When sunspot penumbral fine-scale structures disappear, does the Evershed flow — the radially outward gas flow that channels along penumbral filaments — shut off throughout the vertical column, or does it persist in layers beneath the observed photosphere? Kubo, Ichimoto, Lites and Shine (2011) traced the temporal relation between the disappearance of more-horizontal fine-scale magnetic structures and the Evershed flow in Hinode spectropolarimetry, and found that small redshifts appear along dark filament cores as the horizontal fields vanish, but could not determine whether these redshifts signal true downward submergence of the magnetic field lines or plasma draining along field lines that merely reorient. This problem asks for the vertical (in particular subphotospheric) stratification of the velocity and magnetic-field vector in individual penumbral fine-scale structures during their formation and disappearance, and for a physical disambiguation of the disappearance-phase redshifts. Fifteen years of follow-up work has mapped the photospheric and chromospheric height dependence of the Evershed effect, constrained the thermal structure down to roughly 70–80 km below the visible surface, produced radiative magnetohydrodynamic simulations predicting a near-surface Evershed flow distinct from deeper overturning outflows, and observed penumbral formation and decay at progressively higher cadence — but no study has measured the subphotospheric flow/field stratification of individual filaments or directly resolved the redshift degeneracy, so the problem remains open.

Background

A sunspot consists of a dark umbra surrounded by a penumbra of radially elongated bright and dark filaments. The penumbra hosts the Evershed effect: a predominantly horizontal, radially outward flow of gas of order a few km/s that channels along the more inclined magnetic fields of the dark filament cores, discovered spectroscopically in 1909. Modern high-resolution observations show the penumbra has an interlocking-comb magnetic structure (also called the uncombed or fluted penumbra): nearly vertical magnetic spines alternate with more horizontal intra-spine fields that carry the Evershed flow and associated downflows, especially in the outer penumbra where the flow returns to the solar interior below the visible surface. Spectropolarimetric inversions — fitting the four Stokes parameters (the quantities describing the intensity and polarization state of light) of polarized line profiles to infer temperature, vector magnetic field, and velocity as functions of optical depth — are the standard diagnostic; the visible solar surface is conventionally defined as the geometric height where the continuum optical depth τ=1\tau=1, and photospheric spectral lines sample a range of heights around it.

Kubo, Ichimoto, Lites and Shine (2011, ApJ 731, 84) used data from the spectropolarimeter of the Japanese Hinode solar-orbiting observatory to study the temporal relation between the disappearance of penumbral fine-scale structure and the Evershed flow. They tracked individual more-horizontal magnetic structures as they vanished and found the Evershed flow weakens in step with the disappearance, while small redshifts (line shifts toward longer wavelength, indicating motion toward the observer's line of sight, i.e. downward at disk center) appear along dark filament cores as the horizontal fields disappear. Three issues they explicitly left open define this problem. First, the vertical stratification of velocity and magnetic-field vector within the fine-scale structures is undetermined: the observations sample essentially one photospheric layer, so it is unknown whether the Evershed flow ceases throughout the vertical column or only in the observed layer while persisting in deeper photospheric layers or below the photosphere, and how any such deeper flow couples to the convection and heating that keep penumbral filaments bright. Second, the small redshifts are diagnostically ambiguous: they could equally record true downward motion (submergence) of the magnetic structure or a flow along field lines that are reorienting from horizontal toward vertical — a degeneracy the single-height data cannot break. Third, resolving the disappearance process at all requires higher-cadence vector-magnetic and Doppler measurements with diagnostics sensitive to several atmospheric heights.

The relevant subsequent literature falls into three strands. Radiative magnetohydrodynamic (MHD) simulations of whole sunspots (Rempel 2011, 2015; Siu-Tapia et al. 2018) now predict a definite vertical structure: the filament-scale Evershed flow is driven by a horizontal Lorentz force concentrated in narrow boundary layers just beneath τ=1\tau=1, peaks near τ=1\tau=1, and falls off rapidly with height, while the mass flux in deeper layers is carried by a separate, larger-scale radially overturning convection system connected to the moat flow, the persistent radial plasma outflow that surrounds mature sunspots. Observationally, depth-dependent inversions and lines forming at different heights have constrained the flow stratification within and slightly above the photosphere (Franz 2011; Tiwari et al. 2015; Khomenko et al. 2015; Murabito et al. 2018), and near-infrared lines formed in deeper layers reach roughly 70–80 km below the visible surface (Borrero et al. 2017). Studies of penumbral formation and decay (Murabito et al. 2016, 2021; Jurčák et al. 2014; Verma et al. 2018; García-Rivas et al. 2024) have established the flow-field evolution on hours-to-days timescales, including evidence that horizontal fields and Evershed-like flows can outlive the visible disappearance of penumbral sectors and that whole filaments can submerge. None of these, however, measures the subphotospheric velocity and vector-field stratification of individual filaments, and none disambiguates the disappearance-phase redshifts.

Problem Statement

Determine the vertical stratification of the velocity field and the vector magnetic field in individual penumbral fine-scale structures (filaments) during their disappearance, and symmetrically during their formation. Specifically: (1) establish whether the Evershed flow associated with a disappearing fine-scale structure ceases throughout the vertical column or only in the observed photospheric layer while persisting in deeper photospheric or subphotospheric layers, and quantify how any such deeper-layer flow relates to the convection and heating of the observed layer; and (2) determine the physical origin of the small redshifts that appear along dark filament cores as the more-horizontal magnetic fields disappear — true downward motion (submergence) of the magnetic structure versus plasma flow along field lines that are reorienting — which requires multi-height, high-cadence vector-magnetic and Doppler measurements capable of breaking this diagnostic degeneracy. These two sub-questions define the completion criterion and apply symmetrically to the formation phase — for a forming fine-scale structure, whether the Evershed flow appears throughout the vertical column or only in the observed photospheric layer, and the physical origin of the line shifts that accompany the appearance of the more-horizontal magnetic fields — so that resolving them for both phases, and not the disappearance phase alone, constitutes a resolution. The target is a height-resolved determination of flow and field through and below the photospheric layer for individual fine-scale structures at formation and decay, rather than a spatially or temporally averaged photospheric characterization of a mature penumbra.

References

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