Formation-height ordering of the Hα and Ca II 854.2 nm line cores in chromospheric downflows and the magnetic-field stratification retrievable from simultaneous Stokes I and V spectropolarimetry

Simultaneous spectropolarimetry in Hα (656.28 nm) and the Ca II infrared line at 854.2 nm is a candidate multi-height probe of the solar chromospheric magnetic field, but its height content in dynamically active regions is not established. From Dunn Solar Telescope observations of a pore hosting a reconnection-driven energetic event, Nagaraju, Sankarasubramanian & Rangarajan (2020) inferred from the downflow intensity profiles that the Ca II 854.2 nm line core may form higher than the Hα core — a reversal of the standard ordering — and found that their Stokes I and V inversions retrieved no height variation of the line-of-sight magnetic field, with field-gradient nodes degrading the fits. Later work confirmed the standard ordering (Hα core Stokes V forming on average about 500 km above the Ca II 854.2 nm core) only for average conditions of a 3D radiative-magnetohydrodynamic simulation, demonstrated two-height magnetic retrievals from the same observational data, and quantified gradient-induced biases of the weak-field approximation; however, the downflow-specific formation-height ordering was never rigorously tested, and a continuous magnetic-field gradient retrieval from this line pair was never demonstrated. The open problem is to establish, by rigorous forward modeling and/or observational demonstration, the relative formation heights of the two line cores in strong chromospheric downflows and the height stratification of the chromospheric line-of-sight magnetic field that simultaneous Stokes I and V profiles of these lines can actually constrain.

Background

The solar chromosphere is the roughly 2000 km thick, magnetically dominated layer between the visible solar surface (photosphere) and the million-degree corona; measuring its magnetic field is a prerequisite for understanding energy transport, waves, and reconnection-driven energetic events. The standard diagnostic is spectropolarimetry: measuring the four Stokes parameters, where $I$ is the intensity and $Q$, $U$, $V$ encode linear and circular polarization, the last produced mainly by the Zeeman effect (the splitting and polarization of a spectral line in a magnetic field). The most widely used visible-light chromospheric magnetic diagnostic is the Ca II infrared line at 854.2 nm (a member of the Ca II infrared triplet, abbreviated CaIR or Ca II 8542), whose line core samples the mid-chromosphere (Lagg et al. 2017). The Hα line of neutral hydrogen at 656.28 nm is present across nearly all chromospheric plasma conditions, but it is difficult to model: its level populations are set by non-local thermodynamic equilibrium (NLTE) radiative transfer in which the populations depend on the radiation field rather than the local temperature, and its interpretation requires three-dimensional (3D) radiative transfer rather than a one-dimensional plane-parallel atmosphere (Leenaarts et al. 2012). A line's formation height is not a single number: it is summarized from contribution or response functions, which quantify how much the emergent intensity at each wavelength is contributed by, or responds to perturbations of, each atmospheric depth, usually expressed on the optical-depth scale $\log\tau_{500}$ at 500 nm. Common inference tools are the weak-field approximation (WFA), valid when Zeeman splitting is much smaller than the Doppler width, in which $V\propto B_{LOS}\,dI/d\lambda$ so circular polarization directly yields the line-of-sight (LOS) field $B_{LOS}$, and NLTE inversion codes such as NICOLE (Socas-Navarro et al. 2015) and STiC (de la Cruz Rodríguez et al. 2019), which fit a height-stratified model atmosphere to the observed Stokes profiles. A magnetic canopy is the fan of field lines expanding with height from strong-flux concentrations such as pores (small sunspots without penumbrae), which can overlie adjacent regions of opposite photospheric polarity, so chromospheric lines may sample a different field topology than photospheric lines at the same disk position. Ellerman bombs (EBs) are small-scale magnetic reconnection events in the lower atmosphere, recognized by 'mustache' brightenings in the wings of Hα and other chromospheric lines; they are often associated with surge flows (collimated plasma ejections) and strong downflows (Vissers et al. 2015).

Nagaraju, Sankarasubramanian & Rangarajan (2020) observed a pore simultaneously in Hα and Ca II 854.2 nm with the SPINOR instrument at the Dunn Solar Telescope on 4 December 2008, covering a small-scale energetic event (SSEE) that evolved like a progressive reconnection between newly emerged opposite-polarity field and the pore's canopy field. In the strong downflows at event onset, the Ca II 854.2 nm profiles were redshifted away from line core while Hα was redshifted including its line core, suggesting — contrary to the accepted picture in which the Hα core forms above, or at most at comparable heights to, the Ca II 854.2 nm core — that in these downflows the Ca II 854.2 nm core formed higher than the Hα core. The authors explicitly stated that more rigorous analysis is required to confirm this. Their preliminary NICOLE inversions of the Ca II 854.2 nm Stokes $I$ and $V$ profiles (Stokes $Q$ and $U$ were at the noise level of about $10^{-3}I_c$, and the telescope calibration was outdated) retrieved a temperature enhancement that appeared placed too low to reproduce the observed wing enhancement, and retrieved no height variation of $B_{LOS}$; adding magnetic-field gradient nodes worsened the fits. Earlier 1D analysis had also warned that Hα Stokes $V$ can carry photospheric sensitivity (Socas-Navarro & Uitenbroek 2004), while 3D modeling showed Hα retains chromospheric opacity even in flaring active regions (Bjørgen et al. 2019). Together these raise the two linked questions that still lack a settled answer: which heights these two line cores actually sample in dynamic downflow conditions, and what magnetic-field height stratification their simultaneous Stokes $I$ and $V$ profiles can constrain.

Problem Statement

Determine, by rigorous analysis — for example 3D radiative-magnetohydrodynamic forward modeling with contribution/response-function analysis of dynamic events and/or event-specific inversions of the existing observations — the relative formation heights of the Hα (656.28 nm) and Ca II 854.2 nm line cores in strong chromospheric downflow regions, and in particular whether the suggested reversal, in which the Ca II 854.2 nm core forms higher than the Hα core during the strong downflows accompanying reconnection-driven energetic events, is real or an artifact of the intensity-profile argument. On this basis, establish what height stratification of the chromospheric line-of-sight magnetic field — including its continuous gradients, not merely two discrete height samples — can and cannot be constrained from simultaneous Stokes $I$ and $V$ profiles of these two lines, with quantified uncertainties and systematic biases (including weak-field-approximation biases under field gradients). An answer must state explicitly, for the downflow regimes it studies, whether the standard ordering holds or reverses and, where it reverses, which physical conditions govern the reversal, and must characterize both the retrievable part of the magnetic stratification and the failure modes (gradients that the data cannot constrain).

References

1. Nagaraju, K., Sankarasubramanian, K., & Rangarajan, K. E. 2020, 'Diagnosing chromospheric magnetic field through simultaneous spectropolarimetry in Hα and Ca II 854.2 nm', Proceedings of the International Astronomical Union 15 (IAU Symposium S354), 46–52. DOI 10.1017/s1743921320000186, https://doi.org/10.1017/s1743921320000186
2. Leenaarts, J., Carlsson, M., & Rouppe van der Voort, L. 2012, 'The formation of the Hα line in the solar chromosphere', The Astrophysical Journal 749, 136. DOI 10.1088/0004-637X/749/2/136, https://doi.org/10.1088/0004-637X/749/2/136
3. Socas-Navarro, H., & Uitenbroek, H. 2004, 'On the Diagnostic Potential of Hα for Chromospheric Magnetism', The Astrophysical Journal 603, L129. DOI 10.1086/383147, https://doi.org/10.1086/383147
4. Lagg, A., Lites, B., Harvey, J., Gosain, S., & Centeno, R. 2017, 'Measurements of Photospheric and Chromospheric Magnetic Fields', Space Science Reviews 210, 37. DOI 10.1007/s11214-015-0219-y, https://doi.org/10.1007/s11214-015-0219-y
5. Vissers, G. J. M., Rouppe van der Voort, L. H. M., Rutten, R. J., Carlsson, M., & De Pontieu, B. 2015, 'Ellerman Bombs at High Resolution. III. Simultaneous Observations with IRIS and SST', The Astrophysical Journal 812, 11. DOI 10.1088/0004-637X/812/1/11, https://doi.org/10.1088/0004-637X/812/1/11
6. Socas-Navarro, H., de la Cruz Rodríguez, J., Asensio Ramos, A., Trujillo Bueno, J., & Ruiz Cobo, B. 2015, 'An open-source, massively parallel code for non-LTE synthesis and inversion of spectral lines and Zeeman-induced Stokes profiles', Astronomy & Astrophysics 577, A7. DOI 10.1051/0004-6361/201424860, https://doi.org/10.1051/0004-6361/201424860
7. Nagaraju, K., Sankarasubramanian, K., & Rangarajan, K. E. 2020, 'Hα full line spectropolarimetry as diagnostics of chromospheric magnetic field', Journal of Astrophysics and Astronomy 41, 10. DOI 10.1007/s12036-020-9627-9, https://doi.org/10.1007/s12036-020-9627-9
8. Centeno, R. 2018, 'On the Weak Field Approximation for Ca 8542 Å', The Astrophysical Journal 866, 89. DOI 10.3847/1538-4357/aae087, https://doi.org/10.3847/1538-4357/aae087
9. de la Cruz Rodríguez, J., Leenaarts, J., Danilovic, S., & Uitenbroek, H. 2019, 'STiC: A multiatom non-LTE PRD inversion code for full-Stokes solar observations', Astronomy & Astrophysics 623, A74. DOI 10.1051/0004-6361/201834464, https://doi.org/10.1051/0004-6361/201834464
10. Mathur, H., Nagaraju, K., Joshi, J., & de la Cruz Rodríguez, J. 2023, 'Do Hα Stokes V Profiles Probe the Chromospheric Magnetic Field? An Observational Perspective', The Astrophysical Journal 946, 38. DOI 10.3847/1538-4357/acbf49, https://doi.org/10.3847/1538-4357/acbf49
11. Kawabata, Y., Quintero Noda, C., Katsukawa, Y., Kubo, M., Matsumoto, T., & Oba, T. 2024, 'Multiline Stokes Synthesis of Ellerman Bombs: Obtaining Seamless Information from Photosphere to Chromosphere', The Astrophysical Journal 960, 26. DOI 10.3847/1538-4357/acf9fc, https://doi.org/10.3847/1538-4357/acf9fc
12. Mathur, H., Nagaraju, K., Yadav, R., & Joshi, J. 2024, 'Simultaneous Spectropolarimetric Observations in the Hα and Ca ii 8662 Å Lines of an Active Region', The Astrophysical Journal 971, 30. DOI 10.3847/1538-4357/ad54ba, https://doi.org/10.3847/1538-4357/ad54ba
13. Mathur, H., Joshi, J., Moe, T. E., Pereira, T. M. D., & Nagaraju, K. 2025, 'The Hα Line as a Probe of Chromospheric Magnetic Fields', The Astrophysical Journal Letters 987, L39. DOI 10.3847/2041-8213/ade8ea, https://doi.org/10.3847/2041-8213/ade8ea
14. Carlsson, M., Hansteen, V. H., Gudiksen, B. V., Leenaarts, J., & De Pontieu, B. 2016, 'A publicly available simulation of an enhanced network region of the Sun', Astronomy & Astrophysics 585, A4. DOI 10.1051/0004-6361/201527226, https://doi.org/10.1051/0004-6361/201527226
15. Bjørgen, J. P., Leenaarts, J., Rempel, M., Cheung, M. C. M., Danilovic, S., de la Cruz Rodríguez, J., & Sukhorukov, A. V. 2019, 'Three-dimensional modeling of chromospheric spectral lines in a simulated active region', Astronomy & Astrophysics 631, A33. DOI 10.1051/0004-6361/201834919, https://doi.org/10.1051/0004-6361/201834919