Separation of polarized dust emission in Planck observations with Scattering Transforms

Abstract

Polarized dust emission is a major astrophysical foreground contaminant of the cosmic microwave background polarization (CMB), which must be accurately measured to look for the faint primordial polarization B-modes of inflationary origin. The available maps to date, obtained from Planck space mission data, are noise-dominated in the high Galactic latitude regions that are most relevant for CMB observations. The goal of this work is to obtain better dust polarization maps from Planck observations, by exploiting both the dependence between polarization and total intensity, as well as the non-Gaussian filamentary structure of the dust emission. To this end, we use scattering transforms, which provide a stable and interpretable representation of complex non-Gaussian textures, allowing for a data-driven analysis approach requiring no explicit priors on dust. The analysis is performed locally on Cartesian patches of sky, where Stokes linear polarization parameters, redefined in a local reference frame, are modeled as the sum of a signal of interest and a nuisance term. Using multiple realizations of the random nuisance term, we recover the polarized dust maps by minimizing a composite objective function that enforces multiple statistical constraints in scattering space. The proposed algorithm reconstructs maps of polarized dust emission whose statistics are consistent with those expected from the Planck data once random nuisance realizations are added. This is confirmed in a validation test using a high signal-to-noise sky region as a test case. Comparisons with existing dust polarization maps and models show that our approach better recovers small-scale polarized dust emission, and that our reconstructed power and cross-spectra closely match those of the dust polarization maps. A second set of maps that deterministically reproduce the features of the dust polarized emission is also produced.

Figures (6)

• Figure 1: Signal maps of the patch of interest in our work centered at (l, b) = (315, 78.): Top left: I 353 GHz, Top right: I 857 GHz, Middle left: Q 353 GHz before polarization rotation, Middle right: Q 353 GHz after polarization rotation, Bottom left: U 353 GHz before polarization rotation, Bottom right: U 353 GHz after polarization rotation. In this paper, we only use the data from the right column.
• Figure 2: Top: Results of our component separation algorithm for the Stokes $Q$ component in the rotated polarization reference frame. The map labeled $d_Q$ is the CMB-subtracted Planck map, while $\tilde{s}_Q$ denotes the corresponding component-separated dust emission map. For comparison, the corresponding region of the GNILC map is shown. A random realization of the nuisance component, $c_{Q,i}$, is added to the $\tilde{s}_Q$ map to demonstrate statistical consistency with $d_Q$. Similarly, the recovered nuisance $d_Q - \tilde{s}_Q$ is compared with a random realization of the noise. In addition, we make plot $d_Q - \text{GNILC}$, in order to demonstrate the existence of dust residuals in the recovered nuisance map. Finally, the residual between $\tilde{s}_Q$ and the corresponding GNILC map is shown. Bottom: As above, but for the high-SNR region used for validation. Note that in this case the GNILC map is filtered to facilitate comparison with the results above. Finally, at the bottom tow we compare the true signal $s_Q$ with the average $\langle \tilde{s}_Q \rangle$ of ensembles obtained by using different initial conditions, as well as the residual between the true signal $s_Q$ and the recovered $\langle\tilde{s}_Q\rangle$, as well as with the recovered GNILC.
• Figure 3: Top: Power spectra of the maps shown in Fig. \ref{['fig:Results_Q']}a. The solid blue line shows the initial Planck map $d_Q$, while the dashed blue line (with $1\sigma$ margin) corresponds to the recovered map after adding the nuisance. The dashed purple line correspond to the recovered dust signal $\tilde{s}_Q$. For comparison, the power spectrum of the true polarized dust emission is approximated by taking the cross-spectrum of the two half-ring maps (dashed black-dotted line). The solid purple line corresponds to the average recovered signal $\langle \tilde{s}_Q \rangle$ (see Sec. \ref{['section3.2']}). Finally, the solid and dashed green lines correspond to the nuisance (with $1\sigma$ margin) and recovered nuisance maps. For comparison, the power spectrum of the filtered GNILC map is also shown in orange. Bottom: As above, but for the maps of Fig. \ref{['fig:Results_Q']}b. In this case, the power spectrum of the true polarized dust emission (solid black line) is known.
• Figure 4: Results for the North patch. Top: observed $d_Q$ component (left), and reconstructed $\langle s_Q \rangle$ (right). Middle and Bottom: As above but for the $U$ and polarized intensity $P$ components, respectively.
• Figure 5: Various cross spectra between the recovered maps and the expected spectra from the data. Top: Validation on the Orion region (true map indicated by $s_Q$). Bottom: application to the North patch.