Planck 2015 results. X. Diffuse component separation: Foreground maps
- Adam, R. et al
- arXiv:1502.01588
 | Zodiacal light extrapolation from HFI to LFI and WMAP frequency channels in terms of full-sky mean brightness temperature. The dotted line shows the power-law fit to the HFI observations between 100 and 353\,GHz, $s(\nu) = 0.70\,\mu\textrm{K}_{\textrm{RJ}}\, (\nu/100\,\textrm{GHz})^{1.31}$, and the vertical grey lines indicate the central frequencies of the LFI and WMAP frequency bands. The intersection between the dotted and grey lines defines the extrapolation to low frequencies. |
 | $\chi^2$ (\emph{top}) and residual maps, $\d_{\nu}-\s_{\nu}$ (\emph{bottom}), for a \texttt{Commander} analysis that includes all \Planck\ channel maps. These residual maps correspond to channels that are rejected from the baseline analysis due to instrumental systematics. No regularization noise has been added to the high-frequency channels in this case. The sharp ring-like features at high Galactic latitudes correspond to far sidelobe residuals; the broad features extending between the north and south ecliptic poles correspond to destriping errors; and the Galactic plane features correspond to calibration, bandpass, and modelling residuals. |
 | $\chi^2$ (\emph{top}) and residual maps, $\d_{\nu}-\s_{\nu}$ (\emph{bottom}), for a \texttt{Commander} analysis that includes all \Planck\ channel maps. These residual maps correspond to channels that are rejected from the baseline analysis due to instrumental systematics. No regularization noise has been added to the high-frequency channels in this case. The sharp ring-like features at high Galactic latitudes correspond to far sidelobe residuals; the broad features extending between the north and south ecliptic poles correspond to destriping errors; and the Galactic plane features correspond to calibration, bandpass, and modelling residuals. |
 | $\chi^2$ (\emph{top}) and residual maps, $\d_{\nu}-\s_{\nu}$ (\emph{bottom}), for a \texttt{Commander} analysis that includes all \Planck\ channel maps. These residual maps correspond to channels that are rejected from the baseline analysis due to instrumental systematics. No regularization noise has been added to the high-frequency channels in this case. The sharp ring-like features at high Galactic latitudes correspond to far sidelobe residuals; the broad features extending between the north and south ecliptic poles correspond to destriping errors; and the Galactic plane features correspond to calibration, bandpass, and modelling residuals. |
 | $\chi^2$ (\emph{top}) and residual maps, $\d_{\nu}-\s_{\nu}$ (\emph{bottom}), for a \texttt{Commander} analysis that includes all \Planck\ channel maps. These residual maps correspond to channels that are rejected from the baseline analysis due to instrumental systematics. No regularization noise has been added to the high-frequency channels in this case. The sharp ring-like features at high Galactic latitudes correspond to far sidelobe residuals; the broad features extending between the north and south ecliptic poles correspond to destriping errors; and the Galactic plane features correspond to calibration, bandpass, and modelling residuals. |
 | $\chi^2$ (\emph{top}) and residual maps, $\d_{\nu}-\s_{\nu}$ (\emph{bottom}), for a \texttt{Commander} analysis that includes all \Planck\ channel maps. These residual maps correspond to channels that are rejected from the baseline analysis due to instrumental systematics. No regularization noise has been added to the high-frequency channels in this case. The sharp ring-like features at high Galactic latitudes correspond to far sidelobe residuals; the broad features extending between the north and south ecliptic poles correspond to destriping errors; and the Galactic plane features correspond to calibration, bandpass, and modelling residuals. |
 | $\chi^2$ (\emph{top}) and residual maps, $\d_{\nu}-\s_{\nu}$ (\emph{bottom}), for a \texttt{Commander} analysis that includes all \Planck\ channel maps. These residual maps correspond to channels that are rejected from the baseline analysis due to instrumental systematics. No regularization noise has been added to the high-frequency channels in this case. The sharp ring-like features at high Galactic latitudes correspond to far sidelobe residuals; the broad features extending between the north and south ecliptic poles correspond to destriping errors; and the Galactic plane features correspond to calibration, bandpass, and modelling residuals. |
 | $\chi^2$ (\emph{top}) and residual maps, $\d_{\nu}-\s_{\nu}$ (\emph{bottom}), for a \texttt{Commander} analysis that includes all \Planck\ channel maps. These residual maps correspond to channels that are rejected from the baseline analysis due to instrumental systematics. No regularization noise has been added to the high-frequency channels in this case. The sharp ring-like features at high Galactic latitudes correspond to far sidelobe residuals; the broad features extending between the north and south ecliptic poles correspond to destriping errors; and the Galactic plane features correspond to calibration, bandpass, and modelling residuals. |
 | $\chi^2$ (\emph{top}) and residual maps, $\d_{\nu}-\s_{\nu}$ (\emph{bottom}), for a \texttt{Commander} analysis that includes all \Planck\ channel maps. These residual maps correspond to channels that are rejected from the baseline analysis due to instrumental systematics. No regularization noise has been added to the high-frequency channels in this case. The sharp ring-like features at high Galactic latitudes correspond to far sidelobe residuals; the broad features extending between the north and south ecliptic poles correspond to destriping errors; and the Galactic plane features correspond to calibration, bandpass, and modelling residuals. |
 | $\chi^2$ (\emph{top}) and residual maps, $\d_{\nu}-\s_{\nu}$ (\emph{bottom}), for a \texttt{Commander} analysis that includes all \Planck\ channel maps. These residual maps correspond to channels that are rejected from the baseline analysis due to instrumental systematics. No regularization noise has been added to the high-frequency channels in this case. The sharp ring-like features at high Galactic latitudes correspond to far sidelobe residuals; the broad features extending between the north and south ecliptic poles correspond to destriping errors; and the Galactic plane features correspond to calibration, bandpass, and modelling residuals. |
 | $\chi^2$ (\emph{top}) and residual maps, $\d_{\nu}-\s_{\nu}$ (\emph{bottom}), for a \texttt{Commander} analysis that includes all \Planck\ channel maps. These residual maps correspond to channels that are rejected from the baseline analysis due to instrumental systematics. No regularization noise has been added to the high-frequency channels in this case. The sharp ring-like features at high Galactic latitudes correspond to far sidelobe residuals; the broad features extending between the north and south ecliptic poles correspond to destriping errors; and the Galactic plane features correspond to calibration, bandpass, and modelling residuals. |
 | $\chi^2$ (\emph{top}) and residual maps, $\d_{\nu}-\s_{\nu}$ (\emph{bottom}), for a \texttt{Commander} analysis that includes all \Planck\ channel maps. These residual maps correspond to channels that are rejected from the baseline analysis due to instrumental systematics. No regularization noise has been added to the high-frequency channels in this case. The sharp ring-like features at high Galactic latitudes correspond to far sidelobe residuals; the broad features extending between the north and south ecliptic poles correspond to destriping errors; and the Galactic plane features correspond to calibration, bandpass, and modelling residuals. |
 | Processing masks (PM) used in the joint temperature analysis, including 99.6\,\% and 61\,\% of the sky, respectively. The former is used for calibration and bandpass estimation, and the latter for monopole and dipole estimation. |
 | Processing masks (PM) used in the joint temperature analysis, including 99.6\,\% and 61\,\% of the sky, respectively. The former is used for calibration and bandpass estimation, and the latter for monopole and dipole estimation. |
 | Spectral energy densities (SEDs) for the main astrophysical components included in the present analysis, in brightness temperature. From left to right and top to bottom, panels show: (1) synchrotron emission; (2) free-free emission; (3) spinning dust emission; (4) CO line emission; (5) thermal dust emission; and (6) the thermal Sunyaev-Zeldovich effect. For each case, several parameter combinations are shown to illustrate their effect on the final observable spectrum. Vertical grey bands indicate the centre frequencies of the observations listed in Table~\ref{tab:data}, but for clarity true bandwidths are suppressed. In each panel, the black dashed line shows the CMB brightness temperature corresponding to a thermodynamic temperature of $70\,\mu\textrm{K}$, the CMB rms at $1\deg$ FWHM angular scale. |
 | Spectral energy densities (SED) for the main astrophysical components included in the present analysis, in brightness temperature. From left to right and top to bottom, panels show: 1) synchrotron emission; 2) free-free emission; 3) spinning dust emission; 4) CO line emission; 5) thermal dust emission; and 6) the thermal Sunyaev-Zeldovich effect. For each case, several parameter combinations are shown to illustrate their effect on the final observable spectrum. Vertical gray bands indicate the center frequencies of the observations listed in Table~\ref{tab:data}, but for clarity true bandwidths are suppressed. In each panel, the black dashed line shows the CMB brightness temperature corresponding to a thermodynamic temperature of $70\,\mu\textrm{K}$, the CMB rms at $1\deg$ FWHM angular scale. |
 | Spectral energy densities (SEDs) for the main astrophysical components included in the present analysis, in brightness temperature. From left to right and top to bottom, panels show: (1) synchrotron emission; (2) free-free emission; (3) spinning dust emission; (4) CO line emission; (5) thermal dust emission; and (6) the thermal Sunyaev-Zeldovich effect. For each case, several parameter combinations are shown to illustrate their effect on the final observable spectrum. Vertical grey bands indicate the centre frequencies of the observations listed in Table~\ref{tab:data}, but for clarity true bandwidths are suppressed. In each panel, the black dashed line shows the CMB brightness temperature corresponding to a thermodynamic temperature of $70\,\mu\textrm{K}$, the CMB rms at $1\deg$ FWHM angular scale. |
 | Spectral energy densities (SEDs) for the main astrophysical components included in the present analysis, in brightness temperature. From left to right and top to bottom, panels show: (1) synchrotron emission; (2) free-free emission; (3) spinning dust emission; (4) CO line emission; (5) thermal dust emission; and (6) the thermal Sunyaev-Zeldovich effect. For each case, several parameter combinations are shown to illustrate their effect on the final observable spectrum. Vertical grey bands indicate the centre frequencies of the observations listed in Table~\ref{tab:data}, but for clarity true bandwidths are suppressed. In each panel, the black dashed line shows the CMB brightness temperature corresponding to a thermodynamic temperature of $70\,\mu\textrm{K}$, the CMB rms at $1\deg$ FWHM angular scale. |
 | Spectral energy densities (SEDs) for the main astrophysical components included in the present analysis, in brightness temperature. From left to right and top to bottom, panels show: (1) synchrotron emission; (2) free-free emission; (3) spinning dust emission; (4) CO line emission; (5) thermal dust emission; and (6) the thermal Sunyaev-Zeldovich effect. For each case, several parameter combinations are shown to illustrate their effect on the final observable spectrum. Vertical grey bands indicate the centre frequencies of the observations listed in Table~\ref{tab:data}, but for clarity true bandwidths are suppressed. In each panel, the black dashed line shows the CMB brightness temperature corresponding to a thermodynamic temperature of $70\,\mu\textrm{K}$, the CMB rms at $1\deg$ FWHM angular scale. |
 | Spectral energy densities (SEDs) for the main astrophysical components included in the present analysis, in brightness temperature. From left to right and top to bottom, panels show: (1) synchrotron emission; (2) free-free emission; (3) spinning dust emission; (4) CO line emission; (5) thermal dust emission; and (6) the thermal Sunyaev-Zeldovich effect. For each case, several parameter combinations are shown to illustrate their effect on the final observable spectrum. Vertical grey bands indicate the centre frequencies of the observations listed in Table~\ref{tab:data}, but for clarity true bandwidths are suppressed. In each panel, the black dashed line shows the CMB brightness temperature corresponding to a thermodynamic temperature of $70\,\mu\textrm{K}$, the CMB rms at $1\deg$ FWHM angular scale. |
 | Spectral energy densities (SEDs) for the main astrophysical components included in the present analysis, in brightness temperature. From left to right and top to bottom, panels show: (1) synchrotron emission; (2) free-free emission; (3) spinning dust emission; (4) CO line emission; (5) thermal dust emission; and (6) the thermal Sunyaev-Zeldovich effect. For each case, several parameter combinations are shown to illustrate their effect on the final observable spectrum. Vertical grey bands indicate the centre frequencies of the observations listed in Table~\ref{tab:data}, but for clarity true bandwidths are suppressed. In each panel, the black dashed line shows the CMB brightness temperature corresponding to a thermodynamic temperature of $70\,\mu\textrm{K}$, the CMB rms at $1\deg$ FWHM angular scale. |
 | Fractional difference maps on the form $(\d_{\textrm{143-ds1}}-\d_{\textrm{143-ds2}})/\d_{\textrm{143-ds1}}$, as evaluated from the real data (\emph{top}) and from the FFP8 simulation (\emph{bottom}), both smoothed to $40\arcm$ FWHM. The 1\,\% difference observed along the Galactic plane is caused by a mismatch between the measured bandpass profiles (which are used to construct the FFP8 simulations) and those corresponding to in-flight observations. See Sect.~\ref{sec:instrumental_effects} for further discussion, and Sect.~\ref{sec:baseline} for explicit corrections. |
 | Fractional difference maps on the form $(\d_{\textrm{143-ds1}}-\d_{\textrm{143-ds2}})/\d_{\textrm{143-ds1}}$, as evaluated from the real data (\emph{top}) and from the FFP8 simulation (\emph{bottom}), both smoothed to $40\arcm$ FWHM. The 1\,\% difference observed along the Galactic plane is caused by a mismatch between the measured bandpass profiles (which are used to construct the FFP8 simulations) and those corresponding to in-flight observations. See Sect.~\ref{sec:instrumental_effects} for further discussion, and Sect.~\ref{sec:baseline} for explicit corrections. |
 | \emph{Top left}: effective low-frequency foreground spectral index as measured from the combination of \Planck, \WMAP, and 408\,MHz, with no attempt to disentangle synchrotron, free-free, and spinning dust emission into separate components. However, higher-frequency components (CMB, CO, thermal dust, etc.) are fitted component-by-component, as in the baseline model. Note the very steep spectral indices, $\beta_{\textrm{lf}}\lesssim-3.6$, near the Galactic plane, with dust-like morphology. These can only be reasonably explained in terms of spinning dust.\quad \emph{Top right}: ratio between the 857 and 545\,GHz frequency maps, smoothed to $1\deg$ FWHM, highlighting the spatially varying temperature of thermal dust. The mask is defined by any region for which the 545\,GHz amplitude is smaller than ten times the 545\,GHz monopole.\quad \emph{Bottom left}: difference between the 100-ds1 and 100-ds2 detector maps, smoothed to $1\deg$, demonstrating the presence of CO $J$=1$\rightarrow$0 emission in these channels.\quad \emph{Bottom right}: difference between the \WMAP\ W3 and W2 differencing assembly maps, smoothed to $1\deg$ FWHM. The excess signal near the Galactic centre is due to line emission in the 94\,GHz channels. The peak amplitude of the difference map is 740\muK. |
 | \emph{Top left}: effective low-frequency foreground spectral index as measured from the combination of \Planck, \WMAP, and 408\,MHz, with no attempt to disentangle synchrotron, free-free, and spinning dust emission into separate components. However, higher-frequency components (CMB, CO, thermal dust, etc.) are fitted component-by-component, as in the baseline model. Note the very steep spectral indices, $\beta_{\textrm{lf}}\lesssim-3.6$, near the Galactic plane, with dust-like morphology. These can only be reasonably explained in terms of spinning dust.\quad \emph{Top right}: ratio between the 857 and 545\,GHz frequency maps, smoothed to $1\deg$ FWHM, highlighting the spatially varying temperature of thermal dust. The mask is defined by any region for which the 545\,GHz amplitude is smaller than ten times the 545\,GHz monopole.\quad \emph{Bottom left}: difference between the 100-ds1 and 100-ds2 detector maps, smoothed to $1\deg$, demonstrating the presence of CO $J$=1$\rightarrow$0 emission in these channels.\quad \emph{Bottom right}: difference between the \WMAP\ W3 and W2 differencing assembly maps, smoothed to $1\deg$ FWHM. The excess signal near the Galactic centre is due to line emission in the 94\,GHz channels. The peak amplitude of the difference map is 740\muK. |
 | \emph{Top left}: effective low-frequency foreground spectral index as measured from the combination of \Planck, \WMAP, and 408\,MHz, with no attempt to disentangle synchrotron, free-free, and spinning dust emission into separate components. However, higher-frequency components (CMB, CO, thermal dust, etc.) are fitted component-by-component, as in the baseline model. Note the very steep spectral indices, $\beta_{\textrm{lf}}\lesssim-3.6$, near the Galactic plane, with dust-like morphology. These can only be reasonably explained in terms of spinning dust.\quad \emph{Top right}: ratio between the 857 and 545\,GHz frequency maps, smoothed to $1\deg$ FWHM, highlighting the spatially varying temperature of thermal dust. The mask is defined by any region for which the 545\,GHz amplitude is smaller than ten times the 545\,GHz monopole.\quad \emph{Bottom left}: difference between the 100-ds1 and 100-ds2 detector maps, smoothed to $1\deg$, demonstrating the presence of CO $J$=1$\rightarrow$0 emission in these channels.\quad \emph{Bottom right}: difference between the \WMAP\ W3 and W2 differencing assembly maps, smoothed to $1\deg$ FWHM. The excess signal near the Galactic centre is due to line emission in the 94\,GHz channels. The peak amplitude of the difference map is 740\muK. |
 | \emph{Top left}: effective low-frequency foreground spectral index as measured from the combination of \Planck, \WMAP, and 408\,MHz, with no attempt to disentangle synchrotron, free-free, and spinning dust emission into separate components. However, higher-frequency components (CMB, CO, thermal dust, etc.) are fitted component-by-component, as in the baseline model. Note the very steep spectral indices, $\beta_{\textrm{lf}}\lesssim-3.6$, near the Galactic plane, with dust-like morphology. These can only be reasonably explained in terms of spinning dust.\quad \emph{Top right}: ratio between the 857 and 545\,GHz frequency maps, smoothed to $1\deg$ FWHM, highlighting the spatially varying temperature of thermal dust. The mask is defined by any region for which the 545\,GHz amplitude is smaller than ten times the 545\,GHz monopole.\quad \emph{Bottom left}: difference between the 100-ds1 and 100-ds2 detector maps, smoothed to $1\deg$, demonstrating the presence of CO $J$=1$\rightarrow$0 emission in these channels.\quad \emph{Bottom right}: difference between the \WMAP\ W3 and W2 differencing assembly maps, smoothed to $1\deg$ FWHM. The excess signal near the Galactic centre is due to line emission in the 94\,GHz channels. The peak amplitude of the difference map is 740\muK. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) CMB intensity maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. The two circular regions close to the North Galactic Pole in the rms map correspond to the Coma and Virgo clusters, for which the thermal SZ efect is fitted together with the primary diffuse components. Note also that the rms map includes statistical errors alone, not modelling errors, and they are therefore only meaningful in regions where the corresponding $\chi^2$ is acceptable; see Fig.~\ref{fig:chisq_map}. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) CMB intensity maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. The two circular regions close to the North Galactic Pole in the rms map correspond to the Coma and Virgo clusters, for which the thermal SZ efect is fitted together with the primary diffuse components. Note also that the rms map includes statistical errors alone, not modelling errors, and they are therefore only meaningful in regions where the corresponding $\chi^2$ is acceptable; see Fig.~\ref{fig:chisq_map}. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) synchrotron intensity maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) synchrotron intensity maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) free-free emission measure maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) free-free emission measure maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) spinning dust intensity maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. The top panel shows the sum of the two spinning dust components in the baseline model, evaluated at 30\,GHz, whereas the bottom shows the standard deviation of only the primary spinning dust component, evaluated at 22.8\,GHz. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) spinning dust intensity maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. The top panel shows the sum of the two spinning dust components in the baseline model, evaluated at 30\,GHz, whereas the bottom shows the standard deviation of only the primary spinning dust component, evaluated at 22.8\,GHz. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) thermal dust intensity maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) thermal dust intensity maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) 94/100\,GHz line emission maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) 94/100\,GHz line emission maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) CO $J$=1$\rightarrow$0 line emission maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) CO $J$=1$\rightarrow$0 line emission maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) CO $J$=2$\rightarrow$1 line emission maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. The two circular regions close to the North Galactic Pole in the rms map correspond to the Coma and Virgo clusters, for which the thermal SZ effect is fitted together with the primary diffuse components. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) CO $J$=2$\rightarrow$1 line emission maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. The two circular regions close to the North Galactic Pole in the rms map correspond to the Coma and Virgo clusters, for which the thermal SZ effect is fitted together with the primary diffuse components. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) CO $J$=3$\rightarrow$2 line emission maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) CO $J$=3$\rightarrow$2 line emission maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) spinning dust peak frequency maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) spinning dust peak frequency maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) thermal dust spectral index maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) thermal dust spectral index maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) thermal dust temperature maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (\emph{top}) and posterior rms (\emph{bottom}) thermal dust temperature maps derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Maximum posterior (free-free) electron temperature map derived from the joint baseline analysis of \Planck, \WMAP, and 408\,MHz observations. |
 | Detector map and differencing assembly re-calibration factors for \Planck\ and \WMAP, as reported in Table~\ref{tab:monopole}. |
 | Residual maps, $\d_{\nu}-\s_{\nu}$, for each detector data set included in the baseline joint \Planck, \WMAP, and 408\,MHz temperature analysis. All panels employ linear colour scales. |
 | \emph{Top}: $\chi^2$ per pixel for joint baseline \Planck, \WMAP, and 408\,MHz intensity analysis.\quad \emph{Middle}: confidence mask derived by smoothing the $\chi^2$ map to $1\deg$ FWHM, and thresholding at a value of $\chi^2_{\textrm{max}}=50$. Its primary application is for the low-$\ell$ 2015 \Planck\ temperature likelihood, and it is accordingly denoted LM93 (93\,\% likelihood mask); see \citet{planck2014-a13} for further details.\quad \emph{Bottom}: histogram of $\chi^2$ values outside the conservative PM61 mask. The grey dashed line shows the best-fit $\chi^2$ distribution with a variable degree of freedom and scaling, used to account for prior and noise modelling effects; see Sect.~\ref{sec:baseline} for further discussion. |
 | \emph{Top}: $\chi^2$ per pixel for joint baseline \Planck, \WMAP, and 408\,MHz intensity analysis.\quad \emph{Middle}: confidence mask derived by smoothing the $\chi^2$ map to $1\deg$ FWHM, and thresholding at a value of $\chi^2_{\textrm{max}}=50$. Its primary application is for the low-$\ell$ 2015 \Planck\ temperature likelihood, and it is accordingly denoted LM93 (93\,\% likelihood mask); see \citet{planck2014-a13} for further details.\quad \emph{Bottom}: histogram of $\chi^2$ values outside the conservative PM61 mask. The grey dashed line shows the best-fit $\chi^2$ distribution with a variable degree of freedom and scaling, used to account for prior and noise modelling effects; see Sect.~\ref{sec:baseline} for further discussion. |
 | \emph{Top}: $\chi^2$ per pixel for joint baseline \Planck, \WMAP, and 408\,MHz intensity analysis.\quad \emph{Middle}: confidence mask derived by smoothing the $\chi^2$ map to $1\deg$ FWHM, and thresholding at a value of $\chi^2_{\textrm{max}}=50$. Its primary application is for the low-$\ell$ 2015 \Planck\ temperature likelihood, and it is accordingly denoted LM93 (93\,\% likelihood mask); see \citet{planck2014-a13} for further details.\quad \emph{Bottom}: histogram of $\chi^2$ values outside the conservative PM61 mask. The grey dashed line shows the best-fit $\chi^2$ distribution with a variable degree of freedom and scaling, used to account for prior and noise modelling effects; see Sect.~\ref{sec:baseline} for further discussion. |
 | High-resolution maximum-posterior (\emph{top}) and half-ring half-difference (\emph{bottom}) CMB amplitude maps. |
 | High-resolution maximum-posterior (\emph{top}) and half-ring half-difference (\emph{bottom}) CMB amplitude maps. |
 | High-resolution maximum-posterior (\emph{top}) and half-ring half-difference (\emph{bottom}) CO $J$=2$\rightarrow$1 amplitude maps. |
 | High-resolution maximum-posterior (\emph{top}) and half-ring half-difference (\emph{bottom}) CO $J$=2$\rightarrow$1 amplitude maps. |
 | High-resolution maximum-posterior (\emph{top}) and half-ring half-difference rms (\emph{bottom}) thermal dust amplitude maps. |
 | High-resolution maximum-posterior (\emph{top}) and half-ring half-difference rms (\emph{bottom}) thermal dust amplitude maps. |
 | High-resolution maximum-posterior (\emph{top}) and half-ring half-difference rms (\emph{bottom}) thermal dust spectral index maps. |
 | High-resolution maximum-posterior (\emph{top}) and half-ring half-difference rms (\emph{bottom}) thermal dust spectral index maps. |
 | Fractional difference between the template amplitudes derived when fitting the GASS \ion{H}{i} survey data at high Galactic latitudes to: (1) the raw \Planck\ and \WMAP\ temperature maps; and to (2) the sum of the spinning and thermal dust models derived by \commander\ in this paper. |
 | Fractional difference of the mean thermal dust SEDs as derived by cross-correlation with the GASS \ion{H}{i} survey data at high Galactic latitudes, updated with the latest \Planck\ 2015 temperature sky maps, \citep{planck2013-XVII} and by \texttt{Commander} in this paper. The dotted horizontal lines indicate fractional differences of $\pm10\,$\%. For comparison purposes, we also show the extrapolation to the 100, 140, and 240$\,\mu\textrm{m}$ DIRBE frequencies. These observations are not included in the fits performed in this paper; see Sect.~\ref{sec:dust} for further discussion. |
 | Comparison of the thermal dust spectral index, $\beta_{\textrm{d}}$, estimated by internal \Planck\ map cross-correlations over \healpix\ $N_{\textrm{side}}=8$ pixels in \citet{planck2014-XXII} and those presented in this paper. The best-fit Gaussian distributions to the two histograms have mean and standard deviations of $\beta_{\textrm{d}}^{\texttt{Comm}} = 1.53\pm0.03$ and $\beta_{\textrm{d}}^{\textrm{cross-corr}} = 1.51\pm0.06$, respectively. |
 | High-resolution CO $J$=1$\rightarrow$0 maps derived from the 2015 \Planck\ sky maps with two different algorithms, denoted Type-1 (\emph{top row}) and Type-2 (\emph{middle row}); and derived from the 2013 \Planck\ sky maps with \texttt{Commander-Ruler} (\emph{bottom row}). Details can be found in \cite{planck2013-p03a}. All maps are smoothed to a common resolution of $15\arcm$ FWHM. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps, all maps smoothed to $15\arcm$ FWHM, centered on the Orion region with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | High-resolution CO $J$=1$\rightarrow$0 maps derived from the 2015 \Planck\ sky maps with two different algorithms, denoted Type-1 (\emph{top row}) and Type-2 (\emph{middle row}); and derived from the 2013 \Planck\ sky maps with \texttt{Commander-Ruler} (\emph{bottom row}). Details can be found in \cite{planck2013-p03a}. All maps are smoothed to a common resolution of $15\arcm$ FWHM. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps, all maps smoothed to $15\arcm$ FWHM, centered on the Orion region with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | High-resolution CO $J$=1$\rightarrow$0 maps derived from the 2015 \Planck\ sky maps with two different algorithms, denoted Type-1 (\emph{top row}) and Type-2 (\emph{middle row}); and derived from the 2013 \Planck\ sky maps with \texttt{Commander-Ruler} (\emph{bottom row}). Details can be found in \cite{planck2013-p03a}. All maps are smoothed to a common resolution of $15\arcm$ FWHM. |
 | High-resolution CO $J$=2$\rightarrow$1 maps derived from the 2015 \Planck\ sky maps with three different algorithms, denoted Type-1 (\emph{top row}), Type-2 (\emph{middle row}) and \texttt{Commander} (\emph{bottom row}), see \cite{planck2013-p03a} for details. All maps are smoothed to a common resolution of $15\arcm$ FWHM. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps, all maps smoothed to $15\arcm$ FWHM, centered on the Orion region with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps, all maps smoothed to $15\arcm$ FWHM, centered on the Orion region with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | High-resolution CO $J$=2$\rightarrow$1 maps derived from the 2015 \Planck\ sky maps with three different algorithms, denoted Type-1 (\emph{top row}), Type-2 (\emph{middle row}) and \texttt{Commander} (\emph{bottom row}), see \cite{planck2013-p03a} for details. All maps are smoothed to a common resolution of $15\arcm$ FWHM. |
 | High-resolution CO $J$=2$\rightarrow$1 maps derived from the 2015 \Planck\ sky maps with three different algorithms, denoted Type-1 (\emph{top row}), Type-2 (\emph{middle row}) and \texttt{Commander} (\emph{bottom row}), see \cite{planck2013-p03a} for details. All maps are smoothed to a common resolution of $15\arcm$ FWHM. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps, all maps smoothed to $15\arcm$ FWHM, centered on the Orion region with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps, all maps smoothed to $15\arcm$ FWHM, centered on the Orion region with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps. All maps smoothed to $15\arcm$ FWHM and centred on the Orion region, with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps. All maps smoothed to $15\arcm$ FWHM and centred on the Orion region, with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps. All maps smoothed to $15\arcm$ FWHM and centred on the Orion region, with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps. All maps smoothed to $15\arcm$ FWHM and centred on the Orion region, with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps. All maps smoothed to $15\arcm$ FWHM and centred on the Orion region, with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | $30\deg \times 30\deg$ zoom-in of various CO emission line maps. All maps smoothed to $15\arcm$ FWHM and centred on the Orion region, with Galactic coordinates $(l,b) = (201\deg,-9\deg)$. |
 | $T$--$T$ scatter plots between Type-1, Type-2, \texttt{Commander} CO maps and the \citet{dame2001} CO\,$J$=1$\rightarrow$0 map, smoothed to $1\deg$ FWHM and pixelized with a \healpix\ resolution parameter $N_{\textrm{side}}=64$. The panels show correlations for $J$=1$\rightarrow$0 (\emph{top left}), $J$=2$\rightarrow$1 (\emph{top right}) and $J$=3$\rightarrow$2 (\emph{bottom left}) line maps; the bottom right panel show correlations between the baseline $1\deg$ FWHM \texttt{Commander} CO maps and the (smoothed) Type-1, Type-2 and the high-resolution \texttt{Commander} $J$=2$\rightarrow$1 map. |
 | $T$--$T$ scatter plots between Type-1, Type-2, \texttt{Commander} CO maps and the \citet{dame2001} CO\,$J$=1$\rightarrow$0 map, smoothed to $1\deg$ FWHM and pixelized with a \healpix\ resolution parameter $N_{\textrm{side}}=64$. The panels show correlations for $J$=1$\rightarrow$0 (\emph{top left}), $J$=2$\rightarrow$1 (\emph{top right}) and $J$=3$\rightarrow$2 (\emph{bottom left}) line maps; the bottom right panel show correlations between the baseline $1\deg$ FWHM \texttt{Commander} CO maps and the (smoothed) Type-1, Type-2 and the high-resolution \texttt{Commander} $J$=2$\rightarrow$1 map. |
 | $T$--$T$ scatter plots between Type-1, Type-2, \texttt{Commander} CO maps and the \citet{dame2001} CO\,$J$=1$\rightarrow$0 map, smoothed to $1\deg$ FWHM and pixelized with a \healpix\ resolution parameter $N_{\textrm{side}}=64$. The panels show correlations for $J$=1$\rightarrow$0 (\emph{top left}), $J$=2$\rightarrow$1 (\emph{top right}) and $J$=3$\rightarrow$2 (\emph{bottom left}) line maps; the bottom right panel show correlations between the baseline $1\deg$ FWHM \texttt{Commander} CO maps and the (smoothed) Type-1, Type-2 and the high-resolution \texttt{Commander} $J$=2$\rightarrow$1 map. |
 | $T$--$T$ scatter plots between Type-1, Type-2, \texttt{Commander} CO maps and the \citet{dame2001} CO\,$J$=1$\rightarrow$0 map, smoothed to $1\deg$ FWHM and pixelized with a \healpix\ resolution parameter $N_{\textrm{side}}=64$. The panels show correlations for $J$=1$\rightarrow$0 (\emph{top left}), $J$=2$\rightarrow$1 (\emph{top right}) and $J$=3$\rightarrow$2 (\emph{bottom left}) line maps; the bottom right panel show correlations between the baseline $1\deg$ FWHM \texttt{Commander} CO maps and the (smoothed) Type-1, Type-2 and the high-resolution \texttt{Commander} $J$=2$\rightarrow$1 map. |
 | Pixel histograms of high-resolution CO line emission maps, all smoothed to a common resolution of $15\arcm$ FWHM and re-pixelized at \healpix\ resolution $N_{\textrm{side}}=512$. |
 | Comparison of \Planck\ CO $J$=2$\rightarrow$1 maps with the high Galactic latitude CO detections published by \citet{hartmann1998} and \citet{magnani2000} (\emph{top}), and corresponding amplitude histograms including only positions in which no detections were found in the same surveys (\emph{bottom}). |
 | Comparison of \Planck\ CO $J$=2$\rightarrow$1 maps with the high Galactic latitude CO detections published by \citet{hartmann1998} and \citet{magnani2000} (\emph{top}), and corresponding amplitude histograms including only positions in which no detections were found in the same surveys (\emph{bottom}). |
 | Maximum posterior amplitude polarization maps derived from the \Planck\ observations between 30 and 353\,GHz. Left and right columns show the Stokes $Q$ and $U$ parameters, respectively, while rows show, from top to bottom, CMB, synchrotron polarization at 30\,GHz, and thermal dust polarization at 353\,GHz. The CMB map has been highpass-filtered with a cosine-apodized filter between $\ell=20$ and 40, and the Galactic plane (defined by the 17\,\% CPM83 mask shown in Fig.~\ref{fig:chisq_pol_map}) has been replaced with a constrained Gaussian realization \citep{planck2014-a11}. |
 | Maximum posterior amplitude polarization maps derived from the \Planck\ observations between 30 and 353\,GHz. Left and right columns show the Stokes $Q$ and $U$ parameters, respectively, while rows show, from top to bottom, CMB, synchrotron polarization at 30\,GHz, and thermal dust polarization at 353\,GHz. The CMB map has been highpass-filtered with a cosine-apodized filter between $\ell=20$ and 40, and the Galactic plane (defined by the 17\,\% CPM83 mask shown in Fig.~\ref{fig:chisq_pol_map}) has been replaced with a constrained Gaussian realization \citep{planck2014-a11}. |
 | Maximum posterior amplitude polarization maps derived from the \Planck\ observations between 30 and 353\,GHz. Left and right columns show the Stokes $Q$ and $U$ parameters, respectively, while rows show, from top to bottom, CMB, synchrotron polarization at 30\,GHz, and thermal dust polarization at 353\,GHz. The CMB map has been highpass-filtered with a cosine-apodized filter between $\ell=20$ and 40, and the Galactic plane (defined by the 17\,\% CPM83 mask shown in Fig.~\ref{fig:chisq_pol_map}) has been replaced with a constrained Gaussian realization \citep{planck2014-a11}. |
 | Maximum posterior amplitude polarization maps derived from the \Planck\ observations between 30 and 353\,GHz. Left and right columns show the Stokes $Q$ and $U$ parameters, respectively, while rows show, from top to bottom, CMB, synchrotron polarization at 30\,GHz, and thermal dust polarization at 353\,GHz. The CMB map has been highpass-filtered with a cosine-apodized filter between $\ell=20$ and 40, and the Galactic plane (defined by the 17\,\% CPM83 mask shown in Fig.~\ref{fig:chisq_pol_map}) has been replaced with a constrained Gaussian realization \citep{planck2014-a11}. |
 | Maximum posterior amplitude polarization maps derived from the \Planck\ observations between 30 and 353\,GHz. Left and right columns show the Stokes $Q$ and $U$ parameters, respectively, while rows show, from top to bottom, CMB, synchrotron polarization at 30\,GHz, and thermal dust polarization at 353\,GHz. The CMB map has been highpass-filtered with a cosine-apodized filter between $\ell=20$ and 40, and the Galactic plane (defined by the 17\,\% CPM83 mask shown in Fig.~\ref{fig:chisq_pol_map}) has been replaced with a constrained Gaussian realization \citep{planck2014-a11}. |
 | Maximum posterior amplitude polarization maps derived from the \Planck\ observations between 30 and 353\,GHz. Left and right columns show the Stokes $Q$ and $U$ parameters, respectively, while rows show, from top to bottom, CMB, synchrotron polarization at 30\,GHz, and thermal dust polarization at 353\,GHz. The CMB map has been highpass-filtered with a cosine-apodized filter between $\ell=20$ and 40, and the Galactic plane (defined by the 17\,\% CPM83 mask shown in Fig.~\ref{fig:chisq_pol_map}) has been replaced with a constrained Gaussian realization \citep{planck2014-a11}. |
 | $20\deg\times20\deg$ polarization zooms centred on the south ecliptic pole with Galactic coordinates $(l,b) = (276\deg,-30\deg)$ of CMB (\emph{top row}), synchrotron (\emph{middle row}), and thermal dust emission (\emph{bottom row}). Left and right columns show Stokes $Q$ and $U$ parameters, respectively. The object in the lower left quadrant is the Large Magellanic Cloud (LMC). |
 | $20\deg\times20\deg$ polarization zooms centred on the south ecliptic pole with Galactic coordinates $(l,b) = (276\deg,-30\deg)$ of CMB (\emph{top row}), synchrotron (\emph{middle row}), and thermal dust emission (\emph{bottom row}). Left and right columns show Stokes $Q$ and $U$ parameters, respectively. The object in the lower left quadrant is the Large Magellanic Cloud (LMC). |
 | $20\deg\times20\deg$ polarization zooms centred on the south ecliptic pole with Galactic coordinates $(l,b) = (276\deg,-30\deg)$ of CMB (\emph{top row}), synchrotron (\emph{middle row}), and thermal dust emission (\emph{bottom row}). Left and right columns show Stokes $Q$ and $U$ parameters, respectively. The object in the lower left quadrant is the Large Magellanic Cloud (LMC). |
 | $20\deg\times20\deg$ polarization zooms centred on the south ecliptic pole with Galactic coordinates $(l,b) = (276\deg,-30\deg)$ of CMB (\emph{top row}), synchrotron (\emph{middle row}), and thermal dust emission (\emph{bottom row}). Left and right columns show Stokes $Q$ and $U$ parameters, respectively. The object in the lower left quadrant is the Large Magellanic Cloud (LMC). |
 | $20\deg\times20\deg$ polarization zooms centred on the south ecliptic pole with Galactic coordinates $(l,b) = (276\deg,-30\deg)$ of CMB (\emph{top row}), synchrotron (\emph{middle row}), and thermal dust emission (\emph{bottom row}). Left and right columns show Stokes $Q$ and $U$ parameters, respectively. The object in the lower left quadrant is the Large Magellanic Cloud (LMC). |
 | $20\deg\times20\deg$ polarization zooms centred on the south ecliptic pole with Galactic coordinates $(l,b) = (276\deg,-30\deg)$ of CMB (\emph{top row}), synchrotron (\emph{middle row}), and thermal dust emission (\emph{bottom row}). Left and right columns show Stokes $Q$ and $U$ parameters, respectively. The object in the lower left quadrant is the Large Magellanic Cloud (LMC). |
 | \Planck\ polarization amplitude maps, $P=\sqrt{Q^2+U^2}$. The top panel shows synchrotron emission at 30\,GHz, smoothed to an angular resolution of $40\arcm$, and the bottom panel shows thermal dust emission at 353\,GHz, smoothed to an angular resolution of $10\arcm$. |
 | \Planck\ polarization amplitude maps, $P=\sqrt{Q^2+U^2}$. The top panel shows synchrotron emission at 30\,GHz, smoothed to an angular resolution of $40\arcm$, and the bottom panel shows thermal dust emission at 353\,GHz, smoothed to an angular resolution of $10\arcm$. |
 | \Planck\ polarization angle maps for synchrotron emission, smoothed to $40\arcm$ FHWM (\emph{top}) and thermal dust emission, smoothed to $10\arcm$ FWHM (\emph{bottom}). Light blue and red colours indicate polarization angles aligned with meridians ($\psi=0\deg$) and parallels ($\psi=90\deg$), respectively, while yellow and purple indicate polarization angles rotated by $-45$ and $+45\deg$ with respect to the local meridian in the \healpix\ polarization angle convention. Colours are saturated at 10\,$\mu{\textrm K}_{\textrm{RJ}}$. |
 | \Planck\ polarization angle maps for synchrotron emission, smoothed to $40\arcm$ FHWM (\emph{top}) and thermal dust emission, smoothed to $10\arcm$ FWHM (\emph{bottom}). Light blue and red colours indicate polarization angles aligned with meridians ($\psi=0\deg$) and parallels ($\psi=90\deg$), respectively, while yellow and purple indicate polarization angles rotated by $-45$ and $+45\deg$ with respect to the local meridian in the \healpix\ polarization angle convention. Colours are saturated at 10\,$\mu{\textrm K}_{\textrm{RJ}}$. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | Polarization residual maps, $\d_{\nu}-\s_{\nu}$. Each row corresponds to one frequency map, with 30\,GHz in the top row and 353\,GHz in the bottom row; left and right columns show the Stokes $Q$ and $U$ parameters, respectively. All panels employ the same linear colour scale. |
 | \emph{Top}: $\chi^2$ per pixel for the polarization analysis of \Planck\ observations between 30 and 353\,GHz, summed over Stokes $Q$ and $U$ parameters. \emph{Middle}: \texttt{Commander} polarization mask (CPM), defined as the product of the CO $J$=1$\rightarrow$0 emission map thresholded at $0.5\,\textrm{K}_{\textrm{RJ}}\,\textrm{km}\,\textrm{s}^{-1}$, and the smoothed $\chi^2$ map thresholded at a value of 26. This mask retains a total of 83\% of the sky. \emph{Bottom}: Histogram of $\chi^2$ values outside the conservative CPM83 mask. The grey dashed line shows the best-fit $\chi^2$ distribution with a variable degree of freedom and scaling, used to account for noise modelling effects. |
 | \emph{Top}: $\chi^2$ per pixel for the polarization analysis of \Planck\ observations between 30 and 353\,GHz, summed over Stokes $Q$ and $U$ parameters. \emph{Middle}: \texttt{Commander} polarization mask (CPM), defined as the product of the CO $J$=1$\rightarrow$0 emission map thresholded at $0.5\,\textrm{K}_{\textrm{RJ}}\,\textrm{km}\,\textrm{s}^{-1}$, and the smoothed $\chi^2$ map thresholded at a value of 26. This mask retains a total of 83\% of the sky. \emph{Bottom}: Histogram of $\chi^2$ values outside the conservative CPM83 mask. The grey dashed line shows the best-fit $\chi^2$ distribution with a variable degree of freedom and scaling, used to account for noise modelling effects. |
 | \emph{Top}: $\chi^2$ per pixel for the polarization analysis of \Planck\ observations between 30 and 353\,GHz, summed over Stokes $Q$ and $U$ parameters. \emph{Middle}: \texttt{Commander} polarization mask (CPM), defined as the product of the CO $J$=1$\rightarrow$0 emission map thresholded at $0.5\,\textrm{K}_{\textrm{RJ}}\,\textrm{km}\,\textrm{s}^{-1}$, and the smoothed $\chi^2$ map thresholded at a value of 26. This mask retains a total of 83\% of the sky. \emph{Bottom}: Histogram of $\chi^2$ values outside the conservative CPM83 mask. The grey dashed line shows the best-fit $\chi^2$ distribution with a variable degree of freedom and scaling, used to account for noise modelling effects. |
 | Difference maps (\emph{top}) and fractional difference maps (\emph{bottom}) between the synchrotron (\emph{left}) and thermal dust (\emph{right}) polarization solutions derived with two different HFI temperature-to-polarization leakage templates. The synchrotron polarization amplitude maps are smoothed to $3\deg$ FHWM before computing absolute and fractional differences, and the thermal dust polarization amplitude maps are smoothed to $1\deg$. Maps labelled by a subscript ``1'' correspond to the default leakage templates used in the \Planck\ 2015 release, and maps labelled by a subscript ``2'' correspond to the experimental leakage templates; see \citet{planck2014-a09} for further discussion. |
 | Difference maps (\emph{top}) and fractional difference maps (\emph{bottom}) between the synchrotron (\emph{left}) and thermal dust (\emph{right}) polarization solutions derived with two different HFI temperature-to-polarization leakage templates. The synchrotron polarization amplitude maps are smoothed to $3\deg$ FHWM before computing absolute and fractional differences, and the thermal dust polarization amplitude maps are smoothed to $1\deg$. Maps labelled by a subscript ``1'' correspond to the default leakage templates used in the \Planck\ 2015 release, and maps labelled by a subscript ``2'' correspond to the experimental leakage templates; see \citet{planck2014-a09} for further discussion. |
 | Difference maps (\emph{top}) and fractional difference maps (\emph{bottom}) between the synchrotron (\emph{left}) and thermal dust (\emph{right}) polarization solutions derived with two different HFI temperature-to-polarization leakage templates. The synchrotron polarization amplitude maps are smoothed to $3\deg$ FHWM before computing absolute and fractional differences, and the thermal dust polarization amplitude maps are smoothed to $1\deg$. Maps labelled by a subscript ``1'' correspond to the default leakage templates used in the \Planck\ 2015 release, and maps labelled by a subscript ``2'' correspond to the experimental leakage templates; see \citet{planck2014-a09} for further discussion. |
 | Difference maps (\emph{top}) and fractional difference maps (\emph{bottom}) between the synchrotron (\emph{left}) and thermal dust (\emph{right}) polarization solutions derived with two different HFI temperature-to-polarization leakage templates. The synchrotron polarization amplitude maps are smoothed to $3\deg$ FHWM before computing absolute and fractional differences, and the thermal dust polarization amplitude maps are smoothed to $1\deg$. Maps labelled by a subscript ``1'' correspond to the default leakage templates used in the \Planck\ 2015 release, and maps labelled by a subscript ``2'' correspond to the experimental leakage templates; see \citet{planck2014-a09} for further discussion. |
 | Thermal dust polarization fraction for Galactic emission zero-level corrections of $0\,\mu\textrm{K}$ (\emph{top}) and $34\,\mu\textrm{K}$ (\emph{bottom}). A value of $34\,\mu\textrm{K}$ corresponds to our current best estimate of the residual zodiacal light offset in the 353\,GHz channel \citep{planck2014-a09}. The statistical uncertainty on the Galactic emission zero-level from \ion{H}{i} cross-correlation is 0.0067\,MJy\,sr$^{-1}$ or 23$\,\mu\textrm{K}_{\textrm{CMB}}$. |
 | Thermal dust polarization fraction for Galactic emission zero-level corrections of $0\,\mu\textrm{K}$ (\emph{top}) and $34\,\mu\textrm{K}$ (\emph{bottom}). A value of $34\,\mu\textrm{K}$ corresponds to our current best estimate of the residual zodiacal light offset in the 353\,GHz channel \citep{planck2014-a09}. The statistical uncertainty on the Galactic emission zero-level from \ion{H}{i} cross-correlation is 0.0067\,MJy\,sr$^{-1}$ or 23$\,\mu\textrm{K}_{\textrm{CMB}}$. |
 | Angular $EE$ (\emph{left panel}) and $BB$ (\emph{right panel}) power spectra for polarized synchrotron (at 30\,GHz) and thermal dust emission (at 353\,GHz), evaluated with $1\deg$ FWHM apodization and including a total effective sky fraction of 73\,\% of the sky. The dashed lines show the best-fit power-law models to each case, and the solid black lines shows the best-fit $\Lambda$CDM power spectrum as fitted to temperature observations only \citep{planck2014-a13,planck2014-a15}. The dashed black line in the $BB$ panel shows the spectrum for a model with a tensor-to-scalar ratio of $r=0.05$. |
 | Angular $EE$ (\emph{left panel}) and $BB$ (\emph{right panel}) power spectra for polarized synchrotron (at 30\,GHz) and thermal dust emission (at 353\,GHz), evaluated with $1\deg$ FWHM apodization and including a total effective sky fraction of 73\,\% of the sky. The dashed lines show the best-fit power-law models to each case, and the solid black lines shows the best-fit $\Lambda$CDM power spectrum as fitted to temperature observations only \citep{planck2014-a13,planck2014-a15}. The dashed black line in the $BB$ panel shows the spectrum for a model with a tensor-to-scalar ratio of $r=0.05$. |
 | Amplitude ratio between total polarized foregrounds and CMB as a function of both multipole moment and frequency, defined by $f(\ell,\nu) = [C_{\ell}^{\mathrm{fg}}(\nu)/C_{\ell}^{\mathrm{CMB}}]^{1/2}$, as defined Eq.~\ref{eq:pol_fg_model} with parameters derived from 73\,\% of the sky. The left and right panels show the $EE$ and $BB$ spectra, and the black and red contours in the latter corresponds to tensor-to-scalar ratios of $r=0.0$ and $0.05$, respectively. |
 | Amplitude ratio between total polarized foregrounds and CMB as a function of both multipole moment and frequency, defined by $f(\ell,\nu) = [C_{\ell}^{\mathrm{fg}}(\nu)/C_{\ell}^{\mathrm{CMB}}]^{1/2}$, as defined Eq.~\ref{eq:pol_fg_model} with parameters derived from 73\,\% of the sky. The left and right panels show the $EE$ and $BB$ spectra, and the black and red contours in the latter corresponds to tensor-to-scalar ratios of $r=0.0$ and $0.05$, respectively. |
 | Comparison of the \Planck\ polarized synchrotron map (\emph{top}) and the 9-year \WMAP\ K-band map, scaled to 30\,GHz assuming a spectral index of $\beta_{\textrm{s}}=-3.2$ (\emph{middle}); the bottom row shows the difference between the two maps. All maps are smoothed to a common resolution of $2\deg$ FWHM. |
 | Comparison of the \Planck\ polarized synchrotron map (\emph{top}) and the 9-year \WMAP\ K-band map, scaled to 30\,GHz assuming a spectral index of $\beta_{\textrm{s}}=-3.2$ (\emph{middle}); the bottom row shows the difference between the two maps. All maps are smoothed to a common resolution of $2\deg$ FWHM. |
 | Comparison of the \Planck\ polarized synchrotron map (\emph{top}) and the 9-year \WMAP\ K-band map, scaled to 30\,GHz assuming a spectral index of $\beta_{\textrm{s}}=-3.2$ (\emph{middle}); the bottom row shows the difference between the two maps. All maps are smoothed to a common resolution of $2\deg$ FWHM. |
 | Comparison of the \Planck\ polarized synchrotron map (\emph{top}) and the 9-year \WMAP\ K-band map, scaled to 30\,GHz assuming a spectral index of $\beta_{\textrm{s}}=-3.2$ (\emph{middle}); the bottom row shows the difference between the two maps. All maps are smoothed to a common resolution of $2\deg$ FWHM. |
 | Comparison of the \Planck\ polarized synchrotron map (\emph{top}) and the 9-year \WMAP\ K-band map, scaled to 30\,GHz assuming a spectral index of $\beta_{\textrm{s}}=-3.2$ (\emph{middle}); the bottom row shows the difference between the two maps. All maps are smoothed to a common resolution of $2\deg$ FWHM. |
 | Comparison of the \Planck\ polarized synchrotron map (\emph{top}) and the 9-year \WMAP\ K-band map, scaled to 30\,GHz assuming a spectral index of $\beta_{\textrm{s}}=-3.2$ (\emph{middle}); the bottom row shows the difference between the two maps. All maps are smoothed to a common resolution of $2\deg$ FWHM. |
 | Comparison of the \Planck\ polarized thermal dust map at 353\,GHz (\emph{top}) and the \WMAP\ polarized dust template, scaled to 353\,GHz assuming a scaling factor of $480\,\mu\textrm{K}$ (\emph{middle}). The bottom row shows the difference between the two maps. All maps are pixelized at a \healpix\ resolution of $N_{\textrm{side}}=16$. |
 | Comparison of the \Planck\ polarized thermal dust map at 353\,GHz (\emph{top}) and the \WMAP\ polarized dust template, scaled to 353\,GHz assuming a scaling factor of $480\,\mu\textrm{K}$ (\emph{middle}). The bottom row shows the difference between the two maps. All maps are pixelized at a \healpix\ resolution of $N_{\textrm{side}}=16$. |
 | Comparison of the \Planck\ polarized thermal dust map at 353\,GHz (\emph{top}) and the \WMAP\ polarized dust template, scaled to 353\,GHz assuming a scaling factor of $480\,\mu\textrm{K}$ (\emph{middle}). The bottom row shows the difference between the two maps. All maps are pixelized at a \healpix\ resolution of $N_{\textrm{side}}=16$. |
 | Comparison of the \Planck\ polarized thermal dust map at 353\,GHz (\emph{top}) and the \WMAP\ polarized dust template, scaled to 353\,GHz assuming a scaling factor of $480\,\mu\textrm{K}$ (\emph{middle}). The bottom row shows the difference between the two maps. All maps are pixelized at a \healpix\ resolution of $N_{\textrm{side}}=16$. |
 | Comparison of the \Planck\ polarized thermal dust map at 353\,GHz (\emph{top}) and the \WMAP\ polarized dust template, scaled to 353\,GHz assuming a scaling factor of $480\,\mu\textrm{K}$ (\emph{middle}). The bottom row shows the difference between the two maps. All maps are pixelized at a \healpix\ resolution of $N_{\textrm{side}}=16$. |
 | Comparison of the \Planck\ polarized thermal dust map at 353\,GHz (\emph{top}) and the \WMAP\ polarized dust template, scaled to 353\,GHz assuming a scaling factor of $480\,\mu\textrm{K}$ (\emph{middle}). The bottom row shows the difference between the two maps. All maps are pixelized at a \healpix\ resolution of $N_{\textrm{side}}=16$. |
 | $T$--$T$ correlation plot between the \Planck\ polarized synchrotron map at 30\,GHz and the \WMAP\ K-band map at 23\,GHz for both Stokes $Q$ and $U$ parameters. The dashed coloured lines indicate synchrotron spectral indices of $\beta_{\textrm{s}}=-3.0$ (red), $-3.2$ (green) and $-3.4$ (violet), respectively. |
 | $T$--$T$ correlation plot between the \Planck\ polarized thermal dust map (at 353\,GHz) and the \WMAP\ polarized dust template map (in arbitrary units) for both Stokes $Q$ and $U$ parameters. The dashed black line corresponds to a relative scaling factor of $480\,\mu\textrm{K}_{\textrm{RJ}}$. |
 | Comparison between the polarized dust amplitude maps, $P=\sqrt{Q^2+U^2}$, derived by \texttt{SMICA} and \texttt{Commander} at 353\,GHz. The three panels show the difference map, $\d_{\texttt{SMICA}}-\d_{\texttt{Comm}}$ (\emph{top}), the fractional difference map, $(\d_{\texttt{SMICA}}-\d_{\texttt{Comm}})/\d_{\texttt{Comm}}$ (\emph{middle}), and a $T$--$T$ correlation plot. Units are $\mu\textrm{K}_{\small{\textrm{RJ}}}$. |
 | Comparison between the polarized dust amplitude maps, $P=\sqrt{Q^2+U^2}$, derived by \texttt{SMICA} and \texttt{Commander} at 353\,GHz. The three panels show the difference map, $\d_{\texttt{SMICA}}-\d_{\texttt{Comm}}$ (\emph{top}), the fractional difference map, $(\d_{\texttt{SMICA}}-\d_{\texttt{Comm}})/\d_{\texttt{Comm}}$ (\emph{middle}), and a $T$--$T$ correlation plot. Units are $\mu\textrm{K}_{\small{\textrm{RJ}}}$. |
 | Comparison between the polarized dust amplitude maps, $P=\sqrt{Q^2+U^2}$, derived by \texttt{SMICA} and \texttt{Commander} at 353\,GHz. The three panels show the difference map, $\d_{\texttt{SMICA}}-\d_{\texttt{Comm}}$ (\emph{top}), the fractional difference map, $(\d_{\texttt{SMICA}}-\d_{\texttt{Comm}})/\d_{\texttt{Comm}}$ (\emph{middle}), and a $T$--$T$ correlation plot. Units are $\mu\textrm{K}_{\small{\textrm{RJ}}}$. |
 | Brightness temperature rms as a function of frequency and astrophysical component for temperature (\emph{top}) and polarization (\emph{bottom}). For temperature, each component is smoothed to an angular resolution of $1\deg$ FWHM, and the lower and upper edges of each line are defined by masks covering 81 and 93\,\% of the sky, respectively. For polarization, the corresponding smoothing scale is $40\arcm$, and the sky fractions are 73 and 93\,\%. Note that foreground rms values decrease nearly monotonically with sky fraction, whereas the CMB rms is independent of sky fraction, up to random variations. |
 | Brightness temperature rms as a function of frequency and astrophysical component for temperature (\emph{top}) and polarization (\emph{bottom}). For temperature, each component is smoothed to an angular resolution of $1\deg$ FWHM, and the lower and upper edges of each line are defined by masks covering 81 and 93\,\% of the sky, respectively. For polarization, the corresponding smoothing scale is $40\arcm$, and the sky fractions are 73 and 93\,\%. Note that foreground rms values decrease nearly monotonically with sky fraction, whereas the CMB rms is independent of sky fraction, up to random variations. |