The Evershed flow, a nearly horizontal outflow of magnetized gas along the dark filaments of a sunspot penumbra, loses its spectroscopic signature abruptly (within roughly 500 km) at the outer white-light boundary of the spot. The source study (Wiehr 1996) proposed that this location marks a sharp threshold where the magnetic energy density of the penumbral field falls below the kinetic energy density of surrounding granular convection (a balance field of about 740 G), so that flow and field sink at the border, and asked for direct measurements of the radial field profile B(r)B(r) and of local kinetic energy densities to test this. Later literature has settled parts of the question: the flow is now understood as the horizontal component of overturning magnetoconvection in penumbral filaments (superseding siphon-flow driving), it ends mainly in localized tail downflows while a minority continues into the moat as moving magnetic features (small magnetic flux concentrations streaming across the moat), and the chromospheric inverse Evershed flow is a separate system. A study published in Astronomy & Astrophysics in 2026 reported that, for one stable sunspot, the outer boundary coincides with an invariant field strength of about 625 G, which its authors interpret as the equipartition field. What remains open is the direct, quantitative verification: measuring the equipartition field Beq=4πρ vB_{\mathrm{eq}}=\sqrt{4\pi\rho}\,v empirically at the border, establishing the universality of the boundary field across sunspots and evolutionary phases, and closing the mass and magnetic-flux budget between flow sinking at the boundary and flow continuing into the moat.

Background

A sunspot consists of a dark umbra surrounded by a filamentary penumbra in which the magnetic field is strongly inclined, nearly horizontal in the dark radial filaments. In 1909 John Evershed discovered a systematic radial outflow of gas in the penumbra (the Evershed flow, of order 1-5 km/s), detected spectroscopically as an asymmetry or 'kink' of photospheric absorption lines: the profile is a superposition of an unshifted component from bright penumbral structures and a Doppler-shifted, weaker satellite component from the dark, more horizontal filaments. The line asymmetry, and hence the observable flow, is found only where dark penumbral filaments exist. Field strengths below are given in Gauss (G; 1 G=10−4 T1\,\mathrm{G}=10^{-4}\,\mathrm{T}).

Two classical pictures competed for how this flow ends at the outer edge of the penumbra. In the 'canopy' picture, the penumbral magnetic field and flow fan out with height and continue above the surrounding photosphere, so the flow signature of spectral lines formed at greater height should disappear progressively farther outside the white-light (continuum) boundary. In the second picture the flow is nearly horizontal and simply stops, together with the dark filaments, at the visible sunspot border. The source study (Wiehr, 'The Spatial Structure of the Evershed effect', published as a letter in Astronomy & Astrophysics 309, L4, 1996, from observations of October 1994; the author's full text is accessible as arXiv:1210.2553, posted in 2012, while the 1996 print letter predates Crossref DOI registration for A&A) observed two neighbouring photospheric absorption lines of different formation heights, the neutral-iron line Fe I 5434.5 (formed about 300 km higher) and the neutral-nickel line Ni I 5435.9, and found that both lose their Evershed asymmetries simultaneously within at most 500 km at the white-light border. A canopy would require implausibly steep inclinations (about 60 degrees, against the 6-15 degrees measured classically), so the flow must be nearly horizontal and terminate abruptly, with any downflows confined to scales below the achieved 0.5 arcsec resolution at the border itself.

As a physical cause, the source proposed equipartition between magnetic and kinetic energy density: with a photospheric mass density ρ=5⋅10−7 g/cm3\rho=5\cdot10^{-7}\,\mathrm{g/cm^3} and a granular velocity of v=3 km/sv=3\,\mathrm{km/s}, the kinetic energy density balances the magnetic energy density B2/8πB^2/8\pi at B≈740B\approx740 G, close to typical fields at the penumbral edge; with the radial scaling B∝r−2B\propto r^{-2} assumed in that paper, the magnetic energy density falls as r−4r^{-4}, producing a sharp threshold beyond which the field (and the flow it carries) is dragged down by convection. The author noted that such an abrupt disappearance may conflict with siphon-flow models (pressure-gradient-driven flows along magnetic flux tubes, once the leading explanation of the Evershed effect), while being compatible with convective 'turbulent pumping' of flux below the surface (the downward dragging of magnetic flux by turbulent convection). He also noted one exceptional location outside one filament end, with a Fe I asymmetry without a Ni I counterpart and no continuum depression, probably an unrelated disturbed phenomenon (an Ellerman bomb, a transient brightening caused by magnetic reconnection in the lower atmosphere).

The modern context has changed substantially. High-resolution spectropolarimetric inversions (fits of model atmospheres to observed polarized spectral-line profiles) and radiative magnetohydrodynamic (MHD) simulations now describe penumbral filaments as elongated magnetoconvective cells: hot upflow at the filament head, a strong horizontal outflow along its axis (the Evershed flow), lateral downflow lanes, and a concentrated downflow with fields of opposite polarity at the filament tail, with a net downflow mass flux about three times the upflow at the deepest photospheric layers (Tiwari et al. 2013). Simulations reproduce this and show the Evershed flow is convectively driven, while the moat flow (the annular plasma circulation surrounding a sunspot beyond its penumbra) is largely non-magnetic (Rempel 2015); in simulations, siphon-type pressure-gradient driving accounts for counter-Evershed (inward) flows rather than the normal outflow (Siu-Tapia et al. 2018). Observationally, some Evershed channels continue past the boundary: outward-migrating Evershed clouds become moving magnetic features (MMFs, small magnetic flux concentrations streaming across the moat), which remove magnetic flux from decaying spots (Cabrera Solana et al. 2006; Kubo et al. 2007), and a few supersonic magnetized channels have been detected in the moat itself (Martinez Pillet et al. 2009). At coarser (1-1.5 arcsec) resolution, a magnetized radial outflow continues smoothly beyond the boundary in the sunspot canopy (Rezaei et al. 2006), with the explicit caveat that sub-arcsecond abrupt structure could be blurred. The equipartition strand also has order-of-magnitude empirical support: Kalman (2002) found from photographic and vector-magnetograph data that the outer penumbral boundary closely follows the 750 G isogauss line of the total magnetic field, approximately the photospheric equipartition value. Most recently, Schmassmann et al. (2026, A&A) showed that for a stable sunspot the outer continuum-intensity contour (where the continuum intensity IcI_c falls to 0.9 of the mean quiet-Sun intensity IqsI_{\mathrm{qs}}) coincides with an invariant magnetic-field isocontour of about 625 G to within a quarter arcsecond over nine days, and interpreted this invariant as the equipartition field; during spot decay the two contours detach and granulation persists even in super-equipartition fields. Independent analysis of data from SDO/HMI (the Helioseismic and Magnetic Imager instrument on NASA's Solar Dynamics Observatory satellite) likewise finds a normal field component of roughly 550 G at the photometric boundary of symmetric spots, near the threshold at which granular convection is suppressed (Obridko et al. 2023). The equipartition field is defined by Beq=4πρ vB_{\mathrm{eq}}=\sqrt{4\pi\rho}\,v, the field at which magnetic and kinetic energy densities are equal; 'equipartition' throughout means this local, height-dependent balance.

Problem Statement

Determine, quantitatively and physically, the mechanism that terminates the photospheric Evershed flow at the outer white-light boundary of a sunspot, and in particular whether that boundary is set by the local equipartition between magnetic and kinetic energy density, as proposed in the source study. A complete answer should establish, jointly and consistently: (1) the equipartition test requested by the source - assembling and critically comparing the available co-spatial, high-resolution determinations of the radial magnetic-field profile B(r)B(r) at the penumbral border (including whether a scaling close to B∝r−2B\propto r^{-2} holds at the edge) and of the local kinetic energy density (photospheric density and granular velocity), so that the empirically computed equipartition field Beq=4πρ vB_{\mathrm{eq}}=\sqrt{4\pi\rho}\,v can be compared with the observed boundary field (values of order 550-750 G have been reported or predicted), the numerical balance and its uniqueness evaluated, and the observations that would complete the test identified; (2) the statistical universality of the boundary-defining field across sunspots of different sizes and evolutionary phases (pores, developing, stable, and decaying spots), established from the published determinations and statistics, including the behaviour during decay, where observations show granulation persisting in super-equipartition fields; and (3) the quantitative fate of the flow and its magnetic flux at termination, inferred from published observations and simulations - what fraction of the mass flux sinks in localized downflows at or just inside the border and what fraction continues beyond it as moving magnetic features and magnetized moat channels - such that the abrupt disappearance of the line-asymmetry signature at the white-light border (within about 500 km, as observed) is reconciled with the convective driving of the flow. The siphon-versus-convective driving of the photospheric flow and the connection to the chromospheric inverse Evershed flow have been settled by later literature (convective driving; separate flow systems) and are context, not deliverables; the single Ellerman-bomb-like exception noted in the source is a separate phenomenon and is not part of this problem.

References

  1. E. Wiehr (1996), 'The Spatial Structure of the Evershed effect', Astronomy & Astrophysics 309, L4, arXiv:1210.2553, DOI 10.48550/arXiv.1210.2553, https://arxiv.org/abs/1210.2553 (the author's full text of the 1996 A&A letter, posted on arXiv in 2012; the 1996 print letter has no Crossref DOI)
  2. B. Kalman (2002), 'On the outer boundary of the sunspot penumbra', Solar Physics 209, 109, DOI 10.1023/A:1020985530075, https://doi.org/10.1023/A:1020985530075 (preprint arXiv:astro-ph/0202120, https://arxiv.org/abs/astro-ph/0202120)
  3. R. Rezaei, R. Schlichenmaier, C. Beck, L. R. Bellot Rubio (2006), 'The flow field in the sunspot canopy', Astronomy & Astrophysics 454, 975, DOI 10.1051/0004-6361:20065180, https://doi.org/10.1051/0004-6361:20065180
  4. V. Martinez Pillet, Y. Katsukawa, K. G. Puschmann, B. Ruiz Cobo (2009), 'Supersonic continuation of the Evershed flow outside a sunspot as observed with Hinode', The Astrophysical Journal 701, L79, DOI 10.1088/0004-637X/701/2/L79, https://doi.org/10.1088/0004-637X/701/2/L79 (preprint arXiv:0907.3835, https://arxiv.org/abs/0907.3835)
  5. D. Cabrera Solana, L. R. Bellot Rubio, C. Beck, J. C. del Toro Iniesta (2006), 'Evershed Clouds as Precursors of Moving Magnetic Features around Sunspots', The Astrophysical Journal 649, L41, DOI 10.1086/508260, https://doi.org/10.1086/508260
  6. M. Kubo, T. Shimizu, S. Tsuneta (2007), 'Vector Magnetic Fields of Moving Magnetic Features and Flux Removal from a Sunspot', The Astrophysical Journal 659, 812, DOI 10.1086/512353, https://doi.org/10.1086/512353
  7. M. Kubo, K. Ichimoto, B. W. Lites, R. A. Shine (2011), 'Temporal Relation between Disappearance of Penumbral Fine-Scale Structure and Evershed Flow', The Astrophysical Journal 731, 84, DOI 10.1088/0004-637x/731/2/84, https://doi.org/10.1088/0004-637x/731/2/84
  8. Sanjiv Kumar Tiwari, Michiel van Noort, Andreas Lagg, Sami K. Solanki (2013), 'Structure of sunspot penumbral filaments: a remarkable uniformity of properties', Astronomy & Astrophysics 557, A25, DOI 10.1051/0004-6361/201321391, https://doi.org/10.1051/0004-6361/201321391
  9. S. Esteban Pozuelo, L. R. Bellot Rubio, J. de la Cruz Rodriguez (2016), 'Properties of Supersonic Evershed Downflows', The Astrophysical Journal 832, 170, DOI 10.3847/0004-637x/832/2/170, https://doi.org/10.3847/0004-637x/832/2/170
  10. M. Murabito, P. Romano, S. L. Guglielmino, F. Zuccarello, S. K. Solanki (2016), 'Formation of the Penumbra and Start of the Evershed Flow', The Astrophysical Journal 825, 75, DOI 10.3847/0004-637x/825/1/75, https://doi.org/10.3847/0004-637x/825/1/75
  11. M. Rempel (2015), 'Numerical simulations of sunspot decay: On the penumbra - Evershed flow - moat flow connection', The Astrophysical Journal 814, 125, DOI 10.1088/0004-637x/814/2/125, https://doi.org/10.1088/0004-637x/814/2/125
  12. A. L. Siu-Tapia, M. Rempel, A. Lagg, S. K. Solanki (2018), 'Evershed and Counter-Evershed Flows in Sunspot MHD Simulations', The Astrophysical Journal 852, 66, DOI 10.3847/1538-4357/aaa007, https://doi.org/10.3847/1538-4357/aaa007
  13. V. N. Obridko, D. D. Sokoloff, M. M. Katsova (2023), 'Relating photometric and magnetic properties of structures at solar surface', Journal of Atmospheric and Solar-Terrestrial Physics 252, 106152, DOI 10.1016/j.jastp.2023.106152, https://doi.org/10.1016/j.jastp.2023.106152 (preprint arXiv:2310.10748, https://arxiv.org/abs/2310.10748)
  14. Markus Schmassmann, Nazaret Bello Gonzalez, Jan Jurcak, Rolf Schlichenmaier (2026), 'The magnetic origin of the outer boundaries of sunspots', Astronomy & Astrophysics 706, A218, DOI 10.1051/0004-6361/202558127, https://doi.org/10.1051/0004-6361/202558127 (preprint arXiv:2512.11160, https://arxiv.org/abs/2512.11160, posted December 2025)
  15. Paolo Romano, Francesco Schilliro, Mariachiara Falco (2023), 'Observations of the Chromospheric Evershed Flow of Sunspot Penumbra with the Application of the Self-organizing Map Technique', The Astrophysical Journal 958, 56, DOI 10.3847/1538-4357/acfc20, https://doi.org/10.3847/1538-4357/acfc20 (preprint arXiv:2309.11186, https://arxiv.org/abs/2309.11186)