MHD Modeling of Solar Coronal Magnetic Evolution Driven by Photospheric Flow

Abstract

It is well-known that magnetic fields dominate the dynamics in the solar corona, and new generation of numerical modeling of the evolution of coronal magnetic fields, as featured with boundary conditions driven directly by observation data, are being developed. This paper describes a new approach of data-driven magnetohydrodynamic (MHD) simulation of solar active region (AR) magnetic field evolution, which is for the first time that a data-driven full-MHD model utilizes directly the photospheric velocity field from DAVE4VM. We constructed a well-established MHD equilibrium based on a single vector magnetogram by employing an MHD-relaxation approach with sufficiently small kinetic viscosity, and used this MHD equilibrium as the initial conditions for subsequent data-driven evolution. Then we derived the photospheric surface flows from a time series of observed magentograms based on the DAVE4VM method. The surface flows are finally inputted in time sequence to the bottom boundary of the MHD model to self-consistently update the magnetic field at every time step by solving directly the magnetic induction equation at the bottom boundary. We applied this data-driven model to study the magnetic field evolution of AR 12158 with SDO/HMI vector magnetograms. Our model reproduced a quasi-static stress of the field lines through mainly the rotational flow of the AR's leading sunspot, which makes the core field lines to form a coherent S shape consistent with the sigmoid structure as seen in the SDO/AIA images. The total magnetic energy obtained in the simulation matches closely the accumulated magnetic energy as calculated directly from the original vector magnetogram with the DAVE4VM derived flow field. Such a data-driven model will be used to study how the coronal field, as driven by the slow photospheric motions, reaches a unstable state and runs into eruptions.

MHD Simulation of Homologous Eruptions from Solar Active Region 10930 Caused by Sunspot Rotation

“…the photosphere. The last term B stable 2 h  ^is used to maintain the numerical stability near the PIL (see also Jiang et al 2021a). Here we set…”

Homologous Coronal Mass Ejections Caused by Recurring Formation and Disruption of Current Sheet within a Sheared Magnetic Arcade

“…It also indicates that there is an upper limit for energy of the bipolar field in the core of ARs, and eruption is an efficient way to keep the energy below this limit. Future studies will investigate how this mechanism works in realistic homologous events using data-driven modeling (Jiang et al 2016;Jiang et al 2021a).…”

MHD Simulation of Homologous Eruptions from Solar Active Region 10930 Caused by Sunspot Rotation

“…As a consequence the eruption strength will decrease, because according to Bian et al (2022b), the eruption strength is highly correlated with the magnetic gradient of the main PIL. A more realistic velocity field at photosphere, including rotational, shearing and converge motions, derived from observation could be applied as the boundary condition to get a more self-consistent and realistic evolution (which has been shown in Jiang et al 2021a andJiang et al 2022b). Another key point we have not considered in the current model is the flux emergence process, for which the normal velocity (i.e.…”

“…at the photosphere. The last term η stable ∇ 2 ⊥ B is used to maintain the numerical stability near the PIL (see also Jiang et al 2021a). Here we set:…”