Lamb, Howard, DeForest, Parnell and Welsch (2013) tracked the deaths of nearly 20,000 magnetic features in Hinode/SOT/NFI quiet-Sun magnetograms and found that most removal of visible magnetic flux occurs by dispersal to scales too small and too weak to detect, that the partial feature lifetime attributable to bipolar flux cancellation is about 22 h (roughly three times slower than previous feature-based flux turnover estimates near 8 h), and that the ensemble dispersal is not consistent with simple two-dimensional diffusion. They concluded that processes on spatial scales smaller than those visible to Hinode dominate flux emergence and cancellation, and therefore also the quantity of magnetic flux threading the photosphere. The open problem is to determine how much unsigned magnetic flux threads the quiet-Sun photosphere below current detectability, and to close the flux budget — sub-resolution emergence, cancellation, and cross-scale dispersal — well enough to fix the true, resolution-independent flux turnover time. Later work has sharpened individual pieces (superdiffusive — faster-than-diffusive — dispersal with exponent near 1.5; internetwork appearance and disappearance rates; hidden-flux diagnostics ranging from a few to about 100 G), but the amplitude of the sub-resolution flux remains contested across diagnostics and the mechanism by which flux disappears from the observable surface is, per a 2019 review, still not understood.

Background

The quiet Sun — the portion of the solar surface outside active regions, covering more than 99% of the visible disk over the solar cycle — is threaded by a patchwork of small magnetic fields organized into the magnetic network (field concentrations accumulated along the boundaries of large convective cells called supergranules) and the weaker, mixed-polarity internetwork fields inside those cells. These fields are observed with magnetographs, instruments that map the line-of-sight magnetic field using the Zeeman effect; the Narrowband Filter Imager (NFI) aboard the Hinode satellite's Solar Optical Telescope obtained high-resolution filtergrams in one wing of the Na I D 5896 Å line from which such magnetograms are derived. Discrete concentrations, or magnetic features, are identified and followed in time by feature-tracking codes such as SWAMIS, developed and benchmarked by DeForest, Hagenaar, Lamb, Parnell and Welsch (2007); the apparent birth and death of these features are the measurable proxies for flux emergence into and removal from the photosphere.

Flux cancellation is the collision and mutual disappearance of opposite-polarity features, produced by reconnection or by the submergence or rise of magnetic loops through the photosphere; it is the only observed process that truly removes flux from the surface. Hagenaar, Schrijver and Title (2003) used feature-creation rates in magnetograms from the Michelson Doppler Imager (MDI) aboard the Solar and Heliospheric Observatory (SOHO) to estimate a quiet-Sun flux turnover time (the time for the photospheric flux to be entirely replaced) of about 8 h at solar minimum. Parnell, DeForest, Hagenaar, Johnston, Lamb and Welsch (2009) showed that the distribution of fluxes contained in magnetic features follows a power law over more than five decades, so that at any achievable resolution the smallest detectable features dominate the flux budget — implying that much of the flux resides below the detection threshold. The earlier papers of the Solar Magnetic Tracking series then showed that most apparent new features are born not by bipolar emergence from the interior but by coalescence of previously undetected flux into resolvable concentrations (Lamb et al. 2008), and that Hinode does not resolve the fundamental scale of flux emergence (Lamb et al. 2010).

In the fourth paper of the series, Lamb, Howard, DeForest, Parnell and Welsch (2013) classified the deaths of nearly 20,000 tracked features. Of the deaths that remove visible flux, the vast majority are Disappearances in which the feature's flux is shredded and advected horizontally until it falls below the detection threshold, rather than Cancellations; the ensemble average of the disappearing features is not consistent with a model of planar diffusion, suggesting that the dispersal is constrained by the evolving photospheric velocity field (granulation is the roughly 1000-km-scale convection pattern visible on the solar surface; mesogranulation is an intermediate organizational scale of roughly 5,000 km). The total enclosed flux nonetheless drops by 30–50% in the minutes after death, for which the authors offer two candidate explanations: physical horizontal advection on very small scales, or non-linearity of single line-wing NFI magnetograms (a decrease in the average field within a pixel not producing a proportional decrease in the reported signal). Introducing the concept of a partial lifetime — the lifetime attributable to one death type — they found a partial lifetime due to Cancellation of 22 h, about three times slower than the 8 h turnover estimates, and concluded that sub-resolution processes dominate the flux budget and hence the true turnover time, with direct consequences for the small-scale magnetic energy available to nanoflare coronal-heating models (heating of the solar corona by a very large number of tiny, frequent magnetic energy-release events) and for the turbulent-diffusion input to flux-transport dynamo models (solar-cycle models in which surface flows transport magnetic flux poleward).

Estimating the sub-resolution, or hidden, flux requires indirect diagnostics, because opposite magnetic polarities inside one resolution element cancel their circular-polarization (Stokes V) signals, hiding unsigned flux from Zeeman magnetographs. Hanle-effect depolarization — the modification of scattering polarization in spectral lines by weak turbulent fields — was used by Trujillo Bueno, Shchukina and Asensio Ramos (2004) to argue for a substantial hidden magnetic energy corresponding to turbulent fields near 100 G; Lites et al. (2007) found pervasive horizontal (transverse to the line of sight) flux in Hinode spectropolarimetry; and magnetohydrodynamic simulations with the MURaM code (a radiative magnetohydrodynamic code for solar surface convection; Pietarila Graham, Danilovic and Schüssler 2009; Danilovic, Schüssler and Solanki 2010) showed that weak, tangled, largely unresolved fields can reproduce the observed polarization signals, implying several times more unsigned flux than is directly detected. Stenflo (2011) framed the same problem in terms of collapsed (strong, concentrated) versus uncollapsed (weak, tangled) flux components. These diagnostics still disagree on the hidden-flux amplitude by roughly an order of magnitude, which is the central obstacle to closing the flux budget.

Problem Statement

Determine how much unsigned magnetic flux threads the quiet-Sun photosphere at spatial scales below the detectability of current imaging magnetographs (for reference, Lamb et al. 2013 adopted detection thresholds of 18 and 24 G at the 0.16 arcsec pixel scale of Hinode/SOT/NFI magnetograms), and close the photospheric flux budget — sub-resolution emergence, cancellation, and cross-scale dispersal — so as to fix the true, resolution-independent flux turnover time of the quiet-Sun photospheric magnetic field, as posed by the conclusions of Lamb et al. (2013).

The open aspects of this closure question identified by Lamb et al. (2013) are the following, each an independently refutable sub-claim of the single closure target: (i) quantifying the sub-resolution unsigned (hidden) flux and its distribution across spatial and flux scales, referenced to explicit detection thresholds so that the amount of hidden flux below any given threshold is determined; (ii) quantifying the rates at which flux is injected and removed at sub-observable scales, so that feature-based rates — including the 22 h partial lifetime due to Cancellation, which omits cancellation occurring entirely below the detection threshold — can be corrected into a true turnover time; (iii) determining how the dispersal of flux across the observability threshold departs from two-dimensional diffusion, and whether the observed non-diffusive ensemble signature reflects dispersal constrained by the evolving photospheric velocity field or artifacts of the ensemble and motion-correction analysis; and (iv) determining how much of the apparent loss of enclosed flux following feature death is physical (shredding and horizontal advection to unresolved scales) rather than instrumental (non-linearity of single line-wing filter magnetograms and other measurement biases), the two candidate explanations Lamb et al. (2013) weighed without deciding between them. Resolving any one of these aspects alone does not close the budget: the completion target is a flux budget — sub-resolution emergence, cancellation, and cross-scale dispersal — closed well enough to fix the true, resolution-independent flux turnover time, so partial resolution of the listed aspects leaves the task open.

References

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