The quiet Sun (QS) — the 90%+ of the solar surface outside active regions — carries most of the Sun's photospheric magnetic flux, split into network fields concentrated at supergranular boundaries and weaker internetwork fields inside supergranular cells. Whether internetwork fields are modulated by the 11-year solar cycle is the key observational discriminator between the two candidate origins of QS magnetism: a local small-scale (fluctuation) dynamo operating on convective turbulence, which predicts near-cycle-invariance, and turbulent tangling of the large-scale, cycle-dependent global dynamo field, which predicts cycle modulation. Twelve years of SDO/HMI magnetograms (Korpi-Lagg et al. 2022) find a statistically significant solar-cycle dependence of QS field strength at patch sizes of several supergranules but none at 1-degree (sub-supergranular) patches, a scale selection that includes patches lying entirely in the internetwork, where the root-mean-square field sits at the instrument's noise floor (∼5\sim 5–66 G). The open problem is to determine, with spatial resolution and magnetic sensitivity demonstrably beyond HMI's, whether internetwork fields genuinely lack cycle modulation — and thereby constrain how much of the quiet-Sun field is fed by the local dynamo versus the global one. The literature through 2026 remains in active conflict on exactly this point, and no cycle-spanning internetwork measurement at DKIST-class sensitivity has yet been published.

Background

The solar surface outside sunspots and active regions — the quiet Sun — is covered by ubiquitous weak magnetic fields. They are organized into the network (field concentrations aggregated to the boundaries of supergranules, the ~30–35 Mm-scale convection cells seen as Doppler velocity patterns) and the internetwork (weaker, more transient fields inside the cells). Two mechanisms are debated as the source of this magnetism. First, a local small-scale dynamo (also called fluctuation dynamo): convective turbulence with rotation stretches and amplifies field locally, independent of the 11-year cycle; theoretical work long doubted it could operate in the solar photosphere, where the magnetic Prandtl number (the ratio of magnetic to viscous diffusivity) is small, but numerical simulations now sustain such dynamos approaching solar conditions (Warnecke et al. 2016–2023; Rempel et al. 2023). Second, tangling of the large-scale global-dynamo field: convective turbulence braids the Sun's cycle-dependent poloidal field into small-scale structures, which would imprint a solar-cycle modulation on QS field strength. Because a small-scale dynamo is cycle-independent while tangling inherits the cycle from the global field, the presence or absence of cycle variation of internetwork fields is the classic observational discriminator.

Observational studies have split for over a decade. Hinode (the Solar Optical Telescope Spectropolarimeter on the Japanese Hinode satellite) studies reported internetwork fields independent of the cycle (Jin & Wang 2015a for the vertical inter-network field, 2015b for the intra-network horizontal field; Buehler et al. 2013, whose analysis explicitly supported a local dynamo). Others found weak but real dependence (Lites et al. 2014 for weak internetwork flux; Meunier 2018; Faurobert & Ricort 2021, who found internetwork fluctuation power at low/mid latitudes cycle-independent below 0.5 arcsec but with a global-dynamo contribution at larger scales and high latitudes). Into this debate, Korpi-Lagg, Korpi-Lagg, Olspert & Truong (A&A 665, A141, 2022) analyzed 12 years of full-disk line-of-sight magnetograms from the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory, using an automated pipeline that selected the most magnetically quiet patches under stringent spatial and temporal quietness criteria. They measured the root-mean-square field strength BrmsB_{\mathrm{rms}} (the spatial and temporal rms of the line-of-sight field, in gauss) in two patch sizes: 15-degree patches containing several supergranules (network plus internetwork) and 1-degree patches (about 12 Mm, smaller than one supergranule, some lying entirely in the internetwork). Result: the 15-degree patches show a clear, statistically significant cycle dependence (BrmsB_{\mathrm{rms}} peaking about half a year after the cycle-24 maximum), while the 1-degree patches show none. The internetwork BrmsB_{\mathrm{rms}} is only ~6 G (about 3×10^16 Mx per HMI pixel), dropping to ~5 G or below after an HMI sensitivity improvement in April 2016 — i.e., the quantity being tested for a cycle trend sits at the instrument's noise floor. The authors state the disjunction explicitly: either the internetwork fields are generated by the small-scale dynamo alone, or the instrument's limited spatial resolution (~0.5 arcsec) and magnetic sensitivity prevent any variation from being seen. The same study found the energy of the f-mode (the solar surface gravity oscillation mode, a global helioseismic mode trapped just below the photosphere) at supergranular scale varying out of phase with the sunspot cycle by several years, which they read as evidence of tangling-driven replenishment by the poloidal large-scale field — sharpening the internetwork question as the unresolved end of the picture.

Problem Statement

Determine observationally whether quiet-Sun internetwork (inside-cell, network-free) magnetic fields are modulated by the solar cycle — that is, whether the absence of significant cycle dependence found at 1-degree patch scale in 12 years of SDO/HMI magnetograms (Brms≈5B_{\mathrm{rms}}\approx 5–66 G at the instrument noise floor) reflects genuine physical invariance of these fields or the limited spatial resolution (~0.5 arcsec) and magnetic sensitivity of HMI. An answer must rest on measurements of internetwork field strength (or flux density) at a stated spatial resolution (in arcsec) and per-pixel magnetic sensitivity (in G) that demonstrably exceed HMI's (~0.5 arcsec; noise floor ~5 G), sampled across solar-cycle epochs, and must either (i) detect a statistically significant cycle modulation with quantified amplitude and phase, or (ii) establish a quantified upper bound, with a stated confidence level, on any such modulation at internetwork (inside-cell) scales — a bound too loose to separate genuine internetwork invariance from an instrumental sensitivity limit does not resolve the question. Either outcome must then be used to constrain the partition between the two candidate origins: a local small-scale (fluctuation) dynamo, which predicts near-invariance, and turbulent tangling of the cycle-dependent large-scale global-dynamo field, which predicts modulation; a genuine null result tightens the bound on the tangling contribution, while a detection quantifies it.

References

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