Counter-Evershed flows (CEFs) are photospheric inflows along penumbral filaments toward the umbra of otherwise mature sunspots; they are common but usually short-lived (median lifetime of about 10.6 hr), although a long-lived subpopulation persists for a day or more (exceptionally ~2 days). In realistic radiative magnetohydrodynamic sunspot simulations, the corresponding inflows are driven as siphon flows but are transient, decaying within roughly 10 hours and reverting to the normal Evershed outflow. The open problem is to give a physically complete, observationally testable account of the CEF lifecycle: what trigger conditions form a CEF in a well-developed penumbra; what mechanism maintains the long-lived observed events and how such a CEF is terminated or reversed into a normal Evershed flow; and which observables discriminate among the candidate origins — siphon-driven inflow, inflow driven by magnetoconvection, inflow associated with emerging sub-surface magnetic flux, and inflow inherited from coalescence of satellite flux with the spot.

Background

A sunspot consists of a dark umbra surrounded by a filamentary penumbra in which the magnetic field is strongly inclined. In the photosphere (the visible surface layer, conventionally characterized by the optical depth τ=1\tau = 1 level), penumbral filaments carry the Evershed flow, a nearly horizontal outflow of several km s−1^{-1} directed radially outward. Two mechanisms have historically been proposed to drive penumbral flows. In the siphon-flow picture, a penumbral filament behaves as a magnetic flux tube whose two endpoints (footpoints) anchor in regions of different magnetic field strength; the stronger field at one footpoint squeezes the gas (magnetic pressure balances total pressure), setting up a gas-pressure difference that drives a steady flow along the tube toward the stronger-field footpoint. In the magneto-convective picture, the penumbra is filled with elongated overturning convection cells in strongly inclined magnetic field, and the Evershed flow is the field-aligned component of this convection. Radiative three-dimensional magnetohydrodynamic (MHD) simulations — which solve the equations of compressible MHD including radiative energy transport and realistically sustain a penumbra — reproduce the normal Evershed flow (NEF) and identify overturning magnetoconvection as its dominant driver (Rempel 2011; Scharmer et al. 2008, whose idealized MHD simulations likewise showed overturning penumbral convection).

Rarely, well-developed penumbrae also display a counter-Evershed flow (CEF): a fast inflow directed from the middle or outer penumbra toward the umbra along otherwise normal-looking penumbral filaments, with line-of-sight speeds of ~1–5 km s−1^{-1} along the filaments, supersonic downflows exceeding 9 km s−1^{-1}, and extreme redshifts exceeding 20 km s−1^{-1} at the inner penumbral boundary in the exceptional event of Siu-Tapia et al. 2017, which lasted about two days. Earlier isolated reports include Kleint & Sainz Dalda 2013 and Louis et al. 2014. The observational determination of the driving force is blocked by a fundamental limitation: spectropolarimetric inversions — fits of polarized line profiles that infer height-dependent physical parameters — return properties on a log-optical-depth scale without a true geometrical height scale and cannot measure vertical (sub-photospheric) gradients, so the force balance along CEF-carrying filaments could not be evaluated.

Siu-Tapia et al. 2018 analyzed the driving forces of both flows in a 100-solar-hour radiative MHD sunspot simulation. The NEF is driven by overturning convection in the inclined field, while the CEFs that appear spontaneously in some penumbral sectors are well described as siphon flows: pressure gradients along filaments whose outer footpoints are not strengthened relative to the inner ones, with the radial Lorentz force (the magnetic part of the momentum equation's force density) also contributing to the inward acceleration. However, the simulated CEFs are highly variable and transient, persisting up to about 10 hours — much shorter than the multi-day observed events — and the mechanism by which a CEF is reversed back into an outflow was left unstudied (magnetic reconnection was suggested as a likely ingredient). The same paper notes that chromospheric-height inverse-Evershed-like inflows near the simulation's top boundary may be contaminated by the boundary treatment, and that a connection between the photospheric CEF and the chromospheric inverse Evershed flow (IEF; an inflow at chromospheric heights, for which Prasad et al. 2022 find a siphon-type driver) is compelling but unquantified. Subsequent surveys established that CEFs are common but usually short-lived: Castellanos Durán et al. 2021 found 384 CEFs in 97 active regions (83.5% of active regions host at least one), with a median lifetime of 10.6 hours and two populations depending on association with light bridges (dark, filamentary structures crossing the umbra). Castellanos Durán et al. 2023 followed three long-lived CEFs (24–50 hours): two formed as intrusions consistent with sub-surface magnetic flux emergence, one likely resulted from satellite-spot coalescence; field-strength enhancements at the umbra–penumbra boundary — the pressure-gradient source a siphon driver requires — were present for two of the three events but absent for the third, and the decay of two CEFs proceeded by expulsion through the penumbra at ~65–117 m s−1^{-1}, apparently related to the surrounding normal Evershed flow. No simulation since 2018 has produced a persistent (day-scale) photospheric CEF or identified a maintenance mechanism, and the formation-and-maintenance question is explicitly flagged as open in the most recent dedicated study.

Problem Statement

Determine the physical origin and lifecycle of photospheric counter-Evershed flows in mature sunspot penumbrae, giving one coherent account that (i) identifies the trigger conditions under which a CEF forms within an otherwise well-developed penumbra — distinguishing, at minimum, a siphon-type mechanism driven by gas-pressure gradients set up when the inner endpoint of a penumbral filament is magnetically strengthened, inflows driven by magnetoconvection in the inclined penumbral field, inflows associated with emerging sub-surface magnetic flux, and inflows inherited from coalescence of satellite flux with the spot; (ii) explains what maintains the long-lived CEFs over their observed 24–50 hour (exceptionally ~2-day) lifetimes and by what mechanism such a CEF is terminated or reversed into a normal Evershed outflow, given that siphon-driven CEFs arising spontaneously in realistic radiative MHD simulations persist only about 10 hours before reverting; and (iii) establishes, through forward modeling of polarized radiative transfer and height-resolved inversions, observable diagnostics that discriminate, at minimum, siphon-driven CEFs from inflows driven by magnetoconvection, inflows associated with emerging sub-surface magnetic flux, and inflows inherited from coalescence of satellite flux with the spot. These three components jointly serve the single objective of a physically complete, observationally testable account of the CEF lifecycle, and all three are required for a complete resolution; a submission that resolves only one or two of them is an explicitly labeled partial result, and any answer must also be consistent with, and not silently contradict, the observed lifetime distribution, flow velocities, and endpoint field strengths of the CEF population documented in the literature.

References

  1. Siu-Tapia, A. L., Rempel, M., Lagg, A., & Solanki, S. K. 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 (source paper)
  2. Siu-Tapia, A., Lagg, A., Solanki, S. K., van Noort, M., & Jurčák, J. 2017, 'Normal and counter Evershed flows in the photospheric penumbra of a sunspot', Astronomy & Astrophysics 607, A36, DOI 10.1051/0004-6361/201730647, https://doi.org/10.1051/0004-6361/201730647
  3. Louis, R. E., Beck, C., Mathew, S. K., & Venkatakrishnan, P. 2014, 'Anomalous flows in a sunspot penumbra', Astronomy & Astrophysics 570, A92, DOI 10.1051/0004-6361/201424112, https://doi.org/10.1051/0004-6361/201424112
  4. Kleint, L., & Sainz Dalda, A. 2013, 'Unusual filaments inside the umbra', The Astrophysical Journal 770, 74, DOI 10.1088/0004-637X/770/1/74, https://doi.org/10.1088/0004-637X/770/1/74
  5. Chen, F., Rempel, M., & Fan, Y. 2017, 'Emergence of Magnetic Flux Generated in a Solar Convective Dynamo. I. The Formation of Sunspots and Active Regions, and The Origin of Their Asymmetries', The Astrophysical Journal 846, 149, DOI 10.3847/1538-4357/aa85a0, https://doi.org/10.3847/1538-4357/aa85a0
  6. Rempel, M. 2011, 'Penumbral fine structure and driving mechanisms of large-scale flows in simulated sunspots', The Astrophysical Journal 729, 5, DOI 10.1088/0004-637X/729/1/5, https://doi.org/10.1088/0004-637X/729/1/5
  7. Scharmer, G. B., Nordlund, Å., & Heinemann, T. 2008, 'Convection and the Origin of Evershed Flows in Sunspot Penumbrae', The Astrophysical Journal 677, L149, DOI 10.1086/587982, https://doi.org/10.1086/587982
  8. Siu-Tapia, A., Lagg, A., van Noort, M., Rempel, M., & Solanki, S. K. 2019, 'Superstrong photospheric magnetic fields in sunspot penumbrae', Astronomy & Astrophysics 631, A99, DOI 10.1051/0004-6361/201834083, https://doi.org/10.1051/0004-6361/201834083
  9. Castellanos Durán, J. S., Lagg, A., & Solanki, S. K. 2021, 'How rare are counter Evershed flows?', Astronomy & Astrophysics 651, L1, DOI 10.1051/0004-6361/202141159, https://doi.org/10.1051/0004-6361/202141159
  10. Castellanos Durán, J. S., Korpi-Lagg, A., & Solanki, S. K. 2023, 'Expulsion of Counter Evershed Flows from Sunspot Penumbrae', The Astrophysical Journal 952, 162, DOI 10.3847/1538-4357/acdbc9, https://doi.org/10.3847/1538-4357/acdbc9
  11. Beck, C., & Choudhary, D. P. 2020, 'Temporal Evolution of the Inverse Evershed Flow', The Astrophysical Journal 891, 119, DOI 10.3847/1538-4357/ab75bd, https://doi.org/10.3847/1538-4357/ab75bd
  12. Prasad, A., Ranganathan, M., Beck, C., Choudhary, D. P., & Hu, Q. 2022, 'The magnetic topology of the inverse Evershed flow', Astronomy & Astrophysics 662, A25, DOI 10.1051/0004-6361/202142585, https://doi.org/10.1051/0004-6361/202142585
  13. Wang, Y., Li, C., Rao, S., Yu, H., Li, Z., & Fang, C. 2026, 'Revisiting Evershed Flows with CHASE Spectroscopic Observations', The Astrophysical Journal 999, 221, DOI 10.3847/1538-4357/ae3f9b, https://doi.org/10.3847/1538-4357/ae3f9b