Modeling Active Region Modeling Active Region Magnetic Fields on the Magnetic Fields on the

SunSun

W.P. Abbett W.P. Abbett Space Sciences LaboratorySpace Sciences Laboratory

University of California, BerkeleyUniversity of California, Berkeley

Motivation for Detailed Studies of Active Region Motivation for Detailed Studies of Active Region Evolution:Evolution:

• The ability to predict “space weather” is becoming increasingly important as our society becomes more reliant on ground and space-based technologies that are susceptible to a flux of energetic particles, or fluctuating ionospheric currents.

• Examples of activities disrupted by solar and geomagnetic events: satellite operations, navigation (GPS), manned space flight, polar flights, power distribution networks, HF radio and long-line telephone communication, and pipeline operations.

Motivation for Detailed Studies of Active Region Motivation for Detailed Studies of Active Region Evolution:Evolution:

• CMEs are magnetically driven and many are believed to originate in the low solar corona in and around active region magnetic fields.

• Coronal Mass Ejections (CMEs) are among the primary drivers of space weather.

LASCO C3 Coronagraph: CME of Jan. 15, 1996LASCO C3 Coronagraph: CME of Jan. 15, 1996

And now, a bit closer to the Sun…And now, a bit closer to the Sun…

• In the low corona (where the CME is initiated), magnetic flux is “frozen” into the plasma, and the field is essentially “line-tied” to the photosphere; as such, it evolves in response to changes to the Sun’s photosphericevolves in response to changes to the Sun’s photospheric magnetic fieldmagnetic field .

TRACE 171 Movie of the X-class flare producing NOAAactive region 9906 on April 21, 2002.

TRACE 171 Movie of the corona over a rotating sunspotin NOAA active region 9114 on August 9, 2000.

• Thus, understanding the evolution of the vector magnetic field at the photosphere is a crucial component of the effort to forecast and interpret space weather events.

Active Region Magnetic Fields at the PhotosphereActive Region Magnetic Fields at the Photosphere

• Active regions appear as bipoles, which implies they are the tops of large Omega-shaped loops which have risen through the solar convection zone and emerged into the photosphere.

• On average, bipoles are oriented nearlyparallel to the E-W direction (Hale’s law1919) indicating that the underlying field geometry is nearly toroidal.

• Hale’s law persists for yearsthrough a given solar cycle,thus the toroidal layer mustlie deep in the interior in aregion relatively free fromconvective turbulence.

Full disk MDI magnetogram courtesy of Y. Liu

Cauzzi et. al. (1996)

A Simple Picture of Active Region Magnetic FluxA Simple Picture of Active Region Magnetic Flux

• A toroidal flux layer persists near the “tachocline” --- where the turbulentconvection zone transitions into the stable radiative zone.

• Portions of the toroidal layer succumb to a dynamic or magnetic instabilitycausing a magnetically buoyant flux rope to rise through the convection zone.

• The top of the loop emerges from the high-beta plasma of the convection zone, through the many pressure scale heights of the photosphere, chromosphere and transition region, into the low-beta, tenuous, energetic corona.

Testing this Simple Picture Using Numerical Testing this Simple Picture Using Numerical ModelsModels

• Only recently has it become possible to routinely run 3D numerical simulations of the sub-surface evolution of active region-scale magnetic fields.

• In particular, a numerical solution of the system of MHD equations in the anelastic approximation allows for an exploration of the physics of active region magnetic fields in the solar interior. We can address questions such as:

What is the role of fieldline twist, solar rotation, and field strength on the dynamics of flux emergence? Can simple models accurately represent the physics of sub-surface magnetic structures?

From Abbett et. al. (2000) MDI Magnetogram from Cauzzi et al (1996)

Modeling Magnetic Fields in the Solar Convection Modeling Magnetic Fields in the Solar Convection ZoneZone

Is an interface dynamo necessary to generate active region-strength fields, and can magnetic flux be transported back to the base of the convection zone in the absence of an interfacelayer?

Can magnetic flux tubes remain cohesive during their ascent through the turbulent convection zone? Can we determine how strong the magnetic field must be at the base of the convection zone to be consistent with the ~1000G fields observed at the photosphere?

From Abbett et al. 2003

Coupling Photospheric Fields to a Model Corona: PFSSCoupling Photospheric Fields to a Model Corona: PFSS

Given a representation of the magnetic field at or below the photosphere,can we characterize the magnetic topology of the corona?

• One method is to assume that the vector magnetic field can be derived from a scalar potential --- this assumption coupled with the requirementthat the field be radial far from the photosphere (at the “source surface”),is the basis of the potential field source surfacepotential field source surface (PFSS) extrapolation.

PFSS models of Li & Luhmann

Coupling Photospheric Fields to a Model Corona: FFFCoupling Photospheric Fields to a Model Corona: FFF

• Another method is to assume that the magnetic field is in a force-freeforce-freeequilibrium (i.e. j X B = 0). This type of extrapolation may providean improved representation over the potential field model, particularlynear dynamic active regions.

FFF calculations from Y. Liu (2003)

Coupling Photospheric Fields to a Model Corona: MHDCoupling Photospheric Fields to a Model Corona: MHD

• Another method --- the most computationally expensive technique so far --- is to numerically solve the system of ideal MHD equations.

Why go to all that trouble? MHD models are able to describe thecontinuouscontinuous topological evolution of the corona, thus providing a meansto e.g. follow the dynamic evolution of the open field, and to investigate proposed CME initiation mechanisms.

To drive an MHD model corona, on must first overcome a set ofunique challenges:

1. Unlike PFSS and FFF extrapolations, MHD models require informationabout the flow field at the photospheric boundary --- and that informationis generally not available.

2. To resolve individual active regions while simultaneously following theglobal evolution of the corona requires the implementation of an adaptive,non-uniform mesh.

A First Attempt: A First Attempt:

From Abbett & Fisher (2003)

How Force-free are Emerging Structures?How Force-free are Emerging Structures?

The emergence of modestly twisted magnetic flux tubes into the model corona.

The color table is a measureof how “force-free” the atmosphere is --- the bluer the color the more the current density is aligned with the magnetic field lines.

The difference in “tilt angle”between overlying field linesand those close to the lower boundary reflects the distributionof twist present in the flux ropebelow the surface

From Abbett & Fisher (2003)

Another approach:Another approach:

Magara & Longcope (2003) and Fan (2001) simulate the emergence of highly twisted flux tubes positioned just belowjust below the photosphere --- informationresulting from the buoyant rise of the tube through the entirety of theconvective envelope is lost; however, there is no need to implement an interface boundary.

A Few Caveats:A Few Caveats:

• Note that treating the visible surface as a simple 2D layer or thin 3D slab clearly simplifies the physics of these layers.

Since the goal is not to directly simulate coronal emission, and since we must make the problem computationally tractable at active region spatial scales, we do not treat (in detail) the physics of radiative transport and thermal conduction along field lines. An example of a more “realistic” calculation(Bercik, Stein, Nordlund 2002):

Using Observations to Drive a MHD Model Using Observations to Drive a MHD Model CoronaCorona

• AR8210 is a very complex,CME producing active region.

• Though complex, AR8210 is a MURI candidate event --- mainly because the vectordata at the photosphere isof high quality.

• Can we obtain a flow field that is consistent with theobserved evolution of the Magnetic field?

A high-cadence sequence of MDI vector magnetograms of A high-cadence sequence of MDI vector magnetograms of AR8210 on May 1,1998 (S. Regnier, R. Canfield)AR8210 on May 1,1998 (S. Regnier, R. Canfield)

New Velocity Inversion Techniques:New Velocity Inversion Techniques:

I+LCTI+LCT (Welsch & Fisher) --- Uses acombination of Local CorrelationTracking (LCT) on magnetic elementsalong with the MHD induction equation to obtain a self-consistent flow field.

MEF (Longcope & Klapper) ---constrains the system by minimizingthe spatially integrated square of the velocity field.

• A flow field that satisfies the vertical component of the induction equation is not necessarily unique!

Testing Velocity Inversion TechniquesTesting Velocity Inversion Techniques

Examples of using ANMHD to test velocity inversion techniques.

Putting it all Together (A Work in Progress):Putting it all Together (A Work in Progress):

• I+LCT and MEF provide means to generatevelocity fields from a sequence of vector magnetograms that can be used to updatethe lower boundary layers of an MHD model corona.

Additionally, MHD models require an initialstate, one that

1. Matches the transverse components of the magnetic field observed at the photosphere, and

2. Accurately represents the magnetic topology of the initial atmosphere

Options: PF and FFF extrapolations.

The Global Topology of AR8210The Global Topology of AR8210

Local calculations can go onlyso far! • If CME initiation mechanisms depend on the magnetic topology of the global corona, local calculations performed in isolation may not tell the whole story

Modeling the evolution of open fieldin the global corona is a critical component in the effort to understandand predict space weather --- in fact, recent studies have shown that Active regions are a significant source of the open field in times of heightened solar activity.

Yohkoh SXT reverse image of a trans-equatorial loop emanating from AR8210.

Resolving Active Regions Embedded in a Global Resolving Active Regions Embedded in a Global CoronaCorona

Using the domain decomposition and adaptive mesh refinement toolPARAMESH (MacNeice et. al. 2000) to resolve active region magnetic fields in a global environment:

Toward Tetrahedral MHD/AMR:Toward Tetrahedral MHD/AMR:

Conclusions:Conclusions:

“Sun to Mud” Models

• There is community-wide interest in the development of end-to-end coupled numerical models to be used as operational, real-time space weather forecasting tools.

• The least understood component of the Sun-earth system is the solaratmosphere --- where solar storms originate. To be successful, and to progress beyond idealized calculations, each of the above multi-agency, coordinated efforts ultimately will requirerequire an observationally-based solar model that can routinely provide real time, physical boundary conditionsfor their models.