Incorporating Vector Magnetic Field Measurements into MHD models of the Solar Atmosphere W.P. Abbett Space Sciences Laboratory, UC Berkeley and B.T. Welsch, G.H. Fisher, T. Magara SSL UC Berkeley, NRL

Coupling the Photosphere to Coronal Models --- Relevance to “Sun-to-Mud” Modeling: ► The least understood component of the Sun-earth system is the solar atmosphere ► The least understood component of the Sun-earth system is the solar atmosphere --- where eruptive events and solar storms originate. ► ► CMEs, among the primary drivers of space weather, are magnetically driven and originate in the low corona. Central to our understanding of magnetic field evolution in the solar atmosphere is the strong topological coupling of the coronal field to magnetic field in the photosphere. ► require ► To progress beyond idealized calculations, an end-to-end coupled model of the Sun-Earth system ultimately will require validated models of solar eruptions that can provide the real time, observationally-based boundary conditions needed for successful physics-based space weather forecasting tools.

Characterizing the Evolution of the Coronal Magnetic Field --- Principal Challenges: ► There are no in situ measures of the state of the solar atmosphere. ► There are no in situ measures of the state of the solar atmosphere. All data are obtained via remote sensing. ► Measurements of the vector magnetic field in the corona are extremely challenging; as of yet, no routinely available source of such data exists. ► A common approach: Extrapolate a force-free or potential field from a series of photospheric magnetograms. Non-linear Force Free Field Extrapolation (Y. Liu)PFSS models of Y. Li & J. Luhmann

Coupling Photospheric Fields to a MHD Model Corona continuous Computationally inexpensive, static methods may not adequately describe the continuous topological evolution of the corona near strong active region magnetic fields. MHD models provide a means to follow this dynamic evolution, however: To drive an MHD model corona, one must first overcome a set of challenges: 1.Data-driven MHD models require an accurate time-series of vector magnetic field measurements at the photosphere. 2. Unlike PFSS and FFF extrapolations, MHD models require information about the flow field (electric field) at the photospheric boundary --- and that information is generally not available. 3.MHD models require specification of an initial atmosphere (all components of the magnetic field throughout the volume) consistent with the observed vector field at the lower boundary.

The Photospheric Magnetic Field: NOAA AR-8210 Advantages of AR-8210 as a case study for numerical simulations: There exists quality vector data AR-8210 produced multiple CMEs Candidate event for MURI project Disadvantages: Extremely complex active region Global trans-equatorial connection to another active region A high-cadence sequence of MDI vector magnetograms of CME producing AR-8210 on May 1,1998 (S. Regnier, R. Canfield)

Using Observations to Obtain a Photospheric Velocity Field: A new twist on Local Correlation Tracking (Demoulin & Berger 2003): LCT is a technique that infers the transverse velocity of magnetized plasma from the motion of magnetic features at the visible surface by finding the shift that maximizes the local correlation function between successive images. apparent However, LCT determines only apparent transverse flows --- consider the emergence of a tilted magnetic structure. u LCT = v t – B t (v n /B n ) Welsch & Fisher (2003) Assuming ideal MHD, flows parallel to the magnetic field cannot affect the evolution of magnetic structures --- Welsch & Fisher (2003) point out that this closes the Demoulin & Berger equations, and allows for an algebraic solution for all three components of the velocity field given a time series of vector magnetograms.

“Algebraic Method” applied to NOAA AR-8210 ► ► The results are very promising! However, to incorporate this data into MHD simulations, we must also ensure that the flow-field we obtain is consistent with the observed evolution of magnetic field, as specified by the z-component of the induction equation: Algebraic method applied to AR8210. Apparent velocities determined by G. Fisher’s LCT code; shown are the “true” flows as determined by B. Welsch’s application of the algebraic method.

I+LCT method applied to NOAA AR-8210 (Welsch & Fisher) ► ► Demoulin & Berger’s hypothesis simplifies the z-component of the induction equation, making it possible to determine a velocity field consistent with both LCT and the MHD induction equation. ► ► This method returns such a flow field given vector magnetic field measurements and an apparent flow determined by LCT on resolved magnetic features. ► ► This method is described in detail in Brian Welsch’s poster: SH22A-0177 (Tuesday afternoon) I+LCT method applied to AR8210.

MEF Method Applied to NOAA AR-8210 (Longcope & Klapper) Can we obtain a flow field that is consistent with the observed evolution of the magnetic field without obtaining apparent velocities via LCT? MEF Method: By itself, the z-component of the MHD induction equation is under-determined. MEF constrains the system by minimizing the spatially integrated square of the velocity MEF method applied to AR8210.

Testing and Validation of the New Inversion Techniques ► not necessarily unique ► A velocity field that satisfies the MHD induction equation in the photospheric layers (at the lower boundary of a coronal simulation) is not necessarily unique ANMHD simulations of W. AbbettI+LCT and Algebraic Method applied to ANMHD simulations

Obtaining an Initial Atmosphere from a Vector Magnetogram Data-driven MHD simulations of the corona require an initial specification of the vector magnetic field at all points in the computational domain. Techniques are available to extrapolate the structure of the magnetic field given a photospheric vector magnetogram (e.g. PFSS, FFF). However, two conditions must be met if a given extrapolation is to provide a suitable initial state: 1. It must adequately describe the coronal topology above the active region of interest, and transverse components of the magnetic field must match those specified by the vector magnetogram at the lower boundary. 2. The transverse components of the magnetic field must match those specified by the vector magnetogram at the lower boundary. Unfortunately, potential field extrapolations fail to meet condition 1 in and around strong, dynamic active regions, and (depending on the method used) certain force-free extrapolations can fail to meet condition 2, particularly if the magnetic field of an active region deviates significantly from a force-free configuration. FFF extrapolation of 8210 (Regnier)

How Force-Free is the Photosphere? ► ► T. Magara has recently simulated the emergence of a twisted flux rope through a computational domain that includes the transition layers from the photosphere to the low corona (see SH42B Thursday) Left Left: Fieldline traces from the final timestep Above of a run where a twisted flux tube has emerged into the corona. Above: The vertical component of the magnetic field for slices at different heights (from top left: the photosphere, chromosphere, transition region and low corona).

How Force-Free is the Photosphere? Above: Above: A measure of how force-free a model solar atmosphere is after a twisted flux system has emerged into the model corona: Shown is the value of along field lines --- blue indicates that currents flow along the fieldlines (force-free), and red indicates regions where currents are anti-parallel to the field (not force-free). the atmosphere becomes force-free at and above the chromosphere Thus, current simulations suggest (Magara 2003, Abbett & Fisher 2003) that the atmosphere becomes force-free at and above the chromosphere, and not below.

Other Issues Relevant to the Coupling of Photospheric Observations to Data-driven Coronal Models: ► ► Measurements of the vector magnetic field at the photosphere arise from model dependent inversions of polarization observations, and suffer from ambiguities. ► ► Since observations provide no information about the depth dependence of the magnetic field in the photosphere, the new velocity inversion techniques can only prescribe flows on a plane consistent with the z-component of the induction equation. MHD codes in general require the specification of magnetic fields below the surface to self consistently update all components of the induction equation. ► ► A non-uniform mesh is required to model the dynamic evolution of the global corona while maintaining sufficient resolution in the photosphere in and around active regions to resolve a local pressure scale height (of order 100km). Conclusion: Steady progress is being made toward developing the machinery necessary to drive models of the solar corona with photospheric vector magnetograms.