An Electric-field-driven Global Coronal Magnetohydrodynamics Simulation Model Using Helioseismic and Magnetic Imager Vector-magnetic-field Synoptic Map Data

Abstract

We present the simulation methodology and results of our new data-driven global coronal magnetohydrodynamics (MHD) simulation model. In this model, the solar-surface electric field is first calculated such that the curl will satisfy both the induction equation and the given temporal variations of the solar-surface magnetic field. We use the synoptic maps of the Helioseismic and Magnetic Imager three-component vector-magnetic-field data to specify the solar-surface magnetic-field vector for a period from Carrington Rotations (CRs) 2106 to 2110. A set of whole-Sun three-component electric-field maps are obtained for each CR transition interval of about 27.3 days. Using the inverted electric field as the driving variable, our new global coronal MHD model, with the angular resolution of π/64, can trace the evolution of the three-dimensional coronal magnetic field that matches the specified time-dependent solar-surface magnetic-field maps and simultaneously satisfies the divergence-free condition. A set of additional boundary treatments are introduced to control the contribution of the horizontal components of the magnetic field at the weak-field regions. The strength of the solar-surface magnetic field is limited to 20 Gauss for the sake of computational stability in this study. With these numerical treatments, the nonpotential coronal features, such as twisted loop structures, and their eruptive outward motions are obtained. This present model, capable of introducing three-component solar-surface magnetic-field observation data to coronal MHD simulations, is our first step toward a better model framework for the solar corona and hence solar wind.

The Nonpotentiality of Steady-state Coronal Magnetic Field Derived with Time-relaxation Magnetohydrodynamics Simulations Using Helioseismic and Magnetic Imager Three-component Magnetic Field Data

“…We chose a period of Carrington Rotation (CR) 2106, from 2011 January 20 to February 16. This is the period we have studied in our previous work (Hayashi et al 2022). The synoptic map data from SDO/HMI observations are used to specify the boundary values of the magnetic field, after smoothing with the Gaussian function with the heliocentric angle of about 4°.…”

“…The simulation code is mostly the same as the one used by Hayashi et al (2022). It consists of a set of standard numerical methods, such as the Roe-type linearized Riemann solver, Total Variant Diminishing (TVD), Finite Volume Method (FVM), and third-order Monotonic Upstream Scheme for Conservation Laws (MUSCL; see Hayashi 2005, and references therein).…”

“…Recently, we developed a new boundary treatment in coronal MHD simulation to specify all three components of the magnetic field as the solar surface boundary values (Hayashi et al 2018(Hayashi et al , 2019(Hayashi et al , 2021(Hayashi et al , 2022. In this model, the boundary electric field (  E) is inverted such that it matches the specified temporal variations of all three components of the magnetic field, satisfying the induction equation,…”

“…By including the observation data of the horizontal components (the latitudinal and longitudinal components, B θ and B f , in the case of spherical global coronal simulation) in addition to the normal component (the radial component, B r ) as the boundary values, our MHD simulation model can yield notable nonpotential structures in the local active region (AR) scale (Hayashi et al 2018(Hayashi et al , 2019 and in the global scale (Hayashi et al 2021(Hayashi et al , 2022. In these studies, we used data from the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO; Hoeksema et al 2014;Scherrer et al 2012), such as the vector-magnetic-field data in the form of the active region patch (SHARP) data set (Bobra et al 2014) for simulating the active regions and the synoptic map format (Liu et al 2017) for simulating the global corona.…”

“…In the global coronal modeling, we want to obtain the two types of coronal structures, the open-field coronal holes (and the outward-flowing plasma) and the closed-field coronal streamers (and the confined stagnant plasma). In Hayashi et al (2022), a set of two criteria on the bottom-boundary MHD variables determines whether the simulated magnetic field will follow the specified three-component vector data or only the radial component will. The boundary horizontal components at each bottom-boundary grid are guided by the E-driven boundary model to the specified target values (a) when V r at the boundary grid is substantially small, or (b) when the plasma beta β (=P g /(B 2 /(8π)), where P g is the plasma pressure) is smaller than a prescribed threshold number.…”