Magnetic Field EvolutionÉ

Two different theoretical studies of magnetic field evolution


	The generation of small-scale magnetic fields by a turbulent dynamo, and the observational consequencesÉ

	The evolution of active region magnetic fields, driven by observational dataÉ

	É Illustrating 2 different philosophies for using observational data for research in Solar Physics.

First Approach: Exploration Ð this is how most research in Solar Physics is done today


	Examine the data to formulate new ideas about the underlying physical mechanisms
	Construct simple theoretical models that test those ideas and make generalized predictions
	Advantages: Creative and Easy
	Disadvantages: Can lead to multiple, contradictory theories, with few clear tests between them.

Second Approach: ÒPrognosticÓ Modeling


	Incorporate data directly into a theoretical model to predict some other observable phenomenon
	Compare the output of the model with observations, and adjust model assumptions until agreement is achieved.
	Advantages: Is the only basis for a physics-based forecasting model
	Disadvantages: Assumes the physical mechanisms already well-understood; doesnÕt easily allow for change of paradigm
	This approach is more common in Earth Sciences (e.g. atmospheric and ocean sciences)

Slide 5

The Transport of Magnetic Flux


	The effects of convective turbulence on initially Òneutrally-buoyantÓ active
	region-scale magnetic structures with field strengths near the cohesion limit:

Slide 7

The Turbulent Dynamo

Slide 9

Slide 10

The Turbulent Dynamo and X-ray Flux in Stars

Can we develop a physics-based model of magnetic field evolution that could predict solar flares and coronal mass ejections?


	Since these phenomena are almost certainly magnetically driven, they must incorporate magnetic field observations (line-of-sight and vector magnetogram data)
	Governing evolutionary equations believed to be (pretty) well described by 3-d magnetohydrodynamics (MHD)
	How does one incorporate the observations (the A-word) into an MHD model? Solving this problem is absolutely critical if we ever want to have a predictive (forecasting) model of space weather.

To what extent can we determine the flows in an active region by observing changes in the magnetic field at the photosphere?

Determining the physically consistent flow field is an essential part of this problem


	This is the subject of the Òvelocity shootoutÓ component of WG1 at this workshop
	Shooters: Longcope, Georgeolis, Kusano, Welsch

The LCT, FLCT techniques


	LCT schema in use today have one central idea: proper motions of features in 2 successive images - whether G-band filtergrams, Ha images, or photospheric magnetograms - separated in time by Dt are found by maximizing a cross-correlation function, or minimizing an error function between sub-regions of the images. The concept is generally attributed to November & Simon (1988).
	The FLCT method (which we developed) is similar. For each pixel, we:
		multiply each of the 2 images to be correlated by a Gaussian, of width s, centered at that pixel; crop the resulting altered images 1 and 2 by chopping the insignficant parts of the images;
		compute the cross-correlation function between the two cropped images using standard Fast Fourier Transform (FFT) techniques;
		use cubic-convolution interpolation to find the shifts in x and y that maximize the cross-correlation function to one of two precisions (chosen by the user), either 0.1 or 0.02 pixel; and
		use the shifts in x and y and Dt between images to find the intensity features' apparent motion along the solar surface.

Example of FLCT applied to NOAA AR 8210 (May 1 1998)

The Demoulin & Berger Interpretation of LCT


	Degeneracy: Motions parallel to B do not directly affect apparent motion of magnetic features.
	Apparent horizontal motion U_LCT is from a combination of horizontal motions and vertical motions acting on non-vertical fields.

The Ideal MHD Induction Equation


	How can we ensure that LCT-determined velocities are physically consistent with the magnetic induction equation?
	Only the z-component of the induction equation contains no unobservable vertical derivatives:

ILCT Ð Use LCT to constrain solutions of the induction equation


	Take 2D divergence, then z-component of the curl of this definition, and make the approximation that U=U_LCT:

Apply ILCT to IVM vector magnetogram data for AR 8210


	Vector magnetic field data enables us to find 3-D flow field from ILCT via the equations shown on slide 5. Transverse flows are shown as arrows, up/down flows shown as blue/red contours.

Must have some kind of initial conditions:


	Use Force-free field to initialize field in computational volume

Time dependent boundary conditions for the coronal MHD code


	Write a separate dynamical code for determining boundary evolution (about 4 zones deep)
	Solve magnetic induction, and continuity equations
	Substitute ILCT-derived flow field for the momentum equation (this provides the data driving)
	Fully couple the coronal MHD code to the boundary code

Illustration of 2 coupled codes


	Transparent planes at the bottom illustrate the boundary evolution code

Toward a Data-driven Simulation of AR-8210
4 hrs of solar time, corresponding to the vector magnetogram time sequence

Data Driven Simulations:
Plans for future


	Develop better MHD solution algorithms that are optimized for conditions in the solar atmosphere
	Find longer vector magnetogram sequences so can run simulation longer
	Greatly expand the simulation box size; extend to spherical chunks
	Include a shearing of v_x, v_y in z direction in boundary code to account for observed changes in B_x and B_y.
	Experiment with using LOS magnetograms