Evidence for cloud-to-cloud variations in the ratio of polarized thermal dust emission to starlight polarization

TL;DR

This study tests the spatial uniformity of the polarization ratio $R_{P/p}$ between polarized dust emission and optical starlight polarization in a ~4 deg$^{2}$ sky patch by combining Planck 353 GHz data with densely sampled RoboPol polarimetry. A joint analysis yields $R_{P/p}=-3.67\pm0.05$ MJy sr$^{-1}$, with individual channels giving $R_{Qq}=-5.13\pm0.40$ and $R_{Uu}=-3.64\pm0.20$ MJy sr$^{-1}$, revealing a significant difference between the $Q_s$–$q_v$ and $U_s$–$u_v$ relations. Toy-models show that zero-point miscalibration cannot fully account for this mismatch, while a two-cloud LOS with different $R_{P/p}$ values naturally reproduces the observed slopes and introduces a nonzero intercept. Tomographic decomposition indicates one cloud dominates the $U_s$–$u_v$ correlation while both clouds contribute to $Q_s$–$q_v$, implying spatially varying dust polarimetric properties along the LOS. These results underscore the importance of LOS structure in dust polarization studies and have implications for accurate foreground modeling in future CMB polarization experiments.

Abstract

The correlation between optical starlight polarization and polarized thermal dust emission can be used to infer intrinsic dust properties. This correlation is quantified by the ratio Rp/p, which has been measured to be 5.42 +/- 0.05 MJy sr^-1 at 353 GHz when averaged over large areas of the sky. We investigate this correlation using newly published stellar polarimetric data densely sampling a continuous sky region of ~4 square degrees at intermediate Galactic latitude. We combine RoboPol optical polarization measurements for 1,430 stars with submillimeter data from the Planck satellite at 353 GHz. We perform linear fits between the Planck (Qs, Us) and optical (qv, uv) Stokes parameters, accounting for the differences in resolution between the two datasets as well as the distribution of clouds along the line of sight. We find that in this region of the sky the Rp/p value is 3.67 +/- 0.05 MJy sr^-1, indicating a significantly shallower slope than that found previously using different stellar samples. We also find significant differences in the fitted slopes when fitting the Qs-qv and Us-uv data separately. We explore two explanations using mock data: miscalibration of polarization angle and variations in Rp/p along the line of sight due to multiple clouds. We show that the former can produce differences in the correlations of Qs-qv and Us-uv, but large miscalibration angles would be needed to reproduce the magnitude of the observed differences. Our simulations favor the interpretation that Rp/p differs between the two dominant clouds that overlap on the sky in this region. The difference in Rp/p suggests that the two clouds may have distinct dust polarimetric properties. With knowledge from the tomographic decomposition of the stellar polarization, we find that one cloud appears to dominate the correlation of Us-uv, while both clouds contribute to the correlation of the Qs-qv data.

Figures (8)

• Figure 1: Gnomonic projections of the pixelized Stokes parameter data at optical (top) and submm (bottom) at $N_{\rm{Side}}$ = 256 and distance cut > 450 pc. Top left: $q_{\rm{v}}$, Top right: $u_{\rm{v}}$, Bottom left: $Q_S$, bottom right: $U_S$. The Stokes parameters follow the IAU convention. Pixels with no optical data (outside of the observed sky region) are colored white.
• Figure 2: Correlation between the Stokes parameters from Planck ($Q_S, U_S$) and the fractional Stokes parameters from RoboPol ($q_v, u_v$). Blue points represent the correlation between $U_S$ and $u_v$, while orange points show the correlation between $Q_S$ and $q_v$. The blue dashed line indicates the best-fit line of the joint correlation determined by minimizing $\chi^2$, while solid blue and solid orange correspond to the $U_S-u_v$ and $Q_S-q_v$ fits, respectively. The black dashed line corresponds to the value from Planck2018.
• Figure 3: Comparison of best-fit slope values for different star sample selections. All cases are analyzed at the same $N_{\rm{side}}$ of 256. The slope found in Planck2018 is shown as the black dashed line.
• Figure 4: Distributions of $\Delta \Psi_{\text{s/v}}$ (in degree) for stars with distance $d \geq 2000$ pc (left) and $d \geq 450$ pc (right). The red vertical lines indicate the distribution's median with values reported in the legend.
• Figure 5: Correlation plots and linear fits between $(Q_s, q_v)$ and $(U_s, u_v)$ for two values of the polarization degree, $p = 1.5\%$ (top row) and $p = 2.5\%$ (bottom row). Each column corresponds to a combination of magnetic field orientation $\Psi_{B\perp} = \{30^\circ, 60^\circ\}$ and miscalibration offset $\beta = \{3^\circ, 7^\circ\}$, increasing from left to right. The best-fit values for the slopes (absolute value) and for the intercept obtained for the correlations are given in the legend and the resulting model shown on the scatter plot, in blue for $(Q_s, q_v)$, and orange for $(U_s, u_v)$. They are expressed in MJy sr$^{-1}$. To generate the data, we used $R_p/p = 5.42$ MJy sr$^{-1}$ and $\sigma_{\Psi_{B\perp}} = 5^\circ$, and $\sigma_p = 0.2\%$ to produce some dynamical range.