Chromospheric heating and magnetic topology above the shared penumbra of a delta-spot: Multi-line inversions and multi-height magnetic-field extrapolations

Abstract: We analysed observations of the Fe I 617.3 nm, Ca II 854.2 nm, and Ca II H lines obtained with CRISP and CHROMIS at the SST. Spatially coupled non-LTE inversions constrained the chromospheric atmosphere, while the WFA provided estimates of the chromospheric line-of-sight magnetic field. We combined these photospheric and chromospheric constraints with an HMI magnetogram as input to a multi-height field extrapolation. We characterised the reconstructed topology using the twist number, squashing factor, current density, and field-line connectivity. Results. The Ca II H magnetic signal is concentrated mainly above the strongest photospheric field concentrations, whereas Ca II 854.2 nm yields stronger and more spatially extended line-of-sight fields. The chromosphere above the shared penumbra is approximately 300 K hotter than nearby quiet regions. The selected brightening follows a chromospheric loop, with enhanced temperature and a transition from blueshift to redshift along the structure. The extrapolation recovers field strengths broadly consistent with the inversions and reveals a left-handed, flux-rope-like core following the polarity inversion line. Enhanced currents and connectivity gradients occur near parts of its boundary, where field lines connect the twisted structure to overarching loops. Conclusions. The temperature and velocity patterns and magnetic topology are consistent with reconnection between the twisted polarity-inversion-line field and the surrounding loops, depositing energy in the chromosphere and driving plasma along reconfigured field lines. These signatures do not uniquely establish reconnection, but show that combining high-resolution spectropolarimetric inversions with multi-height extrapolations can relate chromospheric energy release to the local three-dimensional magnetic structure.

• The paper combines non-LTE inversions of Fe I, Ca II 854.2 nm, and Ca II H with physics-informed neural-network extrapolations to map plasma and magnetic structure across a delta-spot shared penumbra.
• The analysis finds chromospheric temperatures about 300 K above nearby quiet regions and identifies a left-handed, strongly twisted structure along the polarity inversion line, with enhanced currents and connectivity gradients.
• The paper links a recurrent brightening to a possible reconnection between the twisted field and surrounding loops, but treats this as a candidate interpretation because the pre-event magnetic field and definitive reconnection signatures are unavailable.

This paper combines high-resolution spectropolarimetric observations with physics-informed neural-network magnetic-field extrapolations to characterize the plasma and magnetic structure above the shared penumbra of a solar $\delta$-spot, and to assess whether a recurrent chromospheric brightening is consistent with magnetic reconnection (2608.19983). The analysis targets active region NOAA 14087, observed on 18 May 2025 with CRISP and CHROMIS at the Swedish 1-m Solar Telescope (SST), and represents one of the first applications of the newly polarimetrically enabled CHROMIS channel for full-Stokes Ca II H spectropolarimetry in an active region.

Observations and inversion strategy

The observations cover the interval 17:49–18:12 UT at heliocentric angle $\mu=0.95$, over a common field of view of approximately $32.5''\times30.3''$ containing both opposite-polarity umbrae and the interspot penumbra. CRISP acquired full-Stokes data in Fe I 617.3 nm and Ca II 854.2 nm (average cadence 27.7 s), while CHROMIS simultaneously observed Ca II H (cadence 24.7 s). Linear polarization in Ca II H fell below the noise level, so only Stokes $I$ and $V$ of that line were retained for inversion.

The atmospheric inference uses the STiC non-LTE inversion code with partial frequency redistribution, applied to roughly $1.2\times10^5$ pixels. Because a direct inversion of all pixels would be prohibitively expensive, the authors built an initial model bank through a PCA plus $k$-means decomposition into 50 clusters, followed by a distance-threshold selection of additional cluster members using a noise-weighted spectral $\chi^2$ metric, yielding about 5,000 inverted representative profiles. These initialized spatially coupled inversions with a fixed node distribution (12 nodes in temperature, 5 each in line-of-sight and microturbulent velocity, and 2 each in the magnetic components). The Ca II H line-core temperature response peaks near $\log\xi=-3.5$, and the line-core intensities of both Ca II lines follow the temperature at this column-mass depth approximately linearly.

Chromospheric magnetic diagnostics and thermal structure

The weak-field approximation (WFA), applied with spatial regularization, was used both to initialize the inversions and to provide two chromospheric $B_{\mathrm{LoS}}$ layers for the extrapolation. The two Ca II diagnostics yield systematically different results: the Ca II H field signal is concentrated above the strongest photospheric field concentrations, whereas Ca II 854.2 nm produces stronger and more spatially extended $\mu=0.95$0 values, including in relatively quiet areas. The authors are explicit that this difference cannot be attributed from the observations alone; it may reflect differing noise and magnetic sensitivity, distinct height sensitivities, or the weakening and lateral expansion of the field with height. This is an important caveat for any quantitative use of these maps as height-resolved magnetometry.

The inversions show that the chromosphere above the shared penumbra is on average approximately 300 K hotter than nearby quiet regions at $\mu=0.95$1. Within this region, a selected brightening follows an apparent loop-like structure, and the line-of-sight velocity transitions from blueshift to redshift along the loop trace, consistent with plasma rising along one leg of an inclined loop and descending beyond the apex. The authors note that this interpretation depends on the assumed loop geometry, since only the line-of-sight velocity component is measured.

Multi-height force-free extrapolation and magnetic topology

The photospheric vector field from Milne–Eddington inversions of Fe I 617.3 nm (pyMilne) was embedded in a coarser SDO/HMI 90-s vector magnetogram to form the lower boundary of a Neural Network Force-Free (NF2) extrapolation, a physics-informed neural network trained to satisfy $\mu=0.95$2 and $\mu=0.95$3 while reproducing the boundary data. The multi-height capability of the code was exploited to insert the WFA-derived Ca II $\mu=0.95$4 maps, letting the network fit the formation height $\mu=0.95$5 of each pixel for both lines. This step assumes $\mu=0.95$6 equals $\mu=0.95$7, which is reasonable but not exact at $\mu=0.95$8.

The extrapolated field strengths agree reasonably with the inversion results, though the extrapolated maps are smoother. Topological analysis above the polarity inversion line (PIL) reveals a left-handed, strongly twisted structure following the PIL above the shared penumbra, isolated as a connected component with twist number $\mu=0.95$9 (core defined by $32.5''\times30.3''$0), surrounded by a weakly twisted domain. Enhanced electric currents occur along parts of the boundary of this flux-rope-like core, and enhanced squashing-factor surfaces ($32.5''\times30.3''$1 and 2.5) mark strong connectivity gradients nearby. The authors emphasize that this volume is a twist-based proxy rather than a uniquely bounded flux rope, and they tested the stability of the inferred twist against integration-step and seed-position perturbations.

The reconnection candidate

Traced field lines rooted near the brightening connect the PIL-following twisted structure to overarching loops, passing close to a high-current-density region that coincides spatially with the chromospheric brightening. Taken together with the temperature enhancement and the blueshift-to-redshift progression, the authors propose that reconnection between the twisted PIL field and surrounding loops deposited energy in the chromosphere and drove plasma along the reconfigured field. They are careful to state that these signatures are indirect and do not uniquely demonstrate reconnection, particularly because the magnetic configuration prior to the event is unavailable — the event occurred before the observations. The event is therefore classified as a reconnection candidate whose interpretation is consistent with, but not proven by, the combined diagnostics.

Limitations and open questions

Several limitations bear directly on the results. The Ca II H Stokes $32.5''\times30.3''$2 signal is noise-dominated over much of the field of view, so magnetic constraints from this line are reliable only in strong-field concentrations, and the discrepancy between the two Ca II WFA field maps remains unexplained. The identification of $32.5''\times30.3''$3 with $32.5''\times30.3''$4 at the chromospheric layers introduces a geometric approximation. The flux rope is defined by a twist threshold rather than a physical boundary condition, and the reconnection interpretation rests on a single frame of a time series in which the pre-event field is unobserved. The paper explicitly leaves open whether the recurrent brightenings — and a more energetic event that occurred shortly after the SST observations ended — are accompanied by systematic evolution of $32.5''\times30.3''$5, the high-$32.5''\times30.3''$6 layers, current concentrations, or connectivity; a time-dependent analysis of the full sequence is required to test whether the non-potential field progressively built up or reorganized before the larger event.

Conclusion

The paper demonstrates a methodological synthesis: spatially coupled multi-line non-LTE inversions (Fe I 617.3 nm, Ca II 854.2 nm, Ca II H) combined with multi-height PINN-based force-free extrapolations, using the newly available Ca II H spectropolarimetry as an upper-chromospheric magnetic constraint. The principal physical results are a $32.5''\times30.3''$7300 K chromospheric temperature enhancement above the $32.5''\times30.3''$8-spot shared penumbra, a left-handed twisted structure along the sheared PIL, and a reconnection candidate whose thermal, velocity, and topological signatures are mutually consistent. The authors appropriately frame the reconnection claim as a plausible scenario rather than a demonstration, and identify the temporal evolution of the magnetic topology across the recurrent brightening sequence as the key open question this work sets up.