Chip Manchester, Fang Fang, Bill Abbett, Bart van der Holst

Patterns of Large-Scale Flux Emegence

Outline Much more advanced simulations of

flux emergence in a realistic convection zone and corona (Abbett 2007)

Confirm earlier simulations and show that shear flows driven by the Lorentz force are extremely robust.

Shear flows dominate the transport of magnetic energy from the convection zone into the corona

Lorentz-force driven shear flow are a mechanism by which energy builds up for CMEs, flares, filament eruptions

Emergence of a 3D Flux Rope in a Simple Polytropic Atmosphere

Fan 2001, Manchester et al. 2004

The Lorentz Force Drives the Shearing!!

Shearing motions transport Bx flux into the expanding portion of the flux rope and tends to return Bx to constant values along field lines to restore force balance

Current Sheet Formation

Shear Afven waves cause axial flux to accumulate where the rope expands

The sheared core lifts off and erupts forming a current sheet

In Parker’s picture, localized expansion along the length of the rope, causes torsional Alfven waves that transport azimuthal flux

Cosmical Magnetic Fields 1979

Flux Rope Eruption Rope eruption occurs with the passage of a

shear Alfven wave

Fang et al. ApJ 2010 714, 1649

Separation of Flux Rope at Sigmoid Current Sheet

To the left, an iso-surface of current density and field lines are shown over the photosphere colored to show Bz. Right: Eruption of flux rope into the corona.

Larger Scale Simulations Large simulation recovers similar results

Realistic Simulation of Flux Emergence

Model from upper convection zone to corona Abbett 2007

Parameterized radiative losses

OPAL EOS Magnetic Flux

proportional coronal heating

Fang et al. ApJ 2010 714, 1649

Realistic Convection Zone Model

vertical

velocity shown in gray scale

Emphemeral Region Scale

1018-19 Mx

Magnetic Field Evolution at the Photosphere

Development of sheared field at the photosphere

Comparison of EIS Shear Velocity

The image on the left is an EIS Doppergram of AR10930 observed December 2006 over the western limb of the Sun. The image on the right shows shear flows ½ driven by the Lorentz ½ siphon flow parallel to B

Magnetic Pore Scale

6x1020 Mx 30Mm scale

Flow Patterns are Much More Complicated

White line = PIL Color = Ux

Photospheric Energy Flux

Total energy from horizontal flows is 1x1030 ergs 1% necessary for CMEs and X-class flares

Manchester et al. 2004 Fang et al. 2010

Magnetic Shear in AR6982

Falconer 2001 JGR 106, 25185

MHD Code: BATSRUS(SC/EE/IH/GM)

Block Adaptive Tree Solar-wind Roe-type Upwind Scheme Conservative finite-volume method Shock-capturing Total Variation Diminishing schemes Explicit, implicit & explicit/implicit time stepping Semi-relativistic MHD equations Splitting the magnetic field into B0 + B1

Various methods to control the divergence of B AMR & data structure

Adaptive self-similar blocks Octree data structure

Parallel implementation Fortran-90 with MPI Near-perfect scaling to >1500 PEs (explicit time-stepping) Good scaling to ~256 PEs with implicit time-stepping Highly portable (SGI Origin, Altix, Compaq, PC clusters,

X-serve clusters, etc)

SWMF Performance

Key algorithms to achieve this speed: Concurrent/mixed execution of components. Adaptive grid in BATSRUS (SC, IH and GM). Implicit time stepping in SC/Heat Conduction.

Global Magnetosphere

Ionosphere Electrodynamics

Inner Magnetosphere

Radiation belts

Solar Energetic Particles

Upper Atmosphere

Solar Corona

Eruptive Event Generator Inner

Heliosphere

The SWMF is freely available at http://csem.engin.umich.edu

Polar WindPlasmasphere

Photosphere to Corona

SWMF

Conclusions Flux emergence from a realistic convection zone into

the corona. Shearing mechanism is extremely robust and persists

even in a granular convection zone Shear flows are slower and more structured than in

the idealized polytropic model. Shear velocities are in better agreement with

observations of the photosphere and low corona. The large scale pattern of magnetic shear in active

regions is found, which increases with proximity to the neutral line

Transport of magnetic energy from the convection zone to the corona is dominated by horizontal flows

No Eruptions yet. Scaled to the size of an AR, shear flows would easily provide 1032 ergs.

Beginning simulations of 60x90 Mm & 1022 Mx

Thank You

Recent CME Models That Impose Shear

Magnetic Arcade Models Imposed shearing of foot points with magnetic

reconnect at the base of the arcade (Amari et al. 2003 ApJ 595, 1231 )

Break-out model: Imposed shearing motions and reconnection above the arcade in a quadruple system (Antiochos 1999 ApJ 510, 485)

Velocity and Magnetic Shear in AR 10486 Source of the Halloween Events

Velocity Shear Yang et al. 2004, ApJ 617 L151, Magnetic Shear Liu et al. 2005, ApJ 622, 722