[Paper Review] A 3D Model of AR 11726 Heated by Nanoflares

Joel C. Allred, Adrian Daw+1 more|arXiv (Cornell University)|Jul 2, 2018

Solar and Space Plasma Dynamics1 references3 citations

TL;DR

This study constructs a 3D magnetic field model of active region AR 11726 using HMI magnetograms and SDO/AIA coronal loop observations, then simulates nanoflare heating across 2,848 magnetic field lines to reproduce observed EUV emission from EUNIS and EIS. The best-fit nanoflare frequency distribution is q₀ = 1.0×10⁻³ erg cm⁻³ s⁻¹, α = -2.4, β = 1.5, γ = -1.0, which best matches the 'critical angle' magnetic reconnection model and explains the presence of hot plasma (>6 MK) in closed loops.

ABSTRACT

The Extreme Ultraviolet Normal Incidence Spectrograph (EUNIS) and the Hinode/ EUV Imaging Spectrometer (EIS) observed AR 11726 on 2013 April 23. We present intensity images in numerous atomic lines constructed from these observations. These lines are formed over a wide range of temperatures, and we use their relative intensities to constrain a parameterization of nanoflare heating. We construct a 3D model of the magnetic field in this active region by extrapolating the surface magnetic field into the corona and using SDO/AIA images of coronal loops to ensure that extrapolated magnetic field lines co-align with observed coronal loops. We trace 2848 magnetic field lines within the volume of this active region and model how they fill with hot plasma in response to nanoflare heating. We perform a parameter study to determine how the frequency and energy released in nanoflares scale with magnetic field strength and loop length. From our 3D model, we construct synthetic images of the lines observed by EUNIS and EIS and constrain the parameter study by minimizing the difference between the synthetic and observed images.

Motivation & Objective

• To explain the presence of hot plasma (>6 MK) in closed coronal loops of active region AR 11726, observed via EUNIS and EIS.
• To constrain the nanoflare heating frequency distribution using multi-instrument observations (EUNIS, EIS, SDO/AIA, HMI).
• To construct a 3D magnetic field model by extrapolating surface magnetic fields and aligning with observed coronal loops.
• To simulate how plasma temperature and density evolve in response to nanoflare heating across thousands of magnetic field lines.
• To determine which coronal heating model best reproduces the observed emission by minimizing synthetic vs. observed line intensities.

Proposed method

• Extrapolated HMI photospheric magnetic field data into the corona to build a 3D magnetic field model of AR 11726.
• Traced 2,848 closed magnetic field lines within the active region volume, treating them as coronal loop centers.
• Parameterized nanoflare heating using a power-law frequency distribution: q(E) ∝ E^α × (E/E₀)^β × exp(-E/E₀)^γ, with E₀ as a characteristic energy.
• Performed hydrodynamic simulations of plasma heating and cooling in each loop, tracking temperature and density evolution over time.
• Projected synthetic emission from atomic lines (Fe IX–XV, Mg IX, etc.) along the line of sight and compared to EUNIS and EIS observations.
• Used a χ²-like metric (d = Σ|I_syn − I_obs|² / (N_i × N_l)) to minimize differences between synthetic and observed images and constrain parameters.

Experimental results

Research questions

• RQ1 What nanoflare frequency distribution best reproduces the observed EUV line intensities in AR 11726?
• RQ2 How does the heating rate scale with magnetic field strength and loop length in this active region?
• RQ3 Which coronal heating model is most consistent with the observed hot plasma and emission line profiles?
• RQ4 To what extent does the 3D magnetic field model, constrained by AIA loop morphology, improve the realism of nanoflare simulations?
• RQ5 What is the spatial distribution of volumetric heating and emission measure function (DEM) in AR 11726 under the best-fit nanoflare model?

Key findings

• The best-fit nanoflare frequency distribution is q₀ = 1.0×10⁻³ erg cm⁻³ s⁻¹, α = -2.4, β = 1.5, γ = -1.0, minimizing the difference between synthetic and observed EUNIS/EIS line intensities.
• The time-averaged heating rate reaches ~10⁷ erg cm⁻² s⁻¹ across most of the active region, with the hottest regions receiving nearly two orders of magnitude more heat.
• The emission measure function (DEM) peaks at 3.3 MK and falls off with a slope of -9 in log-log space, with emission at 10 MK being ~5 orders of magnitude weaker than at the peak.
• The DEM slope is consistent with Warren et al. (2012) but steeper than the -12 slope found by Ishikawa et al. (2017) from FOXSI-2 X-ray observations.
• The heating rate scales as B¹·⁵ and L⁻¹, indicating compatibility with the 'critical angle' magnetic reconnection model (Parker, 1988; Berger, 1993).
• The model successfully reproduces observed AIA 193 and 94 Å channel images, confirming the synthetic emission's fidelity to multi-wavelength observations.