Chromospheric magnetograms from SOLIS/VSM showed that the surface density of magnetic flux elements in the Sun's polar caps, after correction for the shrinking area of latitude zones, is roughly flat up to about 70 degrees and declines significantly over the final ~20 degrees toward the pole. The authors suggested that the mechanisms of poleward flux transport 'increasingly lose strength' there, while noting that the meridional flow could not be measured beyond 45-50 degrees latitude. Later work confirmed the depletion with Hinode's high-resolution polar vector magnetograms across cycle 24, but its physical cause is still undecided: an equatorward counter-cell meridional flow (reproduced by surface flux transport simulations with an amplitude of about 3 m/s), enhanced cancellation or diffusive loss of flux elements, and residual projection/visibility selection bias all remain live alternatives. Ecliptic magnetic-feature tracking now measures the surface flow pole to pole and reports intermittent equatorward counter-cells extending from the poles down to about 60 degrees latitude, but foreshortening makes these polar measurements most uncertain, and the first out-of-ecliptic Solar Orbiter observations of 2025 report the polar flux distribution, its viewing-angle dependence, and poleward network migration above 60 degrees without yet settling the near-polar flow profile. The open problem is to determine the near-polar meridional-flow profile and quantitatively attribute the polar-cap flux depletion to flow structure, flux loss, and observational bias.

Background

The Sun's large-scale photospheric magnetic field is redistributed by three transport mechanisms: differential rotation (latitude-dependent rotation rate), supergranular diffusion (the random walk of magnetic elements driven by the convective pattern of supergranulation), and the meridional flow — a slow, axisymmetric north-south plasma flow of roughly 10 m/s that carries magnetic flux from the activity belts toward the poles. In surface flux transport (SFT) models, these ingredients advect and diffuse the flux of decaying active regions so that the polar caps accumulate flux of one polarity, which is then reversed each ~11-year activity cycle; the strength of the polar field is a key predictor of the next cycle and of the heliospheric magnetic field, so the accuracy of the flow profile used at high latitude matters directly. Raouafi, Harvey & Henney (2007) analyzed line-of-sight chromospheric (Ca II 854.2 nm) magnetograms from SOLIS/VSM (the Vector SpectroMagnetograph of the Synoptic Optical Long-term Investigations of the Sun project), applied a radial (center-to-limb) correction, selected flux elements with a top-hat operator, normalized their counts by the observable area of each latitude zone, and found the element density flat up to about 65-70 degrees and significantly declining beyond, with the decline more pronounced for larger elements. They interpreted this as evidence that poleward transport weakens within the last ~20 degrees of latitude, while stressing that direct flow measurements did not extend beyond 45-50 degrees. Two complications frame the question. First, polar observations from the ecliptic plane suffer foreshortening: the effective spatial resolution in heliographic coordinates degrades sharply toward the limb (the Sun's rotation axis is tilted to the line of sight by at most ~7.25 degrees over the year), so a poleward decrease in identified elements could partly be a visibility/selection effect, as Petrie (2015) emphasized. Second, the fate of transported flux is set by more than advection: opposite-polarity elements cancel and diffuse, so a depleted density near the pole could reflect flux loss rather than a weaker flow. Later observations sharpened the phenomenology: Hinode's Spectro-Polarimeter provided high-resolution (about 0.3 arcsec) vector magnetograms of the polar caps from 2012 to 2021, and Yang et al. (2024) found the radial flux density declining from 70 degrees to the pole in both caps through most of cycle 24, confirming the depletion is persistent and not an artifact of one instrument or one cycle phase. On the flow side, magnetic-feature tracking extended measured surface meridional flow well beyond 60 degrees (Hathaway & Rightmire 2010) and eventually to pole-to-pole profiles in which the high-latitude flow drops to zero above about 80 degrees, with intermittent equatorward 'counter-cells' reaching from the poles down to about 60 degrees (Hathaway et al. 2022), while helioseismic inversions of the interior flow explicitly do not constrain latitudes above 60 degrees (Zhao et al. 2013). The remaining gap is therefore not the absence of any flow measurement inside the polar cap, but the reliability of the ecliptic-view tracking signal there — the same tracking study notes that foreshortening makes the polar measurements most uncertain — and its disconnection from the measured flux-element depletion; only out-of-ecliptic observations, now beginning with Solar Orbiter, can image the caps directly (Chitta et al. 2025; Calchetti et al. 2025).

Problem Statement

Determine the physical origin of the observed poleward decline of magnetic flux-element density within the final ~20 degrees of latitude of the Sun's polar caps. This requires, jointly: (1) establishing the surface meridional-flow profile at heliographic latitudes above about 70 degrees with a reliability sufficient to support attribution — reconciling the intermittent equatorward counter-cells reported by ecliptic magnetic-feature tracking with the persistent ~3 m/s counter-cell that surface flux transport simulations of the Hinode polar fields require, and determining the amplitude, latitudinal extent, and dependence on cycle phase of any near-polar counter-cell; and (2) quantitatively attributing the depletion to its candidate causes — weakened poleward advection (including a counter-cell), enhanced cancellation or diffusive loss of transported flux, and residual projection/visibility selection bias in the measurements — with quantified relative contributions. An accepted answer must reconcile the measured flux-element latitude statistics (SOLIS/VSM chromospheric and Hinode photospheric, across different cycle phases) with the inferred flow profile and demonstrate that the attribution is not degenerate under realistic variations of supergranular diffusivity, cancellation, and instrumental visibility. This updates the open problem stated by Raouafi, Harvey & Henney (2007): the mechanisms of poleward flux transport appear to lose strength near the poles, the meridional flow there could not be measured, and the physical cause was left unidentified.

References

  1. N.-E. Raouafi, J. W. Harvey, C. J. Henney, 'Latitude Distribution of Polar Magnetic Flux in the Chromosphere Near Solar Minimum', The Astrophysical Journal 669, 636-641 (2007). DOI: 10.1086/521354, https://doi.org/10.1086/521354 (related conference paper arXiv:0801.0260, posted under the title 'On the Latitude Distribution of the Polar Magnetic Flux as Observed by SOLIS-VSM')
  2. J. Jiang, R. Cameron, D. Schmitt, M. Schuessler, 'Countercell meridional flow and latitudinal distribution of the solar polar magnetic field', The Astrophysical Journal 693, L96-L99 (2009). DOI: 10.1088/0004-637X/693/2/L96, https://doi.org/10.1088/0004-637X/693/2/L96
  3. D. H. Hathaway, L. Rightmire, 'Variations in the Sun's Meridional Flow over a Solar Cycle', Science 327, 1350-1352 (2010). DOI: 10.1126/science.1181990, https://doi.org/10.1126/science.1181990
  4. J. Zhao, R. S. Bogart, A. G. Kosovichev, T. L. Duvall Jr., T. Hartlep, 'Detection of Equatorward Meridional Flow and Evidence of Double-Cell Meridional Circulation inside the Sun', The Astrophysical Journal Letters 774, L29 (2013). DOI: 10.1088/2041-8205/774/2/L29, https://doi.org/10.1088/2041-8205/774/2/L29
  5. G. J. D. Petrie, K. Petrovay, K. Schatten, 'Solar Polar Fields and the 22-Year Activity Cycle: Observations and Models', Space Science Reviews 186, 325-357 (2014). DOI: 10.1007/s11214-014-0064-4, https://doi.org/10.1007/s11214-014-0064-4
  6. G. J. D. Petrie, 'Solar Magnetism in the Polar Regions', Living Reviews in Solar Physics 12, 5 (2015). DOI: 10.1007/LRSP-2015-5, https://doi.org/10.1007/LRSP-2015-5
  7. D. H. Hathaway, L. A. Upton, S. S. Mahajan, 'Variations in differential rotation and meridional flow within the Sun's surface shear layer 1996-2022', Frontiers in Astronomy and Space Sciences 9, 1007290 (2022). DOI: 10.3389/fspas.2022.1007290, https://doi.org/10.3389/fspas.2022.1007290 (preprint arXiv:2212.10619)
  8. S. Yang, J. Jiang, Z. Wang, Y. Hou, C. Jin, Q. Song, Y. Luo, T. Li, J. Zhang, Y. Zhang, G. Zhou, Y. Deng, J. Wang, 'Meridional Flow in the Solar Polar Caps Revealed by Magnetic Field Observation and Simulation', The Astrophysical Journal 970, 183 (2024). DOI: 10.3847/1538-4357/ad61e2, https://doi.org/10.3847/1538-4357/ad61e2 (preprint arXiv:2407.18576)
  9. S. Yang, C. Jin, Q. Song, Y. Zhang, Y. Li, Y. Hou, T. Li, G. Zhou, Y. Deng, J. Wang, 'Variations of the Vector Magnetic Structures in the Solar Polar Regions Observed by Hinode', The Astrophysical Journal 993, 9 (2025). DOI: 10.3847/1538-4357/ae0b61, https://doi.org/10.3847/1538-4357/ae0b61
  10. L. P. Chitta, D. Calchetti, J. Hirzberger, G. Valori, E. R. Priest, S. K. Solanki, D. Berghmans, C. Verbeeck, E. Kraaikamp, K. Albert, T. Appourchaux, F. J. Bailen, L. R. Bellot Rubio, J. Blanco Rodriguez, A. Feller, A. Gandorfer, L. Gizon, A. Lagg, A. Moreno Vacas, D. Orozco Suarez, J. Schou, U. Schuhle, J. Sinjan, H. Strecker, R. Volkmer, J. Woch, X. Li, T. Oba, A. Ulyanov, 'Supergranulation and Poleward Migration of the Magnetic Field at High Latitudes of the Sun', The Astrophysical Journal Letters 993, L45 (2025). DOI: 10.3847/2041-8213/ae10a3, https://doi.org/10.3847/2041-8213/ae10a3
  11. D. Calchetti, S. K. Solanki, J. Hirzberger, G. Valori, L. P. Chitta, J. Blanco Rodriguez, A. Giunta, T. Grundy, K. Albert, T. Appourchaux, F. J. Bailen, L. R. Bellot Rubio, A. Feller, A. Gandorfer, L. Gizon, A. Korpi-Lagg, X. Li, A. Moreno Vacas, T. Oba, D. Orozco Suarez, J. Schou, U. Schuhle, J. Sinjan, H. Strecker, J. C. del Toro Iniesta, A. Ulyanov, R. Volkmer, J. Woch, 'The First out-of-Ecliptic Observations of the Polar Magnetic Field of the Sun', The Astrophysical Journal Letters 995, L60 (2025). DOI: 10.3847/2041-8213/ae2850, https://doi.org/10.3847/2041-8213/ae2850 (preprint arXiv:2512.03611)