Simulating the photospheric to coronal plasma using magnetohydrodynamic characteristics III: validation including gravity, flux emergence, and an eruption

TL;DR

This work validates a data-driven MHD boundary driving framework (CHAR) against a ground-truth simulation that includes gravity, stratification, flux emergence, and eruption, demonstrating that boundary data interpolated from photospheric observations can drive full MHD evolution with high fidelity. The driven DD simulation reproduces emergence, topological restructuring, and eruption, with magnetic/kinetic energy and Poynting flux budgets matching GT within a few percent to ~10%, and eruption timing aligned within a small margin. The results support applying data-driven, characteristics-based boundary driving to solar synoptic observations, enabling reliable AR evolution modeling from pre-emergence to eruption. The study also identifies limitations related to optimization degeneracies and suggests avenues for improvement and cross-code validation for real observational deployment.

Abstract

Solar eruptions arise from instabilities or loss of equilibria in the solar atmosphere, but routinely inferring the precise magnetic and plasma properties that lead to eruptions is not currently practical using synoptic solar observations. Data driven simulations offer an appealing alternative. We test our boundary data-driven magnetohydrodynamic (MHD) approach, based on the method of characteristics, on a simulation that includes full MHD, a stratified atmosphere, and the emergence of a model solar magnetic active region, from the photosphere upwards. The driven simulation is tested against a larger, ab initio ``Ground Truth'' simulation that extends downward into the convection zone. Our driven simulation accurately reproduces the dynamic emergence of the active region above the photosphere, the formation of key topological features throughout the corona, and the subsequent eruption of mass and magnetic field. The total emerged energy matches to better than one percent, the ratio of emerged to eruptive energy is $\approx2\%$, and the actual values of each energy term agree to within $10\%$ between the two cases. Crucially, the data injection cadence, when properly scaled, matches the cadence of synoptic observations of the Sun's surface magnetic field, and is three to four orders of magnitude longer than the inherent CFL time step of the simulations. The stability of the code and fidelity of the results over an entire active region lifetime, from emergence to eruption, strongly suggests that our method will produce reliable results when driven using solar synoptic observations from existing and anticipated ground and spaced based observatories.

Figures (8)

• Figure 1: Perspective comparison between the GT simulation (left) and DD simulation (right) at time $t=150$. The spatial extent of the image is the same in both panels and extends vertically into the convection zone, which is below the numerical domain of the DD simulation. The flux tube in the convection zone is therefore visible in the left panel but not the right. The same features are displayed for each simulation, consisting of the vertical magnetic field in the $z=0$ plane (grayscale); the current density $j_y$ along the primary axial direction of the flux tube in the $y=0$ plane (Red-blue scale); the temperature in the $y=0$ plane (purple-yellow scale); and selected magnetic field lines in both the emerged flux rope and background magnetic arcade (green lines). The selected time is after substantial emergence and just preceding the rapid rise and eruption of the emerged flux rope. Notable features in both simulations are the sheath current at the top of the emerged flux rope, the quadrupolar magnetic structure in the $y=0$ plane following reconnection between the emerged field and background arcade, and the overall similarity (despite discrepancies in fine details) between the DD and GT simulations. An animation of this figure ($53\, \mathrm{s}$; $t=0:200$) is available in the online material, which shows the initial background arcade with the flux rope confined to the convection zone, followed by its rise into the corona and the eruption. See text for detailed description of the dynamics.
• Figure 2: Axial current $j_y$ in the $y=0$ plane for a zoomed-in view of the emerging flux rope, in the GT simulation (left) and DD simulation (right). The blank portion at the bottom of the DD simulation lies outside of the DD numerical domain (boundary at $z=0$). The animation of this figure ($55\, \mathrm{s}$; $t=0:204.75$) the shows the gradual rising and strengthening of the current sheets during emergence and rapid rise during the eruption. The static figure corresponds to time $t=155$, shortly before the eruption in either simulation. The cross and circle mark the locations of the sheath current and O-point along the $x=0$ line, respectively.
• Figure 3: Unsigned magnetic flux integrated over constant-$z$ planes in the GT (dash-dot) and DD (solid) simulations, as a function of time. The blue, orange, green, and pink lines correspond to the $z=0,30,80,180$ planes, respectively, and are sequential from top to bottom, as the flux decreases with height. The two curves for each height mostly overlap. The legend obscures only effectively constant portions of the $z=80$ and $180$ curves.
• Figure 4: Net mass flux integrated over constant-$z$ planes as a function of time, with the GT values at left and the DD results at right. The upper panels show the mass flux through $z=0$ plane (blue), and the lower plots show flux through the $z=30, 80,\ 180$ planes in orange, green, and pink, respectively. The scales are the same for both simulations, but differ by 3 orders of magnitude for the photospheric (upper) versus coronal (lower) calculations. Note that the GT data in this uses a solid line, unlike other the figures.
• Figure 5: Net Poynting flux calculated through four constant-$z$ layers, $z=0,30,80,180$ for blue, orange, green, and pink curves, respectively, for the GT (dash-dot) and DD (solid) simulations, as a function of time. The blue curve ($z=0$) shows the emergence of the flux rope through the photosphere, while pulses in the orange, green, and pink curves starting around $t=160$ show the successive transport of magnetic energy into higher portions of the atmosphere during the eruption.