MHD modelling of open flux evolution around solar maximum by coronal model COCONUT

TL;DR

This work tackles the open flux problem by using time-evolving MHD coronal modelling with the COCONUT framework, driven by hourly magnetograms during solar maximum CRs $CR_{2282}$ and $CR_{2283}$. It jointly assesses magnetogram preprocessing (10th-order PF vs 50th-order filtered PF) and empirically defined heating terms on the evolution of open-field regions and flux at $1.01\,R_s$, $3\,R_s$, and $0.1\,AU$, comparing with interplanetary data. The results show that while surface open flux can match in-situ estimates, strong reduction occurs in the low corona due to polarity-inversion interfaces within open fields, yielding up to $\sim$45% flux loss at $0.1\,AU$; heating term variations can effectively modulate the unsigned open flux, and high-order magnetogram preprocessing increases both open and closed flux in the low corona but does not alter the open flux far from the Sun. The study emphasizes the need for finer grid resolution around polarity-inversion interfaces, more physically realistic heating, and a time-evolving modelling regime to address the open flux problem, guiding future efforts toward more realistic lower-boundary conditions and inclusion of transient events.

Abstract

To evaluate impact of temporal evolution and commonly used harmonic filtering of magnetograms, and the empirically defined oversimplified heating source terms on open-field distributions, we use a series of hourly-updated magnetograms, preprocessed by the 10th- and 50th-order filtered PF solvers, to drive COCONUT, configured with different heating prescriptions, to mimic coronal evolutions during CRs 2282 and 2283. We evaluate the simulated open magnetic flux at 1.01~$R_s$, 3~$R_s$, and 0.1~AU, and compare them with interplanetary observations. The results show that the simulated unsigned open flux evaluated near the solar surface can be comparable to that derived from interplanetary in situ observations. However, in low corona, numerous small-scale closed-field magnetic structures introduce magnetic polarity inversion interfaces within the open field, cancelling part of the open field near these interfaces during the volume-integration procedure of the finite-volume method. Consequently, the simulated unsigned open flux can be reduced by up to 45% at 0.1~AU and decreases more rapidly in the low corona. The results also indicate that moderate adjustments to the heating source term can effectively regulate the magnitude of the unsigned open magnetic flux. Preprocessing the initial magnetogram by a PF solver with limited spherical harmonics can reduce the open flux in the low corona and alter the distribution of open-field regions, but has little effect on the total unsigned open flux at larger heliocentric distances. The ratio of the maximum to minimum open unsigned magnetic flux can reach 1.4 within a single solar maximum CR. These findings highlight the necessity of considering finer grid resolution around magnetic polarity inversion interfaces, more realistic heating mechanisms, and the time-evolving regime of MHD coronal modelling when further addressing the ``open flux problem".

Figures (7)

• Figure 1: Timing diagrams of the radial velocity $V_r$ ($\rm km~s^{-1}$; left) and proton number density ($\rm 10^3 ~ cm^{-3}$; right) measured by a virtual satellite located at 21.5 $R_s$. The virtual satellite is positioned at the same latitude as Earth but lags by $60^\circ$ in longitude. The solid black, dashed red, and dashed-dot blue lines represent the time-evolving simulation results from Cases 1, 2, and 3, respectively, while the solid grey lines show the radial velocity (left) observed by the WIND spacecraft.
• Figure 2: Timing diagrams of the simulated radial velocity $V_r$ ($\rm km\,s^{-1}$; left) and plasma number density ($10^3\,\rm cm^{-3}$; right) from Cases 1 (top), 2 (middle), and 3 (bottom) at 0.1 AU, evaluated along the latitudes intersected by longitude $0^\circ$, lagging the Sun--Earth line by $60^\circ$ in longitude. The dashed white, dashed orange, and solid black lines denote the magnetic neutral lines (MNLs) derived from Cases 1, 2, and 3, respectively.
• Figure 3: White-light pB images observed by COR2/STEREO-A (first row) and synthesised from the coronal simulation results of Case 1 (second row), Case 2 (third row), and Case 3 (fourth row), respectively, spanning along heliocentric distances from 2.5 to 15 $R_s$ on meridional planes in the STEREO-A view. The orange lines indicate magnetic field lines on the selected meridional planes traced from identical seed points. The evolution of these simulated images during the simulated period is shown in online movie 1.
• Figure 4: Timing diagrams of the radial magnetic field strength measured by the same virtual satellite as in Fig. \ref{['1DTimingDiagram']}, together with the WIND observations scaled by $0.5\times\left(1~\mathrm{AU}/0.1~\mathrm{AU}\right)^2$ (nT; top left), as well as timing diagrams of the simulated areas of open-field regions ($\rm S_{open}$; top right) and the unsigned open magnetic flux ($\Phi_{\rm open}$; bottom left) at 1.01 $R_s$ and 3 $R_s$, and the total unsigned magnetic flux ($\Phi_{\rm total}$; bottom right) across spherical surfaces at 1.01 $R_s$, 3 $R_s$, and 0.1 AU. The magnetic fluxes $\Phi_{\rm open}$ and $\Phi_{\rm total}$ are normalized using the WIND in situ observations, $\Phi_{\rm 1AU}^{\rm ave} = \left| B_{r,\rm 1AU} \right|^{\rm ave} \,\cdot\,4\pi\,(1~\mathrm{AU})^{2}=7.67 \times 10^{14}~{\rm Wb}$, where $\left| B_{r,\rm 1AU} \right|^{\rm ave}$ denotes the average unsigned radial interplanetary magnetic field strength along the Sun-Earth direction, derived from hourly averaged WIND observations during the simulated period. The areas of the open-field regions at $r = r_{\rm Se}$ are normalized by $\rm S_{\rm open~at~3R_s}^{\rm ave}\cdot\left(r_{\rm Se}/3R_s\right)^2$, where $\rm S_{\rm open~at~3R_s}^{\rm ave} = 4.92\times10^{19}~\mathrm{m}^2$ denotes the average open-field area at 3 $R_s$ in Case 3. The black, red, and blue curves correspond to results obtained from Cases 1, 2, and 3, respectively.
• Figure 5: Distributions of the radial magnetic field at 1.01 $R_s$ evaluated at the 264th, 556th, 832nd, 1060th, and 1316th hours for Case 3. The dashed black, solid orange, and solid blue lines overlaid on the magnetic-field contours denote the boundaries of open-field regions derived from Cases 1, 2, and 3, respectively. colour blueEvolution of the radial magnetic field at the inner boundary, as displayed in the top-left panel, during the simulated period is shown in online movie 2.