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Using Electric Fields to Drive Simulations of the Solar Coronal Magnetic Field

Using Electric Fields to Drive Simulations of the Solar Coronal Magnetic Field. George Fisher 1 , Mark Cheung 2 , Marc DeRosa 2 , Maria Kazachenko 1 , Brian Welsch 1 , Todd Hoeksema 3 , Xudong Sun 3 , and the SDO vector magnetogram team 1 Space Sciences Lab, UC Berkeley

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Using Electric Fields to Drive Simulations of the Solar Coronal Magnetic Field

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  1. Using Electric Fields to Drive Simulations of the Solar Coronal Magnetic Field • George Fisher1, Mark Cheung2, Marc DeRosa2, • Maria Kazachenko1, Brian Welsch1, Todd Hoeksema3, Xudong Sun3, and the SDO vector magnetogram team • 1Space Sciences Lab, UC Berkeley • 2Lockheed Martin Solar and Astrophysics Laboratory • 3Stanford University • SHINE Meeting ~ 25 June 2012 ~ Maui, HI

  2. Electric Fields at the photosphere provide critical information for driving time-dependent models of the solar magnetic field • We illustrate this concept by using one of the simplest possible magnetic field models possible for the solar corona, the magneto-frictional model.

  3. Magnetofrictional Scheme • Solve • Velocity proportional to Lorentz forceimplemented via , where is a frictional coefficient that determines relaxation timescale • Was originally implemented in a solar context by Yang, Sturrock & Antiochos (1986) and Craig & Sneyd (1986)

  4. Magnetofrictional Scheme • Our implementation evolves vector potentialvia (guarantees and also allows relative helicity to be calculated easily) • Evolved forward in time using explicit 2nd-order derivatives, spatial discretization on a Yee (1966) grid • Follows scheme pioneered by van Ballegooijen, Priest & Mackay (2000)

  5. Magnetofrictional Scheme • Boundary conditions specified in terms of vector potential at lower boundary; sides and top boundaries are open • We take the approach of using a temporal sequence of magnetogram data to drive the simulation • Others have also used a time-dependent Boundary Conditions with a MF scheme, e.g., Yeates, Mackay & van Ballegooijen (2008)

  6. Data-driven Modeling of AR 11158 • Evolving magneto-frictional scheme enables the construction of time-dependent models of active region coronae • Modeled fields respond to photospheric driving and energy inputs • Allows measurement of buildup of free energy and helicity in response to such driving • AR 11158 on disk from 2011 February 10 – 19 or so

  7. Lower Boundary • Need to determine at lower boundary • Here, we use that were determined by and using methods of Fisher et al. (2012), which make use of time series of Doppler and vector field measurements from HMI. See poster by Kazachenko et al. at this meeting. • AR11158 produced an X2.2 flare on 2011-02-15 01:45

  8. Electric Field Inversion We decompose the partial time derivative of the magnetic vector field B into two unknown functions, the Poloidal and Toroidal potentials. This is the origin of the name Poloidal-Toroidal Decomposition, or PTD. Each of the three variables of the right-hand equation above obeys a 2-d Poisson equation, which depends directly on the magnetic data: See Fisher et al. 2010 (ApJ 715, 242)

  9. Electric Field Inversion Faraday’s law says: From which we infer that: The potential function(s) are very important! Without the potential functions, the PTD electric field does a poor job of reconstructing the actual field in MHD simulation test cases. Currently, we include the following terms in our inversions: The second and third terms represent non-inductive contributions from Doppler shifts, and pattern-motions (derived from e.g. FLCT or DAVE), respectively, from which the inductive contributions have been removed. The fourth term is used to enforce the condition EB=0. See Fisher et al. 2012, Sol. Phys. 277, p153 for details. More information about these techniques can be found in Maria Kazachenko’s poster in the 2012 SHINE meeting.

  10. Caveats and cautions • Consider these as numerical experiments • No momentum or energy equation solved (no concern for heating, radiative losses, etc.) • Cartesian domain (curvature ignored) • Initialized using potential field

  11. AR 11158 • HMI line-of-sight magnetograms, remapped onto a co-rotating Cartesian reference frame

  12. AR 11158 model views from sides top view • Emissivity of fieldlines is prop. to

  13. AR 11158 model top view views from sides • Emissivity of fieldlines is prop. to

  14. AR 11158 model top view views from sides • Emissivity of fieldlines is prop. to

  15. AR 11158 model total energy • Free energy of order 15% or 20% of potential field pot’l energy free energy

  16. AR 11158 model • R X2.2 flare

  17. Summary • Magnetofriction provides a way to perform numerical experiments of data-driven coronal magnetic field evolution • Applied scheme to AR11158, using time series of HMI Doppler and vector magnetogram data to drive the model • Can study buildup of free energy and helicity in the model and the possible ejection of flux

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