What Determines the Brightness of the Magnetically Open Solar Corona?: Insights from Three-dimensional Radiative Magnetohydrodynamic Simulations and Observations

Abstract

We investigate the relationship between solar coronal holes and open-field regions using three-dimensional radiative magnetohydrodynamic (MHD) simulations combined with remote-sensing observations from the Solar Dynamics Observatory (SDO). Our numerical simulations reveal that magnetically open regions in the corona can exhibit brightness comparable to quiet regions, challenging the conventional view that open-field regions are inherently dark coronal holes. We find that the coronal brightness is primarily determined by the total energy input from photospheric magnetic activities, such as the small-scale dynamo, rather than differences in dissipative processes within the corona. Using synthesized EUV intensity maps, we show that brightness thresholds commonly used to identify coronal holes may overlook open-field regions, especially at lower spatial resolutions. Observational analysis utilizing SDO/HMI and AIA synoptic maps supports our simulation results, demonstrating that magnetic field extrapolation techniques, such as the Potential Field Source Surface (PFSS) model, are sensitive to the chosen parameters, including the source surface height. We suggest that discrepancies in estimates of open magnetic flux (the ``open flux problem'') arise both from the modeling assumptions in coronal magnetic field extrapolation and systematic biases in solar surface magnetic field observations. Our findings indicate the need for reconsidering criteria used to identify coronal holes as indicators of open-field regions to better characterize the solar open magnetic flux.

Figures (15)

• Figure 1: Realized strength of small-scale dynamo measured by $\left<|B_z|\right>$ and $\left<|B|\right>$ as a function of the magnetic flux imbalance $\left<Bz\right>$. All quantities are evaluated at the Rosseland-mean optical depth unity ($\tau_R=1$). Each point corresponds to a different simulation case with different values of $B_h^{\rm in}$ and $B^z_{\rm ave}$. Orange shaded regions indicate typical ranges in the quiet Sun.
• Figure 2: Overall structure of the simulated solar corona. Shown are vertical component of magnetic field at the coronal base (2 Mm above the surface; left) and synthesized AIA 193 Å intensity. Each sub-panel corresponds to a different simulation case with different values of $B_h^{\rm in}$ and $B^z_{\rm ave}$. From top to bottom, the inflow magnetic field strength $B_h^{\rm in}$ is set to $0$, $710$ G, $1760$ G, and ${\infty}$, respectively. From left to right, the magnetic flux imbalance $B^z_{\rm ave}$ is set to $3$, $6$, $12$, and $24$ G, respectively. The animated version of this figure shows time evolution of the simulated corona over 30 minutes of physical time.
• Figure 3: Dependence of synthesized AIA 193 Å intensity on the vertical magnetic flux imbalance (left) and the root-mean-square of the vertical magnetic field (right). The average is taken over the whole horizontal domain and the last 2 h of each simulation. Two thin gray horizontal lines indicate the typical intensity of the quiet Sun (top) and the coronal hole (bottom).
• Figure 4: Energy input (top) and dissipation rate (bottom) in the simulated solar corona. Shown are the dependence on the vertical magnetic flux imbalance (left) and the root-mean-square of the vertical magnetic field (right). The average is taken over the whole horizontal domain and the last 2 h of each simulation.
• Figure 5: Spatial distribution of true open-field region (determined by tracing magnetic field lines) and coronal holes defined by the synthesized AIA 193 Å intensity with a threshold value of $20$ DN s$^{-1}$ pix$^{-1}$.