How Important Are Initial Conditions in Models of the Solar Corona?

Many models of the Sun’s upper atmosphere, or corona, use magnetohydrodynamics, in which collections of particles are assumed to behave like an electrically conducting fluid. A recent research article explores how sensitive magnetohydrodynamics models are to the conditions they start with.

A Powerful Modeling Tool

Magnetohydrodynamics simulations are a solar modeler’s bread and butter. These powerful simulations can be applied to everything from the slow shifting of the solar magnetic field as the Sun proceeds through its 11-year solar activity cycle to the rapid release of magnetic energy in solar flares or coronal mass ejections.

With so many ways to implement these models, it’s worth taking the time to consider how choices of model parameters affect the outcome. In other words, how much does what you get out depend on what you put in?

Testing Model Memory

To begin to address this question, Graham Barnes (NorthWest Research Associates) and collaborators studied the impact of initial conditions on magnetohydrodynamics simulations of the solar corona driven by electric fields. Just as the term suggests, initial conditions refer to the state of the model just before the modelers press go. For example, modelers might define the initial strength and direction of magnetic and electric fields and the density, temperature, and motion of the particles.

After a simulation begins, it will often undergo an adjustment period in which the initial quantities “relax” into a steady state. Once this steady state is reached, the model can be “driven,” such as by applying a force to the base of the corona, to study how the system changes over time. Barnes’s team sought to understand whether a model’s “memory” of the initial conditions persists through this relaxation phase. If the initial conditions are washed out during the relaxation phase, that means that any reasonable choice of parameters will do — but if the models retain a clear memory, researchers must choose their initial conditions more carefully.

Relating Relaxed Output to Initial Input

The team focused on the initial state of the magnetic field. They modeled two solar active regions — areas with particularly strong and complex magnetic fields — using data from the Solar Dynamics Observatory’s Helioseismic and Magnetic Imager, which measures the vertical component of the solar magnetic field. They used three methods to derive the initial strength and direction of the magnetic field from the data: a commonly used potential field, a slightly more realistic representation of the corona’s magnetic field (the nonlinear force-free field), and a purely vertical field. Then, Barnes’s team allowed the simulations to relax by letting the magnetic field evolve over time while reverting other quantities, like the density of the solar plasma, back to their initial values at each time step.

Barnes and collaborators found that the initial magnetic field conditions had little impact on the relaxed state of the magnetic field — the simple vertical magnetic field and the more realistic fields had remarkably similar outcomes. What differences did arise tended to show up at the borders of the simulation, where edge effects and boundary conditions play a larger role.

With models appearing to lack a clear memory of the conditions they started with, this work suggests that any reasonable initial magnetic field can be used for electric-field-driven models. More work is needed to understand if this result holds for other types of magnetohydrodynamics models, such as velocity-driven models.

Citation

“Are Electric-Field-Driven Magnetohydrodynamic Simulations of the Solar Corona Sensitive to the Initial Condition?” Graham Barnes et al 2024 ApJ 960 102. doi:10.3847/1538-4357/ad10a7