Polarization Diagnostics Applied to Coronal Mass Ejections and the Background Solar Wind

TL;DR

This work develops a polarization-based framework for the PUNCH mission to simultaneously localize compact CME features in 3D and probe the local radial density falloff of the background solar wind. By relating the degree of polarization $p$ and polarization ratio $PR$ to the LOS geometry and to a density profile $n_e(r)=n_0 r^{-c}$, the authors derive the conditions under which a structure can be treated as a localized superparticle and quantify how the diagnostic transitions to extended-density behavior as the LOS width grows. Forward modeling of a twisted croissant CME within the FORWARD framework demonstrates that polarization measurements can resolve the 3D edge positions, disambiguate front/back trajectories, track halo CMEs, and infer substructure chirality from curvature, providing a rigorous testbed for PUNCH capabilities. The study highlights both the practical localization limits (through the critical width parameter $rac{w}{2d}$) and the complementary value of polarization data for SMB-informed space-weather predictions, while noting the need for complementary tomographic or multi-view approaches to handle noise and complex background structures.

Abstract

The ratio of radially to tangentially polarized Thomson-scattered white light provides a powerful tool for locating the 3D position of compact structures in the solar corona and inner heliosphere, and the Polarimeter to Unify the Corona and Heliosphere (PUNCH) has been designed to take full advantage of this diagnostic capability. Interestingly, this same observable that establishes the position of transient blob-like structures becomes a local measure of the slope of the global falloff of density in the background solar wind. It is thus important to characterize the extent along the line of sight of structures being studied, in order to determine whether they are sufficiently compact for 3D positioning. In this paper, we build from analyses of individual lines of sight to three-dimensional models of coronal mass ejections (CMEs), allowing us to consider how accurately polarization properties of the transient and quiescent solar wind are diagnosed. In this way, we demonstrate the challenges and opportunities presented by PUNCH polarization data for various quantitative diagnostics.

Figures (26)

• Figure 1: Geometry of the system. The superparticle is the grey oval, and the observer is shown as the eyeball on the bottom right, looking along a line of sight with elongation angle $\varepsilon$ (see Appendix \ref{['secAdef']} for definitions of other variables). Also indicated is the cross section of the Thomson Surface (TS), which is significant because it is the location of closest approach to the Sun for each line of sight, and thus strongest illumination. Near the sun, this occurs in or near to the plane of the sky, but for wider elongation angles, the radial closest approaches of the (non-parallel) lines of sight forms the spherical surface shown here. Note that in the mapping of the bottom-left image, the sky plane is the $Y-Z$ plane as is commonly assumed for close-in coronagraph images (since PUNCH is in Earth orbit, the $X-Y-Z$ coordinate system used here are assumed to be Radial-Tangential-Normal (RTN) (see burlaga_84franz_02). For lines of sight farther out, it is more common (and appropriate for the PUNCH mission) to map the structure onto the celestial sphere in an azimuthal-equidistant mapping with grid spacing constant in elongation angle ($\varepsilon$) as seen projected on the $X_{im}-Y_{im}$ image plane (bottom-right inset). See deforest_this_issue for further discussion of this figure.
• Figure 2: Diagnostics obtained for a density distribution $n_e(r)=n_o \cdot r^{-2}$. Top: Ratio of white-light polarized brightness to total brightness ($p$), middle: polarization ratio ($PR$), and bottom: $\tau_{pol}$, all plotted vs elongation angle $\varepsilon$. The blue dash-dotted line shows the asymptotically regained symmetric solutions, $p_{symm}=3/5, PR_{symm}=1/4$, and $\tau_{pol_{symm}}=\operatorname{asin}(\sqrt (1/4))$. Differences are seen between this simplified point-source solution and the solid-black-line complete-form solution, which takes into account the extended disk of the Sun and truncates lines of sight at the observer, as discussed in the text.
• Figure 3: Forward modeled $\tau_{pol}$ for $n_e=r^{-c}$ spherically symmetric density distributions, for choices of (top) $c=1.9,2.1,2.2$ and (bottom) $c=2.5,3,4$, for elongation angles $\varepsilon < 45^\circ$.
• Figure 4: Forward-modeled $\tau_{pol}$ for a global solar wind simulation obtained by GAMERA-Helio model of the solar wind driven by the Wang-Sheeley-Arge Air Force Data Assimilative Photospheric Flux Transport (WSA/ADAPT) model output for Carrington rotation 2065 provornikova_24. The background (non-structured) solar wind has a non-zero value, consistent with a radially-falling off density, as discussed in the text.
• Figure 5: (Left) Center of mass angular position $\tau_{COM}$ for a constant-density wedge of varying LOS linear half-width $\frac{w}{2}$, centered on the Thomson Sphere ($\tau_o = 0$), at line-of-sight elongation angle $\varepsilon = 25^\circ$. (Right) Unsigned $\tau_{pol}$ determined from the polarization ratio (PR) as a function of wedge half-width, which reproduces $\tau_{COM}=\tau_o=0^\circ$ for small LOS widths and asymptotes to $45^\circ$ for the infinite wedge as described in the text. The blue lines are the symmetric solution integrated from $-\frac{w}{2}$ to $\frac{w}{2}$, while the red lines are the asymmetric solutions integrated from $-\frac{w}{2}$ to $\frac{w}{2} < s_{+_{limit}}$, defined in Equation \ref{['Eq-asymmwidth']}. The vertical orange lines are placed at $s_{+_{limit}}$ (see text).