Two fundamentally different Stokes-inversion methods applied to the same Sunrise III/SCIP quiet-Sun spectropolarimetric data agree that the internetwork photosphere is dominated by horizontal magnetic fields at intermediate heights (horizontal-to-line-of-sight field-strength ratio Bratio≈9B_{\rm ratio}\approx 9 at log⁡τ=−1.2\log\tau=-1.2), but diverge in the upper photosphere: the transformer-based inversion SINN yields BratioB_{\rm ratio} rising to about fourteen at log⁡τ=−3.0\log\tau=-3.0, while the node-based code DeSIRe shows a much smaller increase. The source paper excludes two candidate explanations (DeSIRe's use of additional spectral lines, and insufficient linear-polarization sensitivity of the Fe I 846.8 nm line at those layers), leaving the cause undetermined. The problem is to identify the cause of this discrepancy with controlled evidence and establish the physically correct height stratification of the internetwork field topology through the upper photosphere; two systematics acknowledged in the source paper — the residuals in the strongest magnetic concentrations and the bias from analyzing only pixels with 5σ5\sigma polarization detections — bear on this determination.

Background

The quiet Sun is the solar surface outside active regions; its network lanes host kilogauss vertical flux tubes, while the internetwork inside supergranular cells contains weak, small-scale fields whose topology is a key observable of the solar small-scale dynamo (a turbulent dynamo believed to operate in near-surface convection). Because these fields are weak, they are probed by spectropolarimetry: the Zeeman effect splits and polarizes spectral lines, and the four Stokes parameters (II intensity; QQ, UU linear polarization, sensitive to the transverse/horizontal field component; VV circular polarization, sensitive to the line-of-sight component) are inverted, i.e. fitted with model atmospheres, to recover the field vector. Optical depth log⁡τ\log\tau (logarithm of continuum optical depth, a proxy for geometric height: log⁡τ=0\log\tau=0 at the photospheric base, more negative values higher up) stratifies the result. Two inversion methodologies dominate this work. DeSIRe (Departure coefficient aided Stokes Inversion based on Response functions; Ruiz Cobo et al. 2022) is a traditional code that fits observed profiles by iteratively adjusting atmospheric parameters at fixed optical-depth nodes, interpolating between them. SINN (Stokes Inversion based on Neural Networks; the transformer-based inversion of Campbell et al. 2026a) is a deep-learning model, trained exclusively on synthetic Stokes profiles forward-modeled through snapshots of MURaM (a 3D radiative magnetohydrodynamic simulation code), which maps a full Stokes spectrum directly to the stratified atmosphere and is orders of magnitude faster. Sunrise III was a 1-metre balloon-borne solar observatory (2024 flight) whose SCIP instrument (Sunrise Chromospheric Infrared spectroPolarimeter) observed the photospheric Fe I 846.8 nm line with seeing-free, high-sensitivity polarimetry. The topology diagnostic is Bratio=median(Bh)/median(∣BLOS∣)B_{\rm ratio}=\mathrm{median}(B_{\rm h})/\mathrm{median}(|B_{\rm LOS}|), the ratio of the median horizontal to median unsigned line-of-sight field; under the standard single-magnetic-component assumption it is independent of the magnetic filling factor (the fraction of the pixel actually filled with field) and so probes orientation rather than strength. Whether internetwork fields are predominantly horizontal or vertical has been contested since Hinode observations: Lites et al. (2008) found apparent transverse flux several times larger than longitudinal flux; Orozco Suárez & Bellot Rubio (2012) inferred weak, highly inclined hectogauss fields from linear-polarization-selected pixels; Borrero & Kobel (2011, 2012) showed that photon noise and pixel-selection criteria can artificially produce such horizontal dominance; Stenflo (2013) demonstrated that the inferred angular distribution varies systematically with height; Danilovic et al. (2016) showed with 2D spatially coupled inversions that instrumental degradation, inversion methodology, and long temporal integrations all bias the recovered inclination distribution; and Lites et al. (2017) found radiative MHD simulations more isotropic than Milne-Eddington inversions of the same Hinode data (Milne-Eddington inversion: fitting with a simplified atmosphere in which physical properties are constant with height). The Sunrise III analysis by Campbell et al. (2026) is the first to confront this question with two independent inversion methods on data with abundant linear polarization, and their agreement at mid-photospheric heights is a central result; their unexplained divergence in the upper photosphere is the open question addressed by this task.

Problem Statement

Identify the cause of, and thereby resolve, the discrepancy between the transformer-based inversion SINN and the node-based inversion DeSIRe when both are applied to the same Sunrise III/SCIP quiet-Sun spectropolarimetric observations (Fe I 846.8 nm) regarding the height stratification of the internetwork field-topology ratio Bratio=median(Bh)/median(∣BLOS∣)B_{\rm ratio}=\mathrm{median}(B_h)/\mathrm{median}(|B_{\rm LOS}|) in the upper photosphere — SINN yields a rise to about fourteen at log⁡τ=−3.0\log\tau=-3.0 while DeSIRe shows a much smaller increase from the common mid-photospheric value of roughly nine at log⁡τ=−1.2\log\tau=-1.2 — and establish the physically correct stratification. Concretely: (1) determine, with controlled evidence, which mechanism produces the divergence among the plausible candidates — limitations of node-based inversions such as interpolation between optical-depth nodes near the heights of peak sensitivity; genuine differences between the magnetic stratifications the two methods infer; statistical mismatch between the synthetic MURaM training data and the observations, including the Stokes VV amplitude-distribution mismatch — or another cause, noting that use of additional spectral lines by DeSIRe and insufficient linear-polarization sensitivity of the 846.8 nm line at those layers have already been excluded; and (2) state whether the internetwork BratioB_{\rm ratio} for the analyzed (5σ5\sigma-selected) pixel population genuinely rises toward ≈14\approx 14 at log⁡τ=−3.0\log\tau=-3.0 or remains near the mid-photospheric value, with quantified uncertainty, and whether that rise persists for the unbiased internetwork population.

References

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