SPT spectrum at $150\,\mathrm{GHz}$ is also shown, but without any calibration correction. This spectrum is discussed in detail in Appendix~\ref{app:spt}, but is not used elsewhere in this paper. \textit{Bottom}: ACT spectra (weighted averages of the equatorial and southern fields) from D13 at $148$ and $220\,\mathrm{GHz}$, and the $148\times 220\,\mathrm{GHz}$ cross-spectrum, with no extragalactic foreground corrections, recalibrated to the \planck\ spectra as discussed in the text. The solid line in each panel shows the best-fit base \lcdm\ model from the combined \planck+WP+highL\ fits listed in Table~\ref{LCDMForegroundparams}. |
 | \textit{Top}: \planck\ spectra at $100$, $143$ and $217\,\mathrm{GHz}$ without subtraction of foregrounds. \textit{Middle}: SPT spectra from R12 at 95, 150 and $220\,\mathrm{GHz}$, recalibrated to \planck\ using the best-fit calibration, as discussed in the text. The S12 SPT spectrum at $150\,\mathrm{GHz}$ is also shown, but without any calibration correction. This spectrum is discussed in detail in Appendix~\ref{app:spt}, but is not used elsewhere in this paper. \textit{Bottom}: ACT spectra (weighted averages of the equatorial and southern fields) from D13 at $148$ and $220\,\mathrm{GHz}$, and the $148\times 220\,\mathrm{GHz}$ cross-spectrum, with no extragalactic foreground corrections, recalibrated to the \planck\ spectra as discussed in the text. The solid line in each panel shows the best-fit base \lcdm\ model from the combined \planck+WP+highL\ fits listed in Table~\ref{LCDMForegroundparams}. |
 | \textit{Top}: \planck\ spectra at $100$, $143$ and $217\,\mathrm{GHz}$ without subtraction of foregrounds. \textit{Middle}: SPT spectra from R12 at 95, 150 and $220\,\mathrm{GHz}$, recalibrated to \planck\ using the best-fit calibration, as discussed in the text. The S12 SPT spectrum at $150\,\mathrm{GHz}$ is also shown, but without any calibration correction. This spectrum is discussed in detail in Appendix~\ref{app:spt}, but is not used elsewhere in this paper. \textit{Bottom}: ACT spectra (weighted averages of the equatorial and southern fields) from D13 at $148$ and $220\,\mathrm{GHz}$, and the $148\times 220\,\mathrm{GHz}$ cross-spectrum, with no extragalactic foreground corrections, recalibrated to the \planck\ spectra as discussed in the text. The solid line in each panel shows the best-fit base \lcdm\ model from the combined \planck+WP+highL\ fits listed in Table~\ref{LCDMForegroundparams}. |
 | \textit{Top}: \planck\ spectra at $100$, $143$ and $217\,\mathrm{GHz}$ without subtraction of foregrounds. \textit{Middle}: SPT spectra from R12 at 95, 150 and $220\,\mathrm{GHz}$, recalibrated to \planck\ using the best-fit calibration, as discussed in the text. The S12 SPT spectrum at $150\,\mathrm{GHz}$ is also shown, but without any calibration correction. This spectrum is discussed in detail in Appendix~\ref{app:spt}, but is not used elsewhere in this paper. \textit{Bottom}: ACT spectra (weighted averages of the equatorial and southern fields) from D13 at $148$ and $220\,\mathrm{GHz}$, and the $148\times 220\,\mathrm{GHz}$ cross-spectrum, with no extragalactic foreground corrections, recalibrated to the \planck\ spectra as discussed in the text. The solid line in each panel shows the best-fit base \lcdm\ model from the combined \planck+WP+highL\ fits listed in Table~\ref{LCDMForegroundparams}. |
 | \textit{Top}: \planck\ spectra at $100$, $143$ and $217\,\mathrm{GHz}$ without subtraction of foregrounds. \textit{Middle}: SPT spectra from R12 at 95, 150 and $220\,\mathrm{GHz}$, recalibrated to \planck\ using the best-fit calibration, as discussed in the text. The S12 SPT spectrum at $150\,\mathrm{GHz}$ is also shown, but without any calibration correction. This spectrum is discussed in detail in Appendix~\ref{app:spt}, but is not used elsewhere in this paper. \textit{Bottom}: ACT spectra (weighted averages of the equatorial and southern fields) from D13 at $148$ and $220\,\mathrm{GHz}$, and the $148\times 220\,\mathrm{GHz}$ cross-spectrum, with no extragalactic foreground corrections, recalibrated to the \planck\ spectra as discussed in the text. The solid line in each panel shows the best-fit base \lcdm\ model from the combined \planck+WP+highL\ fits listed in Table~\ref{LCDMForegroundparams}. |
 | \textit{Top}: \planck\ spectra at $100$, $143$ and $217\,\mathrm{GHz}$ without subtraction of foregrounds. \textit{Middle}: SPT spectra from R12 at 95, 150 and $220\,\mathrm{GHz}$, recalibrated to \planck\ using the best-fit calibration, as discussed in the text. The S12 SPT spectrum at $150\,\mathrm{GHz}$ is also shown, but without any calibration correction. This spectrum is discussed in detail in Appendix~\ref{app:spt}, but is not used elsewhere in this paper. \textit{Bottom}: ACT spectra (weighted averages of the equatorial and southern fields) from D13 at $148$ and $220\,\mathrm{GHz}$, and the $148\times 220\,\mathrm{GHz}$ cross-spectrum, with no extragalactic foreground corrections, recalibrated to the \planck\ spectra as discussed in the text. The solid line in each panel shows the best-fit base \lcdm\ model from the combined \planck+WP+highL\ fits listed in Table~\ref{LCDMForegroundparams}. |
 | Comparison of the posterior distributions of the foreground parameters for \planck+\WP\ (red) and \planck+\WP+\highL\ (black). |
 | Comparison of the posterior distributions of the foreground parameters for \planck+\WP\ (red) and \planck+\WP+\highL\ (black). |
 | Constraints in the $\Omega_{\rm m}$--$H_0$ plane. Points show samples from the \Planck-only posterior, coloured by the corresponding value of the spectral index $\ns$. The contours (68\% and 95\%) show the improved constraint from \plancklensing+\WP. The degeneracy direction is significantly shortened by including \WP, but the well-constrained direction of constant $\Omm h^3$ (set by the acoustic scale), is determined almost equally accurately from \planck\ alone. |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Marginalized constraints on parameters of the base \LCDM\ model for various data combinations. |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Comparison of the posterior distributions of the foreground parameters for \planck+\WP\ (red) and \planck+\WP+\highL\ (black). |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots, for assessing the quality of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lower sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic cirrus (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | Power spectrum residual plots illustrating the accuracy of the foreground modelling. For each cross-spectrum, there are two sub-figures. The upper sub-figures show the residuals with respect to the \planck+\WP\ best-fit solution (from Table~\ref{LCDMForegroundparams}). The lowers sub-figure show the residuals with respect to the \planck+\WP+\highL\ solution The upper panel in each sub-figure shows the residual between the measured power spectrum and the best-fit (lensed) CMB power spectrum. The lower panels show the residuals after further removing the best-fit foreground model. The lines in the upper panels show the various foreground components. Major foreground components are shown by the solid lines, colour coded as follows: total foreground spectrum (red); Poisson point sources (orange); clustered CIB (blue); thermal SZ (green); and Galactic dust (purple). Minor foreground components are shown by the dotted lines colour coded as follows: kinetic SZ (green); tSZ$\times$CIB cross-correlation (purple). We also show residuals for the two spectra $100\times143$ and $100\times217$ that are not used in the \planck\ likelihood. For these, we have assumed Poisson point-source correlation coefficients of unity. \referee{The $\chi^2$ values of the residuals, and the number of bandpowers, are listed in the lower panels.} |
 | SPT power spectra at high $\ell$ using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the besft-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | SPT power spectra at high multipoles using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the best-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | SPT power spectra at high $\ell$ using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the besft-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | SPT power spectra at high multipoles using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the best-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | SPT power spectra at high $\ell$ using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the besft-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | SPT power spectra at high multipoles using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the best-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | SPT power spectra at high $\ell$ using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the besft-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | SPT power spectra at high multipoles using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the best-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | SPT power spectra at high $\ell$ using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the besft-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | SPT power spectra at high multipoles using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the best-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | SPT power spectra at high $\ell$ using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the besft-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | SPT power spectra at high multipoles using the foreground model developed in this paper. The SPT R12 power spectra for each frequency combination are shown by the blue points, together with $1\,\sigma$ error bars. The foreground components, determined from the \planck+\WP+\highL\ analysis of \lcdm\ models, are shown in the upper panels using the same colour coding as in Fig.~\ref{PlanckandHighL}. Here, the spectrum of the best-fit CMB is shown in red and the total spectra are the upper green curves. The lower panel in each sub-figure shows the residuals with respect to the best-fit base \lcdm\ cosmology+foreground model. The $\chi^2$ values of the residuals, and the number of SPT bandpowers, are listed in the lower panels. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | As Fig.~\ref{SPT}, but for the ACT south and ACT equatorial power spectra. |
 | \Planck\ $TT$ power spectrum. The points in the upper panel show the maximum-likelihood estimates of the primary CMB spectrum computed as described in the text for the best-fit foreground and nuisance parameters of the \planck+\WP+\highL\ fit listed in Table~\ref{LCDMForegroundparams}. The red line shows the best-fit base \lcdm\ spectrum. The lower panel shows the residuals with respect to the theoretical model. The error bars are computed from the full covariance matrix, appropriately weighted across each band (see Eqs.~\ref{PBF1a} and \ref{PBF1b}) and include beam uncertainties and uncertainties in the foreground model parameters. |
 | \Planck\ $TT$ power spectrum. The points in the upper panel show the maximum-likelihood estimates of the primary CMB spectrum computed as described in the text for the best-fit foreground and nuisance parameters of the \planck+\WP+\highL\ fit listed in Table~\ref{LCDMForegroundparams}. The red line shows the best-fit base \lcdm\ spectrum. The lower panel shows the residuals with respect to the theoretical model. The error bars are computed from the full covariance matrix, appropriately weighted across each band (see Eqs.~\ref{PBF1a} and \ref{PBF1b}), and include beam uncertainties and uncertainties in the foreground model parameters. |
 | \planck\ $TE$ (left) and $EE$ spectra (right) computed as described in the text. The red lines show the polarization spectra from the base \lcdm\ \planck+\WP+\highL\ model, {\it which is fitted to the TT data only}. |
 | \planck\ $TE$ (left) and $EE$ spectra (right) computed as described in the text. The red lines show the polarization spectra from the base \lcdm\ \planck+\WP+\highL\ model, {\it which is fitted to the TT data only}. |
 | \planck\ $TE$ (left) and $EE$ spectra (right) computed as described in the text. The red lines show the polarization spectra from the base \lcdm\ \planck+\WP+\highL\ model, {\it which is fitted to the TT data only}. |
 | \planck\ $TE$ (left) and $EE$ spectra (right) computed as described in the text. The red lines show the polarization spectra from the base \lcdm\ \planck+\WP+\highL\ model, {\it which is fitted to the TT data only}. |
 | 68\% and 95\% confidence regions on one-parameter extensions of the base \LCDM\ model for \planck+\WP\ (red) and \planck+\WP+BAO (blue). Horizontal dashed lines correspond to the fixed base model parameter value, and vertical dashed lines show the mean posterior value in the base model for \planck+\WP. |
 | 68\% and 95\% confidence regions on one-parameter extensions of the base \LCDM\ model for \planck+\WP\ (red) and \planck+\WP+BAO (blue). Horizontal dashed lines correspond to the fixed base model parameter value, and vertical dashed lines show the mean posterior value in the base model for \planck+\WP. |
 | \emph{Left}: \planck\ $TT$ spectrum at low multipoles with $68\%$ ranges on the posteriors. The ``rainbow'' band show the best fits to the entire \planck+\WP+\highL\ likelihood for the base \lcdm\ cosmology, colour-coded according to the value of the scalar spectral index $n_{\rm s}$. \emph{Right}: Limits (68\% and 95\%) on the relative amplitude of the base \lcdm\ fits to the \planck+\WP\ likelihood {\it fitted only to the \planck\ $TT$ likelihood} over the multipole range $2 \le \ell \le \ell_{\rm max}$. |
 | \emph{Left}: \planck\ $TT$ spectrum at low multipoles with $68\%$ ranges on the posteriors. The ``rainbow'' band show the best fits to the entire \planck+\WP+\highL\ likelihood for the base \lcdm\ cosmology, colour-coded according to the value of the scalar spectral index $n_{\rm s}$. \emph{Right}: Limits (68\% and 95\%) on the relative amplitude of the base \lcdm\ fits to the \planck+\WP\ likelihood {\it fitted only to the \planck\ $TT$ likelihood} over the multipole range $2 \le \ell \le \ell_{\rm max}$. |
 | \emph{Left}: \planck\ $TT$ spectrum at low multipoles with $68\%$ ranges on the posteriors. The ``rainbow'' band show the best fits to the entire \planck+\WP+\highL\ likelihood for the base \lcdm\ cosmology, colour-coded according to the value of the scalar spectral index $n_{\rm s}$. \emph{Right}: Limits (68\% and 95\%) on the relative amplitude of the base \lcdm\ fits to the \planck+\WP\ likelihood {\it fitted only to the \planck\ $TT$ likelihood} over the multipole range $2 \le \ell \le \ell_{\rm max}$. |
 | \emph{Left}: \planck\ $TT$ spectrum at low multipoles with $68\%$ ranges on the posteriors. The ``rainbow'' band show the best fits to the entire \planck+\WP+\highL\ likelihood for the base \lcdm\ cosmology, colour-coded according to the value of the scalar spectral index $n_{\rm s}$. \emph{Right}: Limits (68\% and 95\%) on the relative amplitude of the base \lcdm\ fits to the \planck+\WP\ likelihood {\it fitted only to the \planck\ $TT$ likelihood} over the multipole range $2 \le \ell \le \ell_{\rm max}$. |
 | \referee{Comparison of the \planck\ and \WMAP-9 power spectra. The green points show the combined \WMAP-9 V+W-band spectrum computed on the same mask used for the $100\times100$\,GHz \planck\ spectrum (with a combined \textit{WMAP}+\planck\ mask for point sources) after rescaling the \WMAP\ power spectrum by a multiplicative factor of $0.974$. The magenta points show the \planck\ $100\times 100$\,GHz spectrum computed on the same mask. The red line shows the best-fit \planck+\WP+\highL\ base \lcdm\ model. The lower panel shows the residuals with respect to this model. The error bars on the \textit{WMAP} points show the instrumental noise together with the noise-signal errors as discussed in the text; errors are not shown for \planck.} |
 | \referee{Comparison of the \planck\ and \WMAP-9 power spectra. The green points show the combined \WMAP-9 V+W-band spectrum computed on the same mask used for the $100\times100$\,GHz \planck\ spectrum (with a combined \textit{WMAP}+\planck\ mask for point sources) after rescaling by a multiplicative factor of $0.974$. The magenta points show the \planck\ $100\times 100$\,GHz spectrum computed on the same mask. The red line shows the best-fit \planck+\WP+\highL\ base \lcdm\ model. The lower panel shows the residuals with respect to this model. The error bars on the \textit{WMAP} points show the instrumental noise together with the noise-signal errors as discussed in the text; errors are not shown for \planck.} |
 | \referee{Variations in $H_0$ and $\ns$ as the maximum multipole in the \planck\ likelihood is increased from $\ell_{\rm max}=1000$ to $2500$. The red points show the changes in parameters determined from 2000 simulations, as described in the text. The blue point shows the changes determined from the real data.} |
 | \referee{Variations in $H_0$ and $\ns$ as the maximum multipole in the \planck\ likelihood is increased from $\ell_{\rm max}=1000$ to $2500$. The red points show the changes in parameters determined from 2000 simulations, as described in the text. The blue point shows the changes determined from the real data.} |
 | \referee{The acoustic scale distance ratio $r_{\rm s}/D_V(z)$ divided by the distance ratio of the best fit \textit{WMAP}-7+SPT base \LCDM\ cosmology of S12. The points are colour coded as follows: green star (6dF); purple squares (SDSS DR7 as analysed by \citealt{Percival:10}); black star (SDSS DR7 as analysed by \citealt{Padmanabhan:2012hf}); blue cross (BOSS DR9); and blue circles (WiggleZ). Error bars show $1\,\sigma$ errors on the data points. The grey band shows the $\pm 1\,\sigma$ range allowed by the \textit{WMAP}-7+SPT data.} |
 | Comparison of parameter constraints from \planck+\WP+\highL\ for three CIB foreground models with different restrictions on the CIB spectral index $\ncib$ (assumed to be the same in the $143$ and $217\,\mathrm{GHz}$ channels). The top six panels show cosmological parameter constraints on $\ns$ (top left) in the base \lcdm\ model and on single-parameter extensions of the \lcdm\ model. These are very stable to the modelling of the CIB. Each sub-plot is obtained from an independent analysis of that model with \COSMOMC. The lower six panels show the constraints on a subset of the foreground parameters in the base \lcdm\ model, some of which change significantly. |
 | \referee{Fits to the joint likelihoods for \planck\ and SPT S12 spectra. (a) Fits using only the $143\times143\, {\rm GHz}$ spectrum in the \planck\ likelihood. The blue points show the SPT data after recalibration and foreground subtraction, using the best-fit solution from the joint likelihood analysis. The magenta points show the foreground-subtracted \planck\ $143\times143\, {\rm GHz}$ spectrum. The lower panel show the residuals with respect to the best-fit \LCDM\ model to the \planck+SPT combined likelihoods (shown by the red line in the top panel) . (b) Foreground-subtracted and recalibrated SPT spectra using the best-fit parameters from the likelihood analysis of the full \planck\ likelihood combined with the SPT S12 likelihood. The magenta points show the best-fit \planck\ \LCDM\ spectrum from Fig.~\ref{Planckbestfitcl} and the red line shows the best-fit \planck+\WP+\highL\ base \LCDM\ model from the full \planck\ likelihood. The residuals with respect to this model are plotted in the lower panel.} |
 | 68\% and 95\% confidence regions on one-parameter extensions of the base \LCDM\ model for \planck+\WP\ (red) and \planck+\WP+BAO (blue). Horizontal dashed lines correspond to the fixed base model parameter value, and vertical dashed lines show the mean posterior value in the base model for \planck+\WP. |
 | Effect on cosmological parameter constraints of replacing the \WMAP\ low-$\ell$ polarization likelihood with a prior of $\tau=0.07\pm 0.013$, which prefers lower values of the optical depth. The top-left sub-plot is $\ns$ in the base \lcdm\ model, while the others are for one-parameter extensions. Each sub-plot shows results from independent \COSMOMC\ analyses of the corresponding model. |
 | \emph{Left}: \planck\ $TT$ spectrum at low multipoles with $68\%$ ranges on the posteriors. The ``rainbow'' band show the best fits to the entire \planck+\WP\ likelihood for the base \lcdm\ cosmology, colour-coded according to the value of the scalar spectral index $n_{\rm s}$. \emph{Right}: Limits (68\% and 95\%) on the relative amplitude of the base \lcdm\ fits to the \planck+\WP\ likelihood {\it fitted only to the \planck\ $TT$ likelihood} over the multipole range $2 \le \ell \le \ell_{\rm max}$. |
 | \referee{Fits to the joint likelihoods for \planck\ and SPT S12 spectra. (a) Fits using only the $143\times143\, {\rm GHz}$ spectrum in the \planck\ likelihood. The blue points show the SPT data after recalibration and foreground subtraction, using the best-fit solution from the joint likelihood analysis. The magenta points show the foreground-subtracted \planck\ $143\times143\, {\rm GHz}$ spectrum. The lower panel show the residuals with respect to the best-fit \LCDM\ model to the \planck+SPT combined likelihoods (shown by the red line in the top panel) . (b) Foreground-subtracted and recalibrated SPT spectra using the best-fit parameters from the likelihood analysis of the full \planck\ likelihood combined with the SPT S12 likelihood. The magenta points show the best-fit \planck\ \LCDM\ spectrum from Fig.~\ref{Planckbestfitcl} and the red line shows the best-fit \planck+\WP+\highL\ base \LCDM\ model from the full \planck\ likelihood. The residuals with respect to this model are plotted in the lower panel.} |
 | \emph{Upper}: comparison of the \lcdm\ constraints on $\ns$ (top-left) and single-parameter extensions of the \lcdm\ model for a variety of data cuts for \planck+\WP. Each sub-plot is obtained from a separate \COSMOMC\ analysis of the corresponding model. The dashed lines show the results from \plik, an alternative likelihood discussed in ~\citet{planck2013-p08}, run here with the same SZ and CIB foreground priors as for the \camspec\ results. For the extended models, the value of the additional parameter in the base \lcdm\ model is shown with the vertical dashed lines. \emph{Lower}: same as the upper set of panels, but for \planck+\WP+\highL. Additional data from the high-$\ell$ CMB experiments significantly reduce the foreground degeneracies. |
 | \referee{A number of separate effects contribute to the difference in $H_0$ inferred from \textit{WMAP}-7+S12 (top of left panel) and $H_0$ inferred from \planck+\WP\ (bottom of left panel), all going in the same direction. These include assumptions about neutrino masses, calibration procedures, differences between \textit{WMAP}-7 and \textit{WMAP}-9, and differences in the relative calibrations between SPT and \textit{WMAP} (as explained in the text). The right panel shows calibration parameter priors (top lines of each pair) and posteriors (bottom lines of each pair). The tighter of the priors shown for \WMAP-7+S12, and that shown for \WMAP-9+S12, come from using \planck\ to provide the relative calibration between \textit{WMAP} and S12. We plot only the posterior for the Planck+S12 relative calibration. Note that the relative-calibration parameter $y^{\rm SPT}_{\rm X}$ is between S12 and the other indicated data set (i.e., \WMAP\ or \Planck).} |
 | \emph{Upper}: comparison of the \lcdm\ constraints on $\ns$ (top-left) and single-parameter extensions of the \lcdm\ model for a variety of data cuts for \planck+\WP. Each sub-plot is obtained from a separate \COSMOMC\ analysis of the corresponding model. The dashed lines show the results from \plik, an alternative likelihood discussed in ~\citet{planck2013-p08}, run here with the same SZ and CIB foreground priors as for the \camspec\ results. For the extended models, the value of the additional parameter in the base \lcdm\ model is shown with the vertical dashed lines. \emph{Lower}: same as the upper set of panels, but for \planck+\WP+\highL. Additional data from the high-$\ell$ CMB experiments significantly reduce the foreground degeneracies. |
 | \emph{Left}: \planck\ $TT$ spectrum at low multipoles with $68\%$ ranges on the posteriors. The ``rainbow'' band show the best fits to the entire \planck+\WP\ likelihood for the base \lcdm\ cosmology, colour-coded according to the value of the scalar spectral index $n_{\rm s}$. \emph{Right}: Limits (68\% and 95\%) on the relative amplitude of the base \lcdm\ fits to the \planck+\WP\ likelihood {\it fitted only to the \planck\ $TT$ likelihood} over the multipole range $2 \le \ell \le \ell_{\rm max}$. |
 | Best-fit temperature power spectra for the base \LCDM\ model for \planck+\WP+\highL\ and for SPT+\textit{WMAP}-7 (upper panel). The parameters defining these models are listed in Table~\ref{SPTparams}. The lower panel shows the residuals of the SPT+\textit{WMAP}-7 best fit with respect to the \planck\ best fit. |
 | Comparison of parameter constraints from \planck+\WP+\highL\ for three CIB foreground models with different restrictions on the CIB spectral index $\ncib$ (assumed to be the same in the $143$ and $217\,\mathrm{GHz}$ channels). The top six panels show cosmological parameter constraints on $\ns$ (top left) in the base \lcdm\ model and on single-parameter extensions of the \lcdm\ model. These are very stable to the modelling of the CIB. Each sub-plot is obtained from an independent analysis of that model with \COSMOMC. The lower six panels show the constraints on a subset of the foreground parameters in the base \lcdm\ model, some of which change significantly. |
 | Effect on cosmological parameter constraints of replacing the \WMAP\ low-$\ell$ polarization likelihood with a prior of $\tau=0.07\pm 0.013$, which prefers lower values of the optical depth. The top-left sub-plot is $\ns$ in the base \lcdm\ model, while the others are for one-parameter extensions. Each sub-plot shows results from independent \COSMOMC\ analyses of the corresponding model. |
 | \emph{Upper}: comparison of the \lcdm\ constraints on $\ns$ (top-left) and single-parameter extensions of the \lcdm\ model for a variety of data cuts for \planck+\WP. Each sub-plot is obtained from a separate \COSMOMC\ analysis of the corresponding model. The dashed lines show the results from \plik, an alternative likelihood discussed in ~\citet{planck2013-p08}, run here with the same SZ and CIB foreground priors as for the \camspec\ results. For the extended models, the value of the additional parameter in the base \lcdm\ model is shown with the vertical dashed lines. \emph{Lower}: same as the upper set of panels, but for \planck+\WP+\highL. Additional data from the high-$\ell$ CMB experiments significantly reduce the foreground degeneracies. |
 | \emph{Upper}: comparison of the \lcdm\ constraints on $\ns$ (top-left) and single-parameter extensions of the \lcdm\ model for a variety of data cuts for \planck+\WP. Each sub-plot is obtained from a separate \COSMOMC\ analysis of the corresponding model. The dashed lines show the results from \plik, an alternative likelihood discussed in ~\citet{planck2013-p08}, run here with the same SZ and CIB foreground priors as for the \camspec\ results. For the extended models, the value of the additional parameter in the base \lcdm\ model is shown with the vertical dashed lines. \emph{Lower}: same as the upper set of panels, but for \planck+\WP+\highL. Additional data from the high-$\ell$ CMB experiments significantly reduce the foreground degeneracies. |
 | {\it Left}: \planck\ best-fit spectrum and SPT S12 spectrum calibrated and foreground corrected from the combined \planck+SPT likelihood analysis, as plotted in Fig.~\ref{PlanckvSPT}(b). The lower panel shows the residuals. The blue line shows the residual of the combined \textit{WMAP}-9+SPTS12 cosmology (which is similar to the \textit{WMAP}-7+SPT S12 model shown in Fig.~\ref{SPTtheory}). The green points show the \textit{WMAP}-9 V+W foreground corrected power spectrum {\it lowered in amplitude by 2.49\%}. {\it Right}: S12 spectrum corrected for foregrounds and relative calibration using the best-fit solution from the combined analysis of \textit{WMAP}-9 and SPT. The blue line shows the best-fit \textit{WMAP}-9+SPT S12 cosmology. The \planck\ points are as plotted in Fig. \ref{PlanckvWMAPvSPT}. The green points show the \textit{WMAP}-9 V+W foreground corrected spectrum {\it as computed by the \textit{WMAP} team} (i.e., with no multiplicative correction relative to \planck). |
 | {\it Left}: \planck\ best-fit spectrum and SPT S12 spectrum calibrated and foreground corrected from the combined \planck+SPT likelihood analysis, as plotted in Fig.~\ref{PlanckvSPT}(b). The lower panel shows the residuals. The blue line shows the residual of the combined \textit{WMAP}-9+SPTS12 cosmology (which is similar to the \textit{WMAP}-7+SPT S12 model shown in Fig.~\ref{SPTtheory}). The green points show the \textit{WMAP}-9 V+W foreground corrected power spectrum {\it lowered in amplitude by 2.49\%}. {\it Right}: S12 spectrum corrected for foregrounds and relative calibration using the best-fit solution from the combined analysis of \textit{WMAP}-9 and SPT. The blue line shows the best-fit \textit{WMAP}-9+SPT S12 cosmology. The \planck\ points are as plotted in Fig. \ref{PlanckvWMAPvSPT}. The green points show the \textit{WMAP}-9 V+W foreground corrected spectrum {\it as computed by the \textit{WMAP} team} (i.e., with no multiplicative correction relative to \planck). |
 | Comparison of the \planck\ and \WMAP\ power spectra. The green points show the combined \textit{WMAP} V+W spectrum computed on the same mask used for the $100\times100$\,GHz \planck\ spectrum (with a combined \textit{WMAP}+\planck\ mask for point source holes) after rescaling by a multiplicative factor of $0.976$. The pink points show the \planck\ $100\times 100$\,GHz spectrum computed on the same mask. The red line shows the best-fit \planck+\WP+\highL\ base \lcdm\ model. The lower panel shows the residuals with respect to this model. The error bars on the \textit{WMAP} points show errors from instrumental noise alone. |
 | Comparison of parameter constraints from \planck+\WP+\highL\ for three CIB foreground models with different restrictions on the CIB spectral index $\ncib$ (assumed to be the same in the $143$ and $217\,\mathrm{GHz}$ channels). The top six panels show cosmological parameter constraints on $\ns$ (top left) in the base \lcdm\ model and on single-parameter extensions of the \lcdm\ model. These are very stable to the modelling of the CIB. Each sub-plot is obtained from an independent analysis of that model with \COSMOMC. The lower six panels show the constraints on a subset of the foreground parameters in the base \lcdm\ model, some of which change significantly. |
 | Effect on cosmological parameter constraints of replacing the \WMAP\ low-$\ell$ polarization likelihood with a prior of $\tau=0.07\pm 0.013$, which prefers lower values of the optical depth. The top-left sub-plot is $\ns$ in the base \lcdm\ model, while the others are for one-parameter extensions. Each sub-plot shows results from independent \COSMOMC\ analyses of the corresponding model. |
 | \emph{Upper}: comparison of the \lcdm\ constraints on $\ns$ (top-left) and single-parameter extensions of the \lcdm\ model for a variety of data cuts for \planck+\WP. Each sub-plot is obtained from a separate \COSMOMC\ analysis of the corresponding model. The dashed lines show the results from \plik, an alternative likelihood discussed in ~\citet{planck2013-p08}, run here with the same SZ and CIB foreground priors as for the \camspec\ results. For the extended models, the value of the additional parameter in the base \lcdm\ model is shown with the vertical dashed lines. \emph{Lower}: same as the upper set of panels, but for \planck+\WP+\highL. Additional data from the high-$\ell$ CMB experiments significantly reduce the foreground degeneracies. |
 | \emph{Upper}: comparison of the \lcdm\ constraints on $\ns$ (top-left) and single-parameter extensions of the \lcdm\ model for a variety of data cuts for \planck+\WP. Each sub-plot is obtained from a separate \COSMOMC\ analysis of the corresponding model. The dashed lines show the results from \plik, an alternative likelihood discussed in ~\citet{planck2013-p08}, run here with the same SZ and CIB foreground priors as for the \camspec\ results. For the extended models, the value of the additional parameter in the base \lcdm\ model is shown with the vertical dashed lines. \emph{Lower}: same as the upper set of panels, but for \planck+\WP+\highL. Additional data from the high-$\ell$ CMB experiments significantly reduce the foreground degeneracies. |