The CLASP2 sounding-rocket experiment measured the four Stokes parameters of the Mg II h&k resonance lines near 280 nm and produced the first height-resolved longitudinal magnetic field maps from the photosphere to the base of the corona. In enhanced-network elements the longitudinal field at the top of the upper chromosphere is consistent with zero (about −5 ± 7 G) while it is about 78 ± 7 G in the middle chromosphere, 164 ± 15 G in the lower chromosphere, and about 220 G in the photosphere. Three explanations are compatible with this drop: network magnetic loops close and return to the photosphere without reaching the top of the chromosphere; the field is present but too weak for Zeeman detection in Mg II h&k; or the field vector becomes nearly perpendicular to the line of sight so the longitudinal component vanishes. This problem asks for a determination of the vector magnetic field geometry in the upper chromosphere of enhanced-network regions, robust enough to discriminate among these three scenarios, through full four-Stokes (I, Q, U, V) inversions of the Mg II h&k (and Mn I) profiles in which the Hanle effect on the linear polarization constrains the transverse and weak-field components, with quantified control of the known degeneracies and of three-dimensional radiative-transfer effects, and delivering absolute field strengths beyond the lower-limit character of the current external-lobe estimates. As of the end of 2025 this discrimination has not been carried out: the needed inversion code now exists and full-Stokes inversion has been demonstrated only on isolated plage and quiet-Sun pixels, with unresolved degeneracies, and no observing campaign has yet targeted the network upper chromosphere with these diagnostics.

Background

The solar atmosphere is stratified into the photosphere (the visible surface), the chromosphere (a roughly 1000–2000 km layer above it), and the million-degree corona. Magnetic fields dominate the structure and energy budget of the chromosphere and corona, but direct measurement of the chromospheric field is far harder than in the photosphere. Two surface magnetic environments matter here: plage, compact patches of strong field in active regions, and the network, the chain-like supergranular-boundary fields; enhanced network is network with plage-like field concentrations but outside active regions. The classical picture, often called the wine-glass or magnetic-canopy picture, is that network fields fan out with height and fill the entire quiet chromosphere above some level as a more or less horizontal canopy.

Spectropolarimetry measures the four Stokes parameters: intensity I, the two linear-polarization components Q and U, and circular polarization V. The Zeeman effect, the splitting and polarization of a spectral line in a magnetic field, makes circular polarization scale with the line-of-sight (longitudinal) field component BLB_L, and in strong fields produces linear polarization scaling with the transverse component. In chromospheric conditions the circular-polarization signal of the Mg II h (280.35 nm) and k (279.64 nm) resonance lines, which form in the middle and upper chromosphere, is usually interpreted through the weak-field approximation (WFA), a linear calibration of V/IV/I on BLB_L valid when Zeeman splitting is much smaller than the Doppler width. Linear polarization, however, is dominated by scattering polarization and its modification by the Hanle effect: the depolarization and rotation that a weak magnetic field (of order tens of gauss for these lines) produces in the linearly polarized scattered radiation. Reliable modeling of the linear polarization of Mg II h&k must also account for partial frequency redistribution (PRD, the partial correlation between absorbed and emitted photon frequencies in resonance scattering, important in strong lines), quantum interference between the upper fine-structure levels (J-state interference), atomic level polarization (population imbalances among magnetic sublevels), and magneto-optical effects (Faraday-like mixing between Q and U along the ray).

CLASP2 (Chromospheric LAyer Spectro-Polarimeter 2), a NASA/NAOJ/IAC/IAS sounding rocket launched on 11 April 2019, recorded the four Stokes profiles over 279.30–280.68 nm — including Mg II h&k, the Mg II subordinate lines, and the Mn I resonance lines at 279.91 and 280.19 nm that sample the upper photosphere and lower chromosphere — with polarization accuracy better than 0.1% along a 196-arcsec slit crossing an active-region plage and its surrounding enhanced network. Applying the WFA to different spectral features, Ishikawa et al. (2021) derived, at each slit position, the longitudinal field at several atmospheric heights: photosphere (Hinode), lower chromosphere (Mn I), middle chromosphere (outer V/I lobes of Mg II h, which are lower limits only), and top of the upper chromosphere (inner V/I lobes of Mg II h&k). In plage the field expands from highly structured photospheric values to a smoother 100–300 G canopy. In an enhanced-network element, by contrast, BLB_L falls from about 220 G in the photosphere to 164 ± 15 G in the lower chromosphere, at least 78 ± 7 G in the middle chromosphere, and a value consistent with zero (−5 ± 7 G, weaker than about 10 G) at the top of the upper chromosphere — evidence that the wine-glass canopy picture is too simplistic for network fields. A reflight, CLASP2.1 (8 October 2021), rastered a two-dimensional field of view but only over an active-region plage near a sunspot.

Interpreting such data quantitatively requires non-LTE (non-local thermodynamic equilibrium) Stokes inversion: finding the atmospheric and magnetic model whose synthesized Stokes profiles fit the observations. The Tenerife Inversion Code (TIC), published in 2022 by the same team, performs full-Stokes inversions including PRD, atomic polarization, and arbitrary magnetic fields, but under a one-dimensional plane-parallel approximation. Its application so far has inverted only intensity and circular polarization (yielding longitudinal fields), except for a 2024 demonstration of complete four-Stokes inversion on four selected CLASP2 pixels (one plage, three quiet Sun). That demonstration showed that horizontal radiative-transfer effects break the axial symmetry of the pumping radiation field even without magnetic fields, so ad-hoc radiation-field-tensor parameters must be introduced in 1D inversions; these introduce degeneracies with the magnetic vector, different field inclinations and azimuths can fit the same Q and U profiles, and the cost is hundreds of CPU-hours per pixel. A fully three-dimensional inversion including PRD and J-state interference does not yet exist.

Problem Statement

For the enhanced-network regions observed by CLASP2 — the two opposite-polarity elements at locations d (63 arcsec) and e (97 arcsec) along the slit, for which the precise values quoted here are the Fig. 4 results at location d: the longitudinal magnetic field at the top of the upper chromosphere is consistent with zero (BL≈−5±7B_L\approx-5\pm7 G, i.e. weaker than about 10 G) while it is at least 78±778\pm7 G in the middle chromosphere, 164±15164\pm15 G in the lower chromosphere, and about 220 G in the photosphere — determine the magnetic field vector geometry in the upper chromosphere with sufficient reliability to discriminate among the three explanations left open by Ishikawa et al. (2021): (i) the network magnetic loops close and return to the photosphere without reaching the top of the upper chromosphere; (ii) the magnetic field in the upper chromosphere of these network regions is present but too weak to be detected through the Zeeman effect in the Mg II h&k lines; (iii) the field vector in the top layers is nearly perpendicular to the line of sight, so the longitudinal component is negligible. A complete answer must: (a) invert the full four Stokes parameters (I, Q, U, V) of the Mg II h&k resonance lines (together with the Mn I lines as photospheric/lower-chromospheric anchors), using the Hanle effect acting on the linear polarization to constrain the transverse and weak-field components that circular polarization cannot see; (b) quantify and control the known obstacles to a unique solution — the degeneracy between non-magnetic symmetry breaking of the radiation field (horizontal radiative-transfer effects) and the magnetic vector, and the inclination–azimuth ambiguity of the Hanle-regime linear polarization; (c) deliver absolute field strengths at the network locations that supersede the lower-limit character of the external-lobe WFA estimates; and (d) state, with quantified confidence, which of scenarios (i)–(iii) the data support. The common scientific objective uniting these requirements is the empirically grounded vector-field stratification of the enhanced-network chromosphere from the photosphere to near the base of the corona, which decides whether the network field closes low, is intrinsically weak, or is predominantly transverse at the top of the chromosphere.

References

  1. Ishikawa R., Trujillo Bueno J., del Pino Alemán T., Okamoto T. J., McKenzie D. E., Auchere F., Kano R., Song D., Yoshida M., Rachmeler L. A., Kobayashi K., Hara H., Kubo M., Narukage N., Sakao T., Shimizu T., Suematsu Y., Bethge C., De Pontieu B., Sainz Dalda A., Vigil G. D., Winebarger A., Alsina Ballester E., Belluzzi L., Štěpán J., Asensio Ramos A., Carlsson M., Leenaarts J. (2021), 'Mapping solar magnetic fields from the photosphere to the base of the corona', Science Advances 7(8):eabe8406, DOI 10.1126/sciadv.abe8406, https://doi.org/10.1126/sciadv.abe8406
  2. Li H., del Pino Alemán T., Trujillo Bueno J., Casini R. (2022), 'TIC: A Stokes Inversion Code for Scattering Polarization with Partial Frequency Redistribution and Arbitrary Magnetic Fields', The Astrophysical Journal 933(2):145, DOI 10.3847/1538-4357/ac745c, arXiv:2205.15666, https://doi.org/10.3847/1538-4357/ac745c
  3. Li H., del Pino Alemán T., Trujillo Bueno J., Ishikawa R., Alsina Ballester E., McKenzie D. E., Auchere F., Kobayashi K., Okamoto T. J., Rachmeler L. A., Song D. (2023), 'Tomography of a Solar Plage with the Tenerife Inversion Code', The Astrophysical Journal 945(2):144, DOI 10.3847/1538-4357/acb76e, arXiv:2301.12792, https://doi.org/10.3847/1538-4357/acb76e
  4. Li H., del Pino Alemán T., Trujillo Bueno J. (2024), 'Full Stokes-vector Inversion of the Solar Mg ii h and k Lines', The Astrophysical Journal 975(1):110, DOI 10.3847/1538-4357/ad7954, arXiv:2409.05328, https://doi.org/10.3847/1538-4357/ad7954
  5. Li H., del Pino Alemán T., Trujillo Bueno J., Ishikawa R., Alsina Ballester E., McKenzie D. E., Belluzzi L., Song D., Okamoto T. J., Kobayashi K., Rachmeler L. A., Bethge C., Auchere F. (2024), 'Mapping the Longitudinal Magnetic Field in the Atmosphere of an Active Region Plage from the Inversion of the Near-ultraviolet CLASP2.1 Spectropolarimetric Data', The Astrophysical Journal 974(2):154, DOI 10.3847/1538-4357/ad6dfb, arXiv:2408.06094, https://doi.org/10.3847/1538-4357/ad6dfb
  6. Li H., del Pino Alemán T., Trujillo Bueno J. (2026), 'Inferring solar magnetic fields from the polarization of the Mg II h and k lines', Reviews of Modern Plasma Physics 10(1):5, DOI 10.1007/s41614-025-00213-7, arXiv:2512.24578, https://doi.org/10.1007/s41614-025-00213-7
  7. Ishikawa R., Trujillo Bueno J., McKenzie D. E., Song D., del Pino Alemán T., Alsina Ballester E., Belluzzi L., Li H., Auchere F., Bethge C., De Pontieu B., Kano R., Kobayashi K., Kobelski A. R., Okamoto T. J., Rachmeler L. A., Sakao T., Štěpán J., Vigil G. D., Winebarger A. (2025), 'Determining the Magnetic Field in the Atmosphere of a Solar Active Region Observed by the CLASP2.1 Sounding Rocket Experiment', The Astrophysical Journal 990(2):200, DOI 10.3847/1538-4357/aded0e, arXiv:2507.09878, https://doi.org/10.3847/1538-4357/aded0e
  8. Song D., Ishikawa R., McKenzie D. E., Trujillo Bueno J., Auchere F., Kano R., Winebarger A., Okamoto T. J., Rachmeler L. A., Kobayashi K., Vigil G. D., Kobelski A. R., Bethge C., Lim E.-K., Belluzzi L., Alsina Ballester E., del Pino Alemán T., Štěpán J. (2025), 'Detection of a Magnetic Discontinuity in the Upper Solar Chromosphere Associated with a Coronal Loop Brightening Observed by CLASP2.1', The Astrophysical Journal 978(2):140, DOI 10.3847/1538-4357/ad94f6, https://doi.org/10.3847/1538-4357/ad94f6
  9. Afonso Delgado D., del Pino Alemán T., Trujillo Bueno J., Ishikawa R., Alsina Ballester E., McKenzie D. E., Belluzzi L., Bethge C., Kobayashi K., Okamoto T. J., Rachmeler L. A., Song D., Štěpán J., de Pontieu B., Kobelski A. R., Vigil G. D., Auchere F., Kano R., Winebarger A. (2025), 'Determining the Magnetic Field of Active Region Plages Using the Whole CLASP2/2.1 Spectral Window', The Astrophysical Journal 991(2):164, DOI 10.3847/1538-4357/adfcd4, arXiv:2508.14347, https://doi.org/10.3847/1538-4357/adfcd4
  10. Rachmeler L. A., Trujillo Bueno J., McKenzie D. E., Ishikawa R., Auchere F., Kobayashi K., Kano R., Okamoto T. J., Bethge C. W., Song D., Alsina Ballester E., Belluzzi L., del Pino Alemán T., Asensio Ramos A., Yoshida M., Shimizu T., Winebarger A., Kobelski A. R., Vigil G. D., De Pontieu B., Narukage N., Kubo M., Sakao T., Hara H., Suematsu Y., Štěpán J., Carlsson M., Leenaarts J. (2022), 'Quiet Sun Center to Limb Variation of the Linear Polarization Observed by CLASP2 Across the Mg ii h and k Lines', The Astrophysical Journal 936(1):67, DOI 10.3847/1538-4357/ac83b8, https://doi.org/10.3847/1538-4357/ac83b8