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A chromospheric resonance cavity in a sunspot mapped with seismology



Sunspots are intense collections of magnetic fields that pierce through the Sun’s photosphere, with their signatures extending upwards into the outermost extremities of the solar corona1. Cutting-edge observations and simulations are providing insights into the underlying wave generation2, configuration3,4 and damping5 mechanisms found in sunspot atmospheres. However, the in situ amplification of magnetohydrodynamic waves6, rising from a few hundreds of metres per second in the photosphere to several kilometres per second in the chromosphere7, has, until now, proved difficult to explain. Theory predicts that the enhanced umbral wave power found at chromospheric heights may come from the existence of an acoustic resonator8,9,10, which is created due to the substantial temperature gradients experienced at photospheric and transition region heights11. Here, we provide strong observational evidence of a resonance cavity existing above a highly magnetic sunspot. Through a combination of spectropolarimetric inversions and comparisons with high-resolution numerical simulations, we provide a new seismological approach to mapping the geometry of the inherent temperature stratifications across the diameter of the underlying sunspot, with the upper boundaries of the chromosphere ranging between 1,300 ± 200 km and 2,300 ± 250 km. Our findings will allow the three-dimensional structure of solar active regions to be conclusively determined from relatively commonplace two-dimensional Fourier power spectra. The techniques presented are also readily suitable for investigating temperature-dependent resonance effects in other areas of astrophysics, including the examination of Earth–ionosphere wave cavities12.

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Fig. 1: The velocity signatures of the magnetized sunspot atmosphere observed on 14 July 2016.
Fig. 2: Doppler velocities and spectral energies of observed and simulated time series.
Fig. 3: Spectral energy gradients of observed and simulated time series.
Fig. 4: Three-dimensional visualization of the geometric extent of the chromosphere above active region NOAA 12565.

Data availability

The data used in this paper are from the observing campaign entitled ‘The Influence of Magnetism on Solar and Stellar Atmospheric Dynamics’ (NSO-SP proposal T1081; principal investigator: D.B.J.), which employed the ground-based Dunn Solar Telescope, USA, during July 2016. Additional supporting observations were obtained from the publicly available NASA’s Solar Dynamics Observatory ( data archive, which can be accessed via The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The numerical code (Lare2D) used in the work can be downloaded from:


  1. 1.

    Borrero, J. M. & Ichimoto, K. Magnetic structure of sunspots. Living Rev. Solar Phys. 8, 4 (2011).

    ADS  Google Scholar 

  2. 2.

    Bogdan, T. J. et al. Waves in the magnetized solar atmosphere. II. Waves from localized sources in magnetic flux concentrations. Astrophys. J. 599, 626–660 (2003).

    ADS  Google Scholar 

  3. 3.

    Lites, B. W., Thomas, J. H., Bogdan, T. J. & Cally, P. S. Velocity and magnetic field fluctuations in the photosphere of a sunspot. Astrophys. J. 497, 464–482 (1998).

    ADS  Google Scholar 

  4. 4.

    Nagashima, K. et al. Observations of sunspot oscillations in G band and CaII H line with Solar Optical Telescope on Hinode. Publ. Astron. Soc. Jpn 59, S631–S636 (2007).

    Google Scholar 

  5. 5.

    Grant, S. D. T. et al. Alfvén wave dissipation in the solar chromosphere. Nat. Phys. 14, 480–483 (2018).

    Google Scholar 

  6. 6.

    Kobanov, N. I. & Makarchik, D. V. Propagating waves in the sunspot umbra chromosphere. Astron. Astrophys. 424, 671–675 (2004).

    ADS  Google Scholar 

  7. 7.

    Tziotziou, K., Tsiropoula, G., Mein, N. & Mein, P. Dual-line spectral and phase analysis of sunspot oscillations. Astron. Astrophys. 463, 1153–1163 (2007).

    ADS  Google Scholar 

  8. 8.

    Hollweg, J. V. A new resonance in the solar atmosphere. I. Theory. Sol. Phys. 62, 227–240 (1979).

    ADS  Google Scholar 

  9. 9.

    Botha, G. J. J., Arber, T. D., Nakariakov, V. M. & Zhugzhda, Y. D. Chromospheric resonances above sunspot umbrae. Astrophys. J. 728, 84 (2011).

    ADS  Google Scholar 

  10. 10.

    Felipe, T. Origin of the chromospheric three-minute oscillations in sunspot umbrae. Astron. Astrophys. 627, A169 (2019).

    ADS  Google Scholar 

  11. 11.

    Snow, B., Botha, G. J. J. & Régnier, S. Chromospheric seismology above sunspot umbrae. Astron. Astrophys. 580, A107 (2015).

    ADS  Google Scholar 

  12. 12.

    Toledo-Redondo, S., Salinas, A., Fornieles, J., Portí, J. & Lichtenegger, H. I. M. Full 3-D TLM simulations of the Earth-ionosphere cavity: effect of conductivity on the Schumann resonances. J. Geophys. Res. Space Phys. 121, 5579–5593 (2016).

    ADS  Google Scholar 

  13. 13.

    Jaeggli, S. A. et al. FIRS: a new instrument for photospheric and chromospheric studies at the DST. Mem. Soc. Astron. Ital. 81, 763 (2010).

    ADS  Google Scholar 

  14. 14.

    Jess, D. B. et al. ROSA: a high-cadence, synchronized multi-camera solar imaging system. Sol. Phys. 261, 363–373 (2010).

    ADS  Google Scholar 

  15. 15.

    Cavallini, F. IBIS: a new post-focus instrument for solar imaging spectroscopy. Sol. Phys. 236, 415–439 (2006).

    ADS  Google Scholar 

  16. 16.

    Socas-Navarro, H., McIntosh, S. W., Centeno, R., de Wijn, A. G. & Lites, B. W. Direct imaging of fine structure in the chromosphere of a sunspot umbra. Astrophys. J. 696, 1683–1688 (2009).

    ADS  Google Scholar 

  17. 17.

    Beck, C., Choudhary, D. P. & Rezaei, R. A three-dimensional view of the thermal structure in a super-penumbral canopy. Astrophys. J. 788, 183 (2014).

    ADS  Google Scholar 

  18. 18.

    Stull, R. An Introduction to Boundary Layer Meteorology (Atmospheric and Oceanographic Sciences Library, Springer, 2012).

  19. 19.

    Reznikova, V. E., Shibasaki, K., Sych, R. A. & Nakariakov, V. M. Three-minute oscillations above sunspot umbra observed with the Solar Dynamics Observatory/Atmospheric Imaging Assembly and Nobeyama Radioheliograph. Astrophys. J. 746, 119 (2012).

    ADS  Google Scholar 

  20. 20.

    Barret, D. & Vaughan, S. Maximum likelihood fitting of X-ray power density spectra: application to high-frequency quasi-periodic oscillations from the neutron star X-ray binary 4U1608-522. Astrophys. J. 746, 131 (2012).

    ADS  Google Scholar 

  21. 21.

    He, J., Wang, L., Tu, C., Marsch, E. & Zong, Q. Evidence of Landau and cyclotron resonance between protons and kinetic waves in solar wind turbulence. Astrophys. J. Lett. 800, L31 (2015).

    ADS  Google Scholar 

  22. 22.

    Arber, T. D., Longbottom, A. W., Gerrard, C. L. & Milne, A. M. A staggered grid, Lagrangian-Eulerian remap code for 3-D MHD simulations. J. Comput. Phys. 171, 151–181 (2001).

    ADS  MathSciNet  MATH  Google Scholar 

  23. 23.

    Asensio Ramos, A., Trujillo Bueno, J. & Landi Degl’Innocenti, E. Advanced forward modeling and inversion of Stokes profiles resulting from the joint action of the Hanle and Zeeman effects. Astrophys. J. 683, 542–565 (2008).

    ADS  Google Scholar 

  24. 24.

    Houston, S. J. et al. The magnetic response of the solar atmosphere to umbral flashes. Astrophys. J. 860, 28 (2018).

    ADS  Google Scholar 

  25. 25.

    Avrett, E. H., Fontenla, J. M. & Loeser, R. Formation of the solar 10830 Å line. In Infrared Solar Physics Vol. 154 (eds Rabin, D. M. et al.) 35–47 (IAU Symposium, 1994).

  26. 26.

    Jess, D. B. et al. The source of 3 minute magnetoacoustic oscillations in coronal fans. Astrophys. J. 757, 160 (2012).

    ADS  Google Scholar 

  27. 27.

    Derks, A., Beck, C. & Martínez Pillet, V. Inferring telescope polarization properties through spectral lines without linear polarization. Astron. Astrophys. 615, A22 (2018).

    ADS  Google Scholar 

  28. 28.

    Cauzzi, G. et al. The solar chromosphere at high resolution with IBIS. I. New insights from the Ca II 854.2 nm line. Astron. Astrophys. 480, 515–526 (2008).

    ADS  Google Scholar 

  29. 29.

    Jess, D. B., Mathioudakis, M., Christian, D. J., Crockett, P. J. & Keenan, F. P. A study of magnetic bright points in the Na I D1 line. Astrophys. J. Lett. 719, L134–L139 (2010).

    ADS  Google Scholar 

  30. 30.

    Stangalini, M., DelMoro, D., Berrilli, F. & Jefferies, S. M. MHD wave transmission in the Sun’s atmosphere. Astron. Astrophys. 534, A65 (2011).

    Google Scholar 

  31. 31.

    Lagg, A., Woch, J., Solanki, S. K. & Krupp, N. Supersonic downflows in the vicinity of a growing pore. Evidence of unresolved magnetic fine structure at chromospheric heights. Astron. Astrophys. 462, 1147–1155 (2007).

    ADS  Google Scholar 

  32. 32.

    Aznar Cuadrado, R., Solanki, S. K. & Lagg, A. Velocity distribution of chromospheric downflows. In Modern Solar Facilities, Advances in Solar Science (eds Kneer, F. et al.) 173–176 (2007).

  33. 33.

    González Manrique, S. J. et al. Fitting peculiar spectral profiles in He I 10830 Å absorption features. Astron. Nachr. 337, 1057–1063 (2016).

    ADS  Google Scholar 

  34. 34.

    González Manrique, S. J. et al. Temporal evolution of arch filaments as seen in He i 10 830 Å. Astron. Astrophys. 617, A55 (2018).

    Google Scholar 

  35. 35.

    Zaghloul, M. R. On the calculation of the Voigt line profile: a single proper integral with a damped sine integrand. Mon. Not. R. Astron. Soc. 375, 1043–1048 (2007).

    ADS  Google Scholar 

  36. 36.

    Henriques, V. M. J. et al. Stable umbral chromospheric structures. Astron. Astrophys. 574, A131 (2015).

    Google Scholar 

  37. 37.

    Bel, N. & Leroy, B. Analytical study of magnetoacoustic gravity waves. Astron. Astrophys. 55, 239 (1977).

    ADS  MATH  Google Scholar 

  38. 38.

    Roberts, B. MHD waves in the solar atmosphere. In Waves, Oscillations and Small-Scale Transients Events in the Solar Atmosphere: Joint View from SOHO and TRACE (SOHO 13) Vol. 547 (ed. Lacoste, H.) 1 (ESA Special Publication, 2004).

  39. 39.

    Löhner-Böttcher, J., BelloGonzález, N. & Schmidt, W. Magnetic field reconstruction based on sunspot oscillations. Astron. Nachr. 337, 1040–1044 (2016).

    ADS  Google Scholar 

  40. 40.

    Jess, D. B. et al. Solar coronal magnetic fields derived using seismology techniques applied to omnipresent sunspot waves. Nat. Phys. 12, 179–185 (2016).

    Google Scholar 

  41. 41.

    Jess, D. B. et al. An inside look at sunspot oscillations with higher azimuthal wavenumbers. Astrophys. J. 842, 59 (2017).

    ADS  Google Scholar 

  42. 42.

    Krishna Prasad, S. et al. The frequency-dependent damping of slow magnetoacoustic waves in a sunspot umbral atmosphere. Astrophys. J. 847, 5 (2017).

    ADS  Google Scholar 

  43. 43.

    Groth, E. J. Probability distributions related to power spectra. Astrophys. J. Suppl. Ser. 29, 285–302 (1975).

    ADS  Google Scholar 

  44. 44.

    Papadakis, I. E. & Lawrence, A. Improved methods for power spectrum modelling of red noise. Mon. Not. R. Astron. Soc. 261, 612–624 (1993).

    ADS  Google Scholar 

  45. 45.

    Morton, R. J., Weberg, M. J. & McLaughlin, J. A. A basal contribution from p-modes to the Alfvénic wave flux in the Sun’s corona. Nat. Astron. 3, 223–229 (2019).

    ADS  Google Scholar 

  46. 46.

    Matthaeus, W. H. et al. Density and magnetic field signatures of interplanetary 1/f noise. Astrophys. J. Lett. 657, L121–L124 (2007).

    ADS  Google Scholar 

  47. 47.

    Huang, S. Y., Hadid, L. Z., Sahraoui, F., Yuan, Z. G. & Deng, X. H. On the existence of the Kolmogorov inertial range in the terrestrial magnetosheath turbulence. Astrophys. J. Lett. 836, L10 (2017).

    ADS  Google Scholar 

  48. 48.

    Sheikholeslami, M., Abelman, S. & Ganji, D. D. Numerical simulation of MHD nanofluid flow and heat transfer considering viscous dissipation. Int. J. Heat Mass Transfer 79, 212–222 (2014).

    Google Scholar 

  49. 49.

    Goldstein, M. L., Roberts, D. A. & Fitch, C. A. Properties of the fluctuating magnetic helicity in the inertial and dissipation ranges of solar wind turbulence. J. Geophys. Res. 99, 11519–11538 (1994).

    ADS  Google Scholar 

  50. 50.

    Maltby, P. et al. A new sunspot umbral model and its variation with the solar cycle. Astrophys. J. 306, 284–303 (1986).

    ADS  Google Scholar 

  51. 51.

    Avrett, E. H. & Loeser, R. Models of the solar chromosphere and transition region from SUMER and HRTS observations: formation of the extreme-ultraviolet spectrum of hydrogen, carbon, and oxygen. Astrophys. J. Suppl. Ser. 175, 229–276 (2008).

    ADS  Google Scholar 

  52. 52.

    Borrero, J. M. et al. VFISV: Very Fast Inversion of the Stokes Vector for the Helioseismic and Magnetic Imager. Sol. Phys. 273, 267–293 (2011).

    ADS  Google Scholar 

  53. 53.

    Schou, J. et al. Design and ground calibration of the Helioseismic and Magnetic Imager (HMI) instrument on the Solar Dynamics Observatory (SDO). Sol. Phys. 275, 229–259 (2012).

    ADS  Google Scholar 

  54. 54.

    Rabello-Soares, M. C., Roca Cortes, T., Jimenez, A., Andersen, B. N. & Appourchaux, T. An estimate of the solar background irradiance power spectrum. Astron. Astrophys. 318, 970–974 (1997).

    ADS  Google Scholar 

  55. 55.

    Felipe, T., Khomenko, E., Collados, M. & Beck, C. Multi-layer study of wave propagation in sunspots. Astrophys. J. 722, 131–144 (2010).

    ADS  Google Scholar 

  56. 56.

    Vernazza, J. E., Avrett, E. H. & Loeser, R. Structure of the solar chromosphere. III. Models of the EUV brightness components of the quiet-sun. Astrophys. J. Suppl. Ser. 45, 635–725 (1981).

    ADS  Google Scholar 

  57. 57.

    Centeno, R., Collados, M. & Trujillo Bueno, J. Spectropolarimetric investigation of the propagation of magnetoacoustic waves and shock formation in sunspot atmospheres. Astrophys. J. 640, 1153–1162 (2006).

    ADS  Google Scholar 

  58. 58.

    Centeno, R., Collados, M. & Trujillo Bueno, J. Wave propagation and shock formation in different magnetic structures. Astrophys. J. 692, 1211–1220 (2009).

    ADS  Google Scholar 

  59. 59.

    Krishna Prasad, S., Jess, D. B. & Khomenko, E. On the source of propagating slow magnetoacoustic waves in sunspots. Astrophys. J. Lett. 812, L15 (2015).

    ADS  Google Scholar 

  60. 60.

    Marsh, M. S. & Walsh, R. W. p-Mode propagation through the transition region into the solar corona. I. Observations. Astrophys. J. 643, 540–548 (2006).

    ADS  Google Scholar 

  61. 61.

    Zhukov, V. I. Oscillations on the Sun in regions with a vertical magnetic field. II. On the calculation of the sunspot umbral oscillations. Astron. Astrophys. 433, 1127–1132 (2005).

    ADS  Google Scholar 

  62. 62.

    Zhugzhda, Y. D. Three-minute oscillations in sunspots: seismology of sunspot atmospheres. Astron. Lett. 33, 622–643 (2007).

    ADS  Google Scholar 

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D.B.J. would like to thank the UK Science and Technology Facilities Council (STFC) for an Ernest Rutherford Fellowship, in addition to a dedicated standard grant that allowed this project to be undertaken. D.B.J. and S.D.T.G. also wish to thank Invest NI and Randox Laboratories Ltd for the award of a Research & Development Grant (059RDEN-1) that allowed the computational techniques employed to be developed. B.S. is supported by STFC research grant ST/R000891/1. S.K.P. wishes to thank the UK STFC for support. A.A.R. is grateful to the Spanish Ministry of Economy and Competitiveness through project AYA2014-60476-P. S.J. acknowledges support from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 682462) and from the Research Council of Norway through its Centres of Excellence scheme (project no. 262622). M.S. is grateful for funding received from the European Research Council under the European Union’s Horizon 2020 Framework Programme for Research and Innovation, grant agreements H2020 PRE-EST (no. 739500) and H2020 SOLARNET (no. 824135), in addition to support from INAF Istituto Nazionale di Astrofisica (PRIN-INAF-2014). D.J.C. would like to thank California State University Northridge for start-up funding. The Dunn Solar Telescope at Sacramento Peak/NM was operated by the National Solar Observatory (NSO). NSO is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under cooperative agreement with the National Science Foundation (NSF). The SDO/AIA imaging employed in this work are courtesy of NASA/SDO and the AIA, EVE and HMI science teams. We wish to acknowledge scientific discussions with the Waves in the Lower Solar Atmosphere (WaLSA; team, which is supported by the Research Council of Norway (project no. 262622). Imagery was produced by the Visualization and Analysis Platform for atmospheric, Oceanic and solar Research (VAPOR;, a product of the Computational Information Systems Laboratory at the National Center for Atmospheric Research.

Author information




D.B.J. and D.J.C. designed the observational instrumentation set-up. D.B.J., S.J.H. and S.K.P. undertook the ground-based observations. D.B.J., S.J.H., A.A.R. and S.D.T.G. performed analysis of the observations. B.S. and G.J.J.B. designed and carried out numerical MHD simulations. D.B.J., B.S., S.J.H., G.J.J.B., S.K.P., P.H.K., S.J., M.S., B.F. and R.J.M. interpreted the observations and simulations. D.B.J., B.S., S.J.H., R.J.M. and S.D.T.G. prepared and processed all data products. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to David B. Jess.

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Extended data

Extended Data Fig. 1 Omnipresent wave motion observed in He i 10830 Å Doppler velocities.

(a) A sample umbral He i Stokes I line profile, normalised by the average continuum intensity, Ic, is presented as a solid black line. The dashed red line displays the fitted absorption profile that is used to calculate the associated Doppler velocity of the He i 10830 Å line core. (b) A time-distance map of the He i 10830 Å line core Doppler velocities, saturated between \(\pm 6\) km/s for clarity, with the vertical dashed pink line highlighting the location of the persistent red-shifted brightening that segregates the umbra into two separate regions.

Extended Data Fig. 2 Segregating the sunspot into two umbrae as a result of a persistent filamentary structure.

(a) An IBIS Ca ii 8542 Å line core image of the NOAA 12565 sunspot, identical to that displayed in Fig. 1e, only now with a dashed blue box highlighting a sub-field that is magnified in panel (b). It is clear to see the persistent chromospheric umbral brightening in panel (b), which is marked using a pink cross. (c) The time-averaged Stokes \(I/{I}_{c}\) intensities along the length of the umbra (extracted along the solid green line in panels a & b), with the vertical dashed pink line marking the position of the persistent chromospheric umbral brightening. The shaded green and blue regions highlight the umbral regions south and north, respectively, of the umbral brightening, with the vertical dashed red lines indicating the centres of gravity of the time-averaged Stokes \(I/{I}_{c}\) intensities for each isolated umbral region.

Extended Data Fig. 3 Spatially resolved spectral energies across the diameter of the sunspot.

Fourier spectral energy, in units of km2/s2, plotted as a function of frequency and distance across the sunspot umbra. The distance corresponding to the persistent umbral brightening, which isolates the umbra into two distinct regions, is indicated by the horizontal dashed pink line. The horizontal dashed green lines represent the barycenters of the two segregated umbral cores that are isolated by the persistent brightening (see, e.g., Extended Data Fig. 2b). The dotted black line traces the weighted spectral energy centroid (in the range of \(3-17\) mHz) across the entire diameter of the sunspot umbra. This panel is a two-dimensional representation of Fig. 2d, which now preserves information along the spatial diameter of the sunspot umbra.

Extended Data Fig. 4 Temperature stratification along the motion path of the simulated wave propagation.

Temperature plotted as a function of wave propagation distance for 5 different stratification models. The solid black line represents the sunspot model50 ‘M’ that has been scaled using outputs from the HAZEL inversions applied to the spectropolarimetric He i 10830 Å data products. The shaded grey region highlights the depth of the embedded resonance cavity along the motion path of the propagating magnetoacoustic waves, which can be visualized as extending from 0 km to the steep temperature gradient associated with the transition region. Here, the wave path spans a distance of 2120 km, which for vertical magnetic fields (i.e., \(\cos \theta =1\)) also corresponds to the upper geometric height of the chromosphere (i.e., 2120 km as indicated by the vertical black dotted line). The blue, orange, green and purple lines depict re-scaled sunspot atmospheres with the depth of the chromospheric resonance cavities resized by 80%, 90%, 110% and 120%, respectively. As before, the coloured vertical dotted lines highlight the upper chromospheric boundary for each re-scaled umbral atmosphere.

Extended Data Fig. 5 Overview of the data-driven model atmospheres used to synthesise MHD wave activity in a sunspot.

Stratified temperature models used as inputs for the Lare2D MHD code to synthesise the propagation and amplification of magnetoacoustic waves manifesting in the chromospheric resonant layers of a sunspot atmosphere. Note that the propagation distance corresponds to the physical distance covered by the propagating magnetoacoustic waves between a height of 0 km and the point when they experience a large temperature gradient (i.e., the commencement of the transition region; see the vertical dotted lines in Extended Data Fig. 4). For a vertically orientated magnetic field line, this also corresponds to the true geometric height of the upper chromosphere. However, if the magnetic field line that the magnetoacoustic waves propagate along is inclined to the solar normal (i.e., \(\cos \theta \ne 1\)), then this angle needs to be factored into the estimate of the true geometric height (see Equation 1 in the main text).

Extended Data Fig. 6 Synthesised spectral gradients for region iii (\(18-27\) mHz) computed with the Lare2D MHD code.

The spectral slopes of region iii (\(18-27\) mHz), which are calculated from the maximum-likelihood fitments of the Fourier spectral energy produced by Lare2D numerical simulations, as a function of the variable resonance depths imposed in the modelled atmospheres. The vertical error bars highlight the maximum-likelihood 1σ fitment uncertainties achieved when measuring the corresponding spectral power-law gradients. The dashed black line maps the linear best-fit line through the data points, while the blue shaded region (bounded by the black dotted lines) highlights the \(95\)% confidence level associated with the fitted line. The shaded green and magenta regions (bounded and centred using solid black lines) highlight sample spectral gradients measured in the observational He i 10830 Å spectral energies, which can be converted into wave propagation distances through the resonance cavity. Note that these wave propagation distances also correspond to the height of the upper chromospheric boundary providing the magnetic field lines are vertically orientated.

Extended Data Fig. 7 Comparison of spectral energies for Lare2D numerical simulations with and without an upper temperature gradient.

(a & b) The simulated velocity time series, which is extracted from the Lare2D computational domain (including the steep transition region temperature gradient; see Extended Data Fig. 4) at an atmospheric height that is compatible with the formation of the He i 10830 Å spectral line, along with its corresponding spectral energy. These two panels are identical to Fig. 2e,f. (c & d) Identical information to panels (a) and (b), only now displaying the velocity time series and spectral energy corresponding to the Lare2D model atmosphere containing no upper transition region temperature gradient (i.e., a flat \( \sim \)\(5000\) K temperature profile from \(1300\) km upwards). Of particular note in panel (d) is the lack of a spectral energy enhancement at \( \sim \)\(20\) mHz, which is only produced in the presence of a resonance cavity. The dashed red lines (panels a and c) highlight a zero velocity for visual reference.

Extended Data Fig. 8 Magnetic field inclination angles derived from HAZEL inversions of the He i 10830 Å spectropolarimetric data.

Inclination angles, with respect to the solar normal, are plotted as a function of distance along the FIRS slit. The distance axis has been scaled to match that of Extended Data Fig. 2c, where ‘0 Mm’ highlights the beginning of the southernmost chromospheric umbra. The grey data points and blue shaded regions indicate locations not employed in the present study, while the black data points and green shaded region (bounded by vertical dotted lines) represent the umbral pixels used to calculate the true geometric extent of the sunspot chromosphere. The green shaded region hosts 35,653 inclination angles (101 pixels across the umbra and 353 time-resolved spectra), which are fitted using a fourth-order polynomial trend line (solid red line) to establish the dominant inclination angles experienced across the umbrae.

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Jess, D.B., Snow, B., Houston, S.J. et al. A chromospheric resonance cavity in a sunspot mapped with seismology. Nat Astron 4, 220–227 (2020).

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