Solar Orbiter's Extreme Ultraviolet Imager has revealed ubiquitous small-scale impulsive brightenings in the quiet Sun (magnetically quiet regions outside sunspots and active regions), nicknamed "campfires" or picoflares with thermal energies of roughly 102010^{20}–102410^{24} erg, below the classical nanoflare regime. Whether these events supply a dominant share of the quiet-Sun coronal heating flux hinges on the slope α\alpha of the event frequency–energy distribution dN/dE∝E−αdN/dE \propto E^{-\alpha} and its behavior below current detection thresholds: by the Hudson criterion, α>2\alpha > 2 makes the energy budget dominated by the smallest, unresolved events, while α<2\alpha < 2 leaves larger events dominant. The problem is to determine this distribution — or a demonstrated departure from a single power law — with systematics controlled well enough to decide whether the event-integrated energy flux meets the quiet-Sun heating requirement, and to establish observationally that the events dissipate energy in the corona rather than in the cooler layers where many of them apparently occur.

Background

The solar corona — the Sun's outer atmosphere at a temperature above one million kelvin — is heated to that state by mechanisms that remain incompletely identified; this is the coronal heating problem. For the quiet Sun (regions outside sunspots and active regions), the required energy flux is approximately 3×1053\times10^{5} erg s−1 cm−2\mathrm{erg\,s^{-1}\,cm^{-2}} (Withbroe & Noyes 1977). Parker (1988) proposed that the corona is heated by a very large number of tiny impulsive energy releases called nanoflares, driven by magnetic reconnection — the reconfiguration of stressed magnetic fields that converts magnetic energy into heat and particle kinetic energy. A central quantitative question for any impulsive heating picture was formulated by Hudson (1991): if events follow a power-law frequency distribution dN/dE∝E−αdN/dE \propto E^{-\alpha}, then for α>2\alpha > 2 the total energy is dominated by the smallest events and extrapolating to unobservably small energies can supply the entire heating budget, whereas for α≤2\alpha \leq 2 the observable larger events dominate and small events cannot power the corona. Measured slopes of flare and microflare distributions in the EUV and X-ray range historically straddle the critical value α≈2\alpha \approx 2, so the question has never been settled by statistics of detectable events alone.

Solar Orbiter, an ESA-led mission launched in 2020, carries the Extreme Ultraviolet Imager (EUI), whose High Resolution EUV channel (HRIEUV_\mathrm{EUV}, imaging the 17.4 nm passband) observed the quiet Sun from roughly 0.5 AU (half the mean Sun–Earth distance) with a spatial resolution near 200 km per pixel. EUI revealed ubiquitous small, brief, loop-shaped brightenings nicknamed "campfires" (Berghmans et al. 2021), and stereoscopic triangulation established that they occur at heights of roughly 1–5 Mm above the photosphere (1 Mm = 1000 km), many near or below the transition region — the thin interface layer where the solar atmosphere rises from the roughly 10410^{4} K chromosphere (the cooler layer beneath the corona) to million-kelvin coronal temperatures (Zhukov et al. 2021). Differential emission measure (DEM) analysis — an inversion of multi-passband EUV images yielding the distribution of plasma emission measure over temperature — allows estimation of each event's thermal energy. Applying this to over 12,000 events, Podladchikova et al. (2025, arXiv:2510.10340) derived energies spanning 102010^{20}–102410^{24} erg, naming this range "picoflares" because it lies below the traditional nanoflare energy scale, and found power-law energy distributions with slopes α=2.32\alpha = 2.32 (for events above a 5σ5\sigma detection threshold) and α=2.82\alpha = 2.82 (above 3σ3\sigma), while concluding conservatively that the detected events supply only about 1% of the quiet-Sun heating power. The companion interpretive Letter that motivates this problem (Podladchikova 2025, arXiv:2510.22822v1) argues that, with α>2\alpha > 2, the extrapolated population of smaller, undetected events would dominate the heating budget — requiring an unobserved minimum event energy of about 1.25×10181.25\times10^{18} erg to sustain the quiet-Sun heating flux — and proposes that two mechanisms operate: fast tearing-mode reconnection (fragmentation of current sheets, i.e., thin layers of intense electric current, into magnetic islands) at loop tops, and anomalous resistivity (collisionless wave–particle dissipation that enhances resistivity by orders of magnitude when the current density exceeds the threshold jcrit=neecsj_\mathrm{crit} = n_e e c_s, set by the electron density, electron charge, and ion sound speed) at loop footpoints. The Letter itself stresses that the dominance conclusion is sensitive to the precise slope: a shallower slope such as α=1.9\alpha = 1.9 would shift energy dominance to larger nanoflares.

Adjacent results frame what remains open. Purkhart & Veronig (2022) analyzed nanoflares of 102410^{24}–102910^{29} erg over a full solar cycle with SDO/AIA (NASA's Solar Dynamics Observatory satellite and its Atmospheric Imaging Assembly full-disk extreme-ultraviolet imager) and found α=2.28±0.03\alpha = 2.28 \pm 0.03, but a mean energy flux an order of magnitude below the quiet-Sun requirement — so at directly detectable energies the observed events do not suffice, and the entire budget question rests on the unmeasured low-energy regime. Narang et al. (2025) observed the smallest and shortest-lived quiet-Sun EUV brightenings to date at 0.293 AU (105 km per pixel, 3 s cadence), finding power-law distributions of event sizes and lifetimes continuing down to the instrumental limits, with about 3600 brightenings appearing per second over the whole Sun — but they explicitly deferred the thermal-energy analysis of these smallest events, so the energy-distribution slope at lowest energies remains unmeasured. A dedicated review (Parenti 2026) concludes that the role of these brightenings in coronal heating is unresolved, noting that many are probably cooler than 1 MK (one million kelvin) and that their appearance rate appears insufficient to compensate coronal radiative losses — raising the further question of whether these events heat the corona at all, or mostly mark energy release in the chromosphere and transition region below it.

Problem Statement

Determine whether small-scale impulsive extreme-ultraviolet brightenings in the quiet Sun (picoflares, with thermal energies of roughly 102010^{20}–102410^{24} erg) supply a dominant fraction of the quiet-Sun coronal heating flux. This requires, as one jointly supporting objective: (1) measuring the frequency–energy distribution dN/dE∝E−αdN/dE \propto E^{-\alpha} of quiet-Sun transient EUV brightenings down to and below 102110^{21} erg, with detection-completeness, differential-emission-measure, volume-modeling, and background-subtraction systematics controlled well enough to decide on which side of the Hudson criterion α=2\alpha = 2 the true low-energy distribution lies, or else demonstrating a departure from a single power law (a physical low-energy cutoff or flattening) and determining the corresponding minimum event energy; (2) using that distribution, computing the event-integrated energy flux, including the unresolved low-energy extrapolation, and comparing it with the quiet-Sun heating requirement of approximately 3×1053\times10^{5} erg s−1 cm−2\mathrm{erg\,s^{-1}\,cm^{-2}}; and (3) establishing observationally (through event heights, plasma temperatures, and dissipation-scale or spectroscopic signatures) whether the energy of these events is dissipated in the corona itself — consistent with reconnection in coronal current sheets, anomalous-resistivity dissipation at loop footpoints, or both — rather than being emitted predominantly from chromospheric and transition-region plasma, so that the inferred budget is a genuine coronal heating budget. An answer consists of the measured distribution with quantified uncertainties, the resulting energy-flux comparison, and the atmospheric-location evidence, sufficient for a specialist to conclude that picoflares dominate, contribute partially, or cannot power quiet-Sun coronal heating.

References

  1. Podladchikova, O. 2025, "The Missing Mechanism: Picoflare Heating in the Solar Corona", arXiv:2510.22822 (v1; v3, 2026, retitled "On the Short Dissipation Scales and Current-Sheet Properties of Low-Coronal EUV Brightenings"), DOI 10.48550/arXiv.2510.22822, https://arxiv.org/abs/2510.22822
  2. Podladchikova, O.; Warmuth, A.; Harra, L.; Dolla, L.; Verbeeck, C.; Mierla, M.; Rodriguez, L.; Parenti, S.; Georgoulis, M. K.; Hofmeister, S. J.; Engler, N.; West, M. J.; Veronig, A. M.; Antolin, P.; Purkhart, S.; Long, D. M.; Buchlin, É.; Haberreiter, M.; Zhukov, A. N.; Safari, H.; Battaglia, A. F.; Soubrié, E.; Büchel, V.; Gissot, S.; De Groof, A.; Gyo, M.; Halain, J. P.; Inhester, B.; Kraaikamp, E.; Müller, D.; Pfiffner, D.; Rochus, P.; Schuller, F.; Smith, P. J.; Schmutz, W.; Stegen, K. 2025, "Picoflares in the Quiet Solar Corona: Solar Orbiter Observations Halfway to the Sun", arXiv:2510.10340 (v3, 29 Nov 2025; v1, 11 Oct 2025, listed 42 authors), DOI 10.48550/arXiv.2510.10340, https://arxiv.org/abs/2510.10340
  3. Parker, E. N. 1988, "Nanoflares and the solar X-ray corona", The Astrophysical Journal 330, 474, DOI 10.1086/166485, https://doi.org/10.1086/166485
  4. Hudson, H. S. 1991, "Solar flares, microflares, nanoflares, and coronal heating", Solar Physics 133, 357, DOI 10.1007/BF00149894, https://doi.org/10.1007/BF00149894
  5. Withbroe, G. L.; Noyes, R. W. 1977, "Mass and Energy Flow in the Solar Chromosphere and Corona", Annual Review of Astronomy and Astrophysics 15, 363, DOI 10.1146/annurev.aa.15.090177.002051, https://doi.org/10.1146/annurev.aa.15.090177.002051
  6. Berghmans, D.; Auchère, F.; Long, D. M.; Soubrié, E.; Mierla, M.; Zhukov, A. N.; Schühle, U.; Antolin, P.; Harra, L.; Parenti, S.; Podladchikova, O.; Aznar Cuadrado, R.; Buchlin, É.; Dolla, L.; Verbeeck, C.; Gissot, S.; Teriaca, L.; Haberreiter, M.; Katsiyannis, A. C.; Rodriguez, L.; Kraaikamp, E.; Smith, P. J.; Stegen, K.; Rochus, P.; Halain, J. P.; Jacques, L.; Thompson, W. T.; Inhester, B. 2021, "Extreme-UV quiet Sun brightenings observed by the Solar Orbiter/EUI", Astronomy & Astrophysics 656, L4, DOI 10.1051/0004-6361/202140380, https://doi.org/10.1051/0004-6361/202140380
  7. Zhukov, A. N.; Mierla, M.; Auchère, F.; Gissot, S.; Rodriguez, L.; Soubrié, E.; Thompson, W. T.; Inhester, B.; Nicula, B.; Antolin, P.; Parenti, S.; Buchlin, É.; Barczynski, K.; Verbeeck, C.; Kraaikamp, E.; Smith, P. J.; Stegen, K.; Dolla, L.; Harra, L.; Long, D. M.; Schühle, U.; Podladchikova, O.; Aznar Cuadrado, R.; Teriaca, L.; Haberreiter, M.; Katsiyannis, A. C.; Rochus, P.; Halain, J.-P.; Jacques, L.; Berghmans, D. 2021, "Stereoscopy of extreme UV quiet Sun brightenings observed by Solar Orbiter/EUI", Astronomy & Astrophysics 656, A35, DOI 10.1051/0004-6361/202141010, https://doi.org/10.1051/0004-6361/202141010
  8. Purkhart, S.; Veronig, A. M. 2022, "Nanoflare distributions over solar cycle 24 based on SDO/AIA differential emission measure observations", Astronomy & Astrophysics 661, A149, DOI 10.1051/0004-6361/202243234, https://doi.org/10.1051/0004-6361/202243234
  9. Narang, N.; Verbeeck, C.; Mierla, M.; Berghmans, D.; Auchère, F.; Shestov, S.; Delouille, V.; Chitta, L. P.; Priest, E.; Lim, D.; Dolla, L. R.; Kraaikamp, E. 2025, "Extreme-ultraviolet transient brightenings in the quiet-Sun corona: Closest perihelion observations with Solar Orbiter/EUI", Astronomy & Astrophysics 699, A138, DOI 10.1051/0004-6361/202554650, https://doi.org/10.1051/0004-6361/202554650
  10. Parenti, S. 2026, "Small EUV Brightenings in the Quiet Solar Atmosphere: New Insights from the Solar Orbiter Mission", Solar Physics 301, article 4, DOI 10.1007/s11207-025-02592-z, https://doi.org/10.1007/s11207-025-02592-z