Deep full-Stokes spectropolarimetry of the solar north pole near an activity maximum (Pastor Yabar et al. 2018) revealed, at both the polar and equatorial limbs but not at disc centre, a population of relatively strong (~600-800 G) magnetic fields with line-of-sight inclinations near 30°/150° and azimuths aligned with the solar radial direction. This population was interpreted as the projection signature of spatially unresolved, granular-scale magnetic loops seen close to the limb — the first indirect evidence for small-scale loops outside disc centre, implying their ubiquity over the entire solar surface and a potentially important energy channel to the chromosphere and corona. The problem is to convert this indirect inference into direct physical characterization: (i) confirm or refute the unresolved-loop interpretation through observations or validated forward modelling at high heliocentric angles, (ii) establish the occurrence statistics and cycle dependence of this loop population, and (iii) quantify its contribution to the energy budget of the upper photosphere, chromosphere, and corona. As of 2026, disc-centre loops have been directly resolved by DKIST at 0.08″, polar vertical-field statistics have been tracked through a full solar cycle by Hinode, and the first out-of-ecliptic polar magnetograms have been taken by Solar Orbiter/PHI, but the polar/limb loop population itself remains neither directly detected nor refuted, and its energetic contribution remains unquantified.

Background

The quiet solar photosphere is pervaded by magnetic fields organized on granular scales (~1 Mm), studied through full-Stokes spectropolarimetry — measurements of the four Stokes parameters I (intensity), Q, U (linear polarization), and V (circular polarization) of magnetically sensitive spectral lines, split by the Zeeman effect. Near-infrared lines such as the Fe I pair at 15648.5 Å and 15652.8 Å have high magnetic sensitivity and permit deep integrations that detect polarization signals over most of the quiet-Sun field of view. The observed Stokes profiles are converted into magnetic field strength, inclination, and azimuth by inversion codes, most commonly under the Milne-Eddington approximation (a plane-parallel atmosphere with a linear source function and a uniform magnetic field per pixel, with a filling factor describing the fractional pixel area occupied by field). The field vector is initially obtained in the line-of-sight (LOS) frame and transformed to the local reference frame (LRF, defined by the local solar normal); this transformation, together with the 180° ambiguity in the azimuth determined from linear polarization (Stokes Q and U alone cannot distinguish a field direction from its opposite), makes vector magnetism at large viewing angles particularly delicate.

At disc centre, high-resolution observations (Hinode, Sunrise) established two coexisting quiet-Sun populations: ubiquitous intermittent horizontal fields, and concentrated vertical kilogauss (kG) patches in intergranular lanes. Small, low-lying magnetic loops of granular size emerge continuously in the internetwork (the magnetic network's weak background); Martínez González & Bellot Rubio (2009) found that a significant fraction of such loops reach the chromosphere, and Martínez González et al. (2010) documented small loops connecting the quiet surface to the hot outer atmosphere. At the poles, Hinode revealed a landscape of strong vertical kG patches of the dominant polarity (Tsuneta et al. 2008), whose statistics vary over the 11-year activity cycle and which seed the next cycle's dynamo.

Pastor Yabar, Martínez González & Collados (2018, A&A 616, A46) observed the north polar region near the cycle-24 maximum with deep 1.565 µm spectropolarimetry, comparing it with a disc-centre region and an equatorial limb region. Both limb datasets (polar and equatorial), but not disc centre, showed an additional population of fields with strengths ~600-800 G, LOS inclinations peaking near 30° and 150°, and LOS azimuths preferentially aligned with the solar radial direction. Because foreshortening — the geometric compression of the projected solar surface near the limb — degrades effective spatial resolution there, the authors modelled this population as granular-scale semi-circular magnetic loops with constant field strength that are resolved at disc centre but spatially unresolved at the limbs; the superposition of the loop flanks and apex reproduces the observed inclination-azimuth signature. This constituted the first indirect evidence for small-scale loops outside disc centre and would imply that such structures are ubiquitous over the entire solar surface, with potential consequences for the energy budget of the photosphere, chromosphere, and corona. The authors themselves listed the essential caveats: the small field of view (so the observed polarity imbalance might be a statistical fluctuation), the simplified loop geometry, unmodelled non-geometrical limb effects (radiative-transfer changes, limb darkening, varying pixel size), the 180° disambiguation assumption of homogeneous azimuth within each patch, the single epoch near one activity maximum, and the lack of any quantitative energetic assessment.

Problem Statement

The common objective is the physical characterization — existence, geometry, occurrence statistics, cycle dependence, and energetic contribution — of the small-scale (granular-size) magnetic loop population that Pastor Yabar et al. (2018) inferred indirectly at the solar poles and limbs. Specifically: (1) Direct confirmation or refutation of the unresolved-loop interpretation of the limb population (field strengths ~600-800 G, line-of-sight inclinations near 30° and 150°, azimuths aligned with the solar radial direction, absent at disc centre): either resolve the individual loops observationally at high heliocentric angles (with ground-based ~0.1″ class spectropolarimetry from a favourable viewing geometry or out-of-ecliptic observations), or validate the interpretation by forward modelling — synthesizing Stokes profiles from realistic three-dimensional loop configurations (non-semi-circular shapes, height-varying field strength, radiative-transfer and limb effects, instrumental degradation including foreshortening) and demonstrating that they reproduce, or cannot reproduce, the observed limb signature under independent disambiguation schemes. (2) Determine the occurrence-rate statistics of this loop population as a function of heliographic position and phase of the 11-year activity cycle, including the comparison between activity minimum and maximum that the single-epoch 2018 data could not provide. (3) Quantify the contribution of this ubiquitous loop population to the energy budget of the upper photosphere, chromosphere, and low corona — the power (per unit area, with uncertainty) channelled by loop emergence, submergence, and reconnection, relative to the radiative losses of those layers.

The three sub-questions are ordered rather than freely conjunctive: (1) is logically prior, so a demonstrated refutation of the unresolved-loop interpretation removes the population that (2) and (3) would characterize — in that case the refutation resolves the existence question and (2) and (3) become inapplicable — whereas confirmation of (1) leaves (2) and (3) as separate, still-open requirements that must also be addressed for a complete answer.

References

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