TRIShUL: Technique for Reconstructing magnetic Interstellar Structure Using starLight polarization

TL;DR

TRIShUL addresses the challenge of reconstructing three-dimensional interstellar magnetic-field structure from starlight polarization by introducing a frequentist, per-LOS tomography framework that uses the cumulative Mahalanobis distance of Stokes parameters to detect discrete dust layers. Breakpoints along distance-sorted stars are identified with a breakpoint-detection algorithm and filtered against spurious detections via a Hotelling’s T-squared test, then mapped to parallax and mean Stokes properties with careful error propagation. Mock tests show robust recovery of dust-layer distances and polarization when the induced polarization exceeds $p_{ m max}\gtrsim 0.1\%$ and at least $\sim10\%$ of stars lie behind the layer, while comparisons with BISP-1 highlight TRIShUL’s prior-free, computationally efficient strengths and its complementary role to Bayesian methods. Real-data applications at high Galactic latitude and near the Galactic plane demonstrate good agreement with literature and illustrate the method’s applicability to upcoming large-scale polarization surveys like Pasiphae. Overall, TRIShUL offers a fast, robust alternative for 3D polarization tomography suitable for big datasets, with potential to inform priors for Bayesian refinements.

Abstract

We present a novel technique to decompose line-of-sight (LOS) stellar polarization as a function of distance, aimed at reconstructing three dimensional (3D) plane-of-sky (POS) magnetic structures in the interstellar medium (ISM). The method assumes that the observed polarization arises from discrete, thin dust layers located at varying distances along the LOS. Using a simple frequentist framework, it identifies structural changes in the distance-sorted cumulative Mahalanobis distance of Stokes parameters (q and u) to detect the locations of dust layers and estimate their associated physical properties (parallax and Stokes parameters) necessary to construct 3D maps. We benchmark the method using mock datasets representative of high-Galactic-latitude regions, incorporating realistic Gaia parallax uncertainties and polarization expected from the upcoming Pasiphae survey. Tests show that the method reliably recovers dust cloud distances and polarization properties when the polarization exceeds 0.1%, and the effective background-star fraction is greater than 10% in samples of about 345 stars. The dependence on background fraction decreases as the intrinsic polarization amplitude of the dust field increases. We apply our method to existing polarization data from two illustrative sightlines, one at intermediate-high Galactic latitude and one near the Galactic plane, with known tomographic solutions, finding excellent agreement with the literature and demonstrating its accuracy across both regions. Comparing with the BISP-1 approach, both methods effectively recover dust cloud properties, but our approach is prior-free and computationally more efficient in determining the optimal number of clouds along the LOS. These advantages make it flexible and broadly applicable for multi-layer dust cloud reconstruction for the upcoming era of large-scale stellar polarization surveys.

Figures (14)

• Figure 1: Simulated LOS with top-left panel showing $q$ (in green) and $u$ (in blue) as a function of distance sorted stellar indices without incorporating turbulence (internal scattering) and measurement uncertainties. The corresponding Mahalanobis distance ($d_{\rm{Maha}}$) and its cumulative effect ($d_{\rm{Maha}}^{\rm{cum}}$) are presented in the middle and bottom-left panels. The respective panel on the right side corresponds to the data, including turbulence-induced intrinsic scatter and measurement uncertainties. The red dashed lines in each panel mark the positions of the clouds.
• Figure 2: Breakpoints (blue lines) detected in the distance-sorted cumulative Mahalanobis distance profiles using the R strucchange package. The top panel corresponds to the mock data shown in the bottom-left panel of Fig. \ref{['fig:Fig1']}, while the bottom panel corresponds to the bottom-right panel of Fig. \ref{['fig:Fig1']}. The vertical dashed red lines indicate the input distances of the dust layers used in the simulations.
• Figure 3: Heat map illustrating the number of false negative cases out of 450 single-cloud mock samples, each with a combination of $p_{\rm{input}}$ and $f_{\rm{bg}}$, evaluated across 10 samples of $\psi$ ranging from $0^\circ$ to $180^\circ$. The color intensity and the number within each cell represent the resulting count of FNs.
• Figure 4: Performance of TRIShUL as a function of input polarization signal for different cloud distances probed by $f_{\rm{bg}}$ (in different colors). The top panel shows the difference between the estimated parallax ($\varpi_{\rm{est}}$) and the parallax of the star closest to the input layer ($\varpi_{\rm{true}}$). The bottom panel corresponds to the difference in estimated Stokes parameters ($\hat{\bar{q}}_{\rm{est}}$, $\hat{\bar{u}}_{\rm{est}}$) from the corresponding true values ($\hat{\bar{q}}_{\rm{true}}$, $\hat{\bar{u}}_{\rm{true}}$). The results corresponding to different $f_{bg}$ are shifted by 0.02% on the $X$-axis for visual clarity. Dashed horizontal lines are the reference to a perfect match between estimated and true parameters.
• Figure 5: Performance testing of our method in recovering parallax (top panel) and Stokes parameters (bottom panel) of both layers in 2-cloud sample tests. The color scheme is defined for different set of $f_{\rm{bg2}}$ and is similar to $f_{\rm{bg}}$ in Fig. \ref{['fig:Fig4']}. The horizontal dashed lines correspond to a perfect match between estimated and true values. Open black circles indicate cases where an additional, spurious layer beyond the second layer is identified, while the first layer is missed. More details about the figure are deferred to the text in Sect. \ref{['sec:3.2']}