Bart van der Holst

Adaptive numerical algorithms in space weather modeling

Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different relevant physics in different domains. A multi-physics system can be modeled by a software framework comprising several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamic (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical schemes. Depending on the application, we find that different time stepping methods are optimal. Several of the time integration schemes exploit the block-based granularity of the grid structure. The framework and the adaptive algorithms enable physics-based space weather modeling and even short-term forecasting.

Studying extreme ultraviolet wave transients with a digital laboratory: Direct comparison of extreme ultraviolet wave observations to global magnetohydrodynamic simulations

In this work, we describe our effort to explore the signatures of large-scale extreme ultraviolet (EUV) transients in the solar corona (EUV waves) using a three-dimensional thermodynamic magnetohydrodynamic model. We conduct multiple simulations of the 2008 March 25 EUV wave (~18:40 UT), observed both on and off of the solar disk by the STEREO-A and B spacecraft. By independently varying fundamental parameters thought to govern the physical mechanisms behind EUV waves in each model, such as the ambient magneto-sonic speed, eruption free energy, and eruption handedness, we are able to assess their respective contributions to the transient signature. A key feature of this work is the ability to synthesize the multi-filter response of the STEREO Extreme UltraViolet Imagers directly from model data, which gives a means for direct interpretation of EUV observations with full knowledge of the three-dimensional magnetic and thermodynamic structures in the simulations. We discuss the implications of our results with respect to some commonly held interpretations of EUV waves (e.g., fast-mode magnetosonic wave, plasma compression, reconnection front, etc.) and present a unified scenario which includes both a wave-like component moving at the fast magnetosonic speed and a coherent driven compression front related to the eruptive event itself.

Magnetohydrodynamic Waves and Coronal Heating: Unifying Empirical and MHD Turbulence Models

We present a new global model of the solar corona, including the low corona, the transition region, and the top of the chromosphere. The realistic three-dimensional magnetic field is simulated using the data from the photospheric magnetic field measurements. The distinctive feature of the new model is incorporating MHD Alfven wave turbulence. We assume this turbulence and its nonlinear dissipation to be the only momentum and energy source for heating the coronal plasma and driving the solar wind. The difference between the turbulence dissipation efficiency in coronal holes and that in closed field regions is because the nonlinear cascade rate degrades in strongly anisotropic (imbalanced) turbulence in coronal holes (no inward propagating wave), thus resulting in colder coronal holes, from which the fast solar wind originates. The detailed presentation of the theoretical model is illustrated with the synthetic images for multi-wavelength EUV emission compared with the observations from SDO AIA and STEREO EUVI instruments for the Carrington rotation 2107.

TOWARD A REALISTIC THERMODYNAMIC MAGNETOHYDRODYNAMIC MODEL OF THE GLOBAL SOLAR CORONA

In this work, we describe our implementation of a thermodynamic energy equation into the global corona model of the Space Weather Modeling Framework and its development into the new lower corona (LC) model. This work includes the integration of the additional energy transport terms of coronal heating, electron heat conduction, and optically thin radiative cooling into the governing magnetohydrodynamic (MHD) energy equation. We examine two different boundary conditions using this model; one set in the upper transition region (the radiative energy balance model), as well as a uniform chromospheric condition where the transition region can be modeled in its entirety. Via observation synthesis from model results and the subsequent comparison to full Sun extreme ultraviolet and soft X-ray observations of Carrington rotation 1913 centered on 1996 August 27, we demonstrate the need for these additional considerations when using global MHD models to describe the unique conditions in the low corona. Through multiple simulations, we examine the ability of the LC model to assess and discriminate between coronal heating models, and find that a relative simple empirical heating model is adequate in reproducing structures observed in the low corona. We show that the interplay between coronal heating and electron heat conduction provides significant feedback onto the three-dimensional magnetic topology in the low corona as compared to a potential field extrapolation, and that this feedback is largely dependent on the amount of mechanical energy introduced into the corona.

Understanding SDO/AIA Observations of the 2010 June 13 EUV Wave Event: Direct Insight from a Global Thermodynamic MHD Simulation

In this work, we present a comprehensive observation and modeling analysis of the 2010 June 13 extreme-ultraviolet (EUV) wave observed by the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory (SDO). Due to extreme advances in cadence, resolution, and bandpass coverage in the EUV regime, the AIA instrument offers an unprecedented ability to observe the dynamics of large-scale coronal wave-like transients known as EUV waves. To provide a physical analysis and further complement observational insight, we conduct a three-dimensional, time-dependent thermodynamic MHD simulation of the eruption and associated EUV wave, and employ forward modeling of EUV observables to compare the results directly observations. We focus on two main aspects: (1) the interpretation of the stark thermodynamic signatures in the multi-filter AIA data within the propagating EUV wave front, and (2) an in-depth analysis of the simulation results and their implication with respect to EUV wave theories. Multiple aspects, including the relative phases of perturbed variables, suggest that the outer, propagating component of the EUV transient exhibits the behavior of a fast-mode wave. We also find that this component becomes decoupled from the evolving structures associated with the coronal mass ejection that are also visible, providing a clear distinction between wave and non-wave mechanisms at play.

Obtaining potential field solutions with spherical harmonics and finite differences

Potential magnetic field solutions can be obtained based on the synoptic magnetograms of the Sun. Traditionally, a spherical harmonics decomposition of the magnetogram is used to construct the current- and divergence-free magnetic field solution. This method works reasonably well when the order of spherical harmonics is limited to be small relative to the resolution of the magnetogram, although some artifacts, such as ringing, can arise around sharp features. When the number of spherical harmonics is increased, however, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. We discuss here two approaches that can mitigate or completely avoid these problems: (1) remeshing the magnetogram onto a grid with uniform resolution in latitude and limiting the highest order of the spherical harmonics to the anti-alias limit; (2) using an iterative finite difference algorithm to solve for the potential field. The naive and the improved numerical solutions are compared for actual magnetograms and the differences are found to be rather dramatic. We made our new Finite Difference Iterative Potential-field Solver (FDIPS) a publicly available code so that other researchers can also use it as an alternative to the spherical harmonics approach.

Global MHD simulations of Mercury's magnetosphere with coupled planetary interior: Induction effect of the planetary conducting core on the global interaction

Mercurys comparatively weak intrinsic magnetic field and its close proximity to the Sun lead to a magnetosphere that undergoes more direct space-weathering interactions than other planets. A unique aspect of Mercurys interaction system arises from the large ratio of the scale of the planet to the scale of the magnetosphere and the presence of a large-size core composed of highly conducting material. Consequently, there is strong feedback between the planetary interior and the magnetosphere, especially under conditions of strong external forcing. Understanding the coupled solar wind-magnetosphere-interior interaction at Mercury requires not only analysis of observations but also a modeling framework that is both comprehensive and inclusive. We have developed a new global MHD model for Mercury in which the planetary interior is modeled as layers of different electrical conductivities that electromagnetically couple to the surrounding plasma environment. This new modeling capability allows us to characterize the dynamical response of Mercury to time-varying external conditions in a self-consistent manner. Comparison of our model results with observations by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft shows that the model provides a reasonably good representation of the global magnetosphere. To demonstrate the capability to model induction effects, we have performed idealized simulations in which Mercurys magnetosphere is impacted by a solar wind pressure enhancement. Our results show that due to the induction effect, Mercurys core exerts strong global influences on the way Mercury responds to changes in the external environment, including modifying the global magnetospheric structure and affecting the extent to which the solar wind directly impacts the surface. The global MHD model presented here represents a crucial step toward establishing a modeling framework that enables self-consistent characterization of Mercurys tightly coupled planetary interior-magnetosphere system.

SIMULATION OF FLUX EMERGENCE FROM THE CONVECTION ZONE TO THE CORONA

Here, we present numerical simulations of magnetic flux buoyantly rising from a granular convection zone into the low corona. We study the complex interaction of the magnetic field with the turbulent plasma. The model includes the radiative loss terms, non-ideal equations of state, and empirical corona heating. We find that the convection plays a crucial role in shaping the morphology and evolution of the emerging structure. The emergence of magnetic fields can disrupt the convection pattern as the field strength increases, and form an ephemeral region-like structure, while weak magnetic flux emerges and quickly becomes concentrated in the intergranular lanes, i.e., downflow regions. As the flux rises, a coherent shear pattern in the low corona is observed in the simulation. In the photosphere, both magnetic shearing and velocity shearing occur at a very sharp polarity inversion line. In a case of U-loop magnetic field structure, the field above the surface is highly sheared while below it is relaxed.

GLOBAL NUMERICAL MODELING OF ENERGETIC PROTON ACCELERATION IN A CORONAL MASS EJECTION TRAVELING THROUGH THE SOLAR CORONA

The acceleration of protons and electrons to high (sometimes GeV/nucleon) energies by solar phenomena is a key component of space weather. These solar energetic particle (SEP) events can damage spacecraft and communications, as well as present radiation hazards to humans. In-depth particle acceleration simulations have been performed for idealized magnetic fields for diffusive acceleration and particle propagation, and at the same time the quality of MHD simulations of coronal mass ejections (CMEs) has improved significantly. However, to date these two pieces of the same puzzle have remained largely decoupled. Such structures may contain not just a shock but also sizable sheath and pileup compression regions behind it, and may vary considerably with longitude and latitude based on the underlying coronal conditions. In this work, we have coupled results from a detailed global three-dimensional MHD time-dependent CME simulation to a global proton acceleration and transport model, in order to study time-dependent effects of SEP acceleration between 1.8 and 8 solar radii in the 2005 May 13 CME. We find that the source population is accelerated to at least 100 MeV, with distributions enhanced up to six orders of magnitude. Acceleration efficiency varies strongly along field lines probing different regions of the dynamically evolving CME, whose dynamics is influenced by the large-scale coronal magnetic field structure. We observe strong acceleration in sheath regions immediately behind the shock.

Dynamic Coupling of Convective Flows and Magnetic Field during Flux Emergence

We simulate the buoyant rise of a magnetic flux rope from the solar convection zone into the corona to better understand the energetic coupling of the solar interior to the corona. The magnetohydrodynamic model addresses the physics of radiative cooling, coronal heating, and ionization, which allow us to produce a more realistic model of the solar atmosphere. The simulation illustrates the process by which magnetic flux emerges at the photosphere and coalesces to form two large concentrations of opposite polarities. We find that the large-scale convective motion in the convection zone is critical to form and maintain sunspots, while the horizontal converging flows in the near-surface layer prevent the concentrated polarities from separating. The footpoints of the sunspots in the convection zone exhibit a coherent rotation motion, resulting in the increasing helicity of the coronal field. Here, the local configuration of the convection causes the convergence of opposite polarities of magnetic flux with a shearing flow along the polarity inversion line. During the rising of the flux rope, the magnetic energy is first injected through the photosphere by the emergence, followed by energy transport by horizontal flows, after which the energy is subducted back to the convection zone by the submerging flows.