LargeScale Inflows Around Active Regions: Consequences on Surface Magnetic Field Dispersal

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Large-Scale Inflows Around Active
RegionsConsequences on Surface Magnetic Field
Dispersal

• Marc DeRosa, Karel Schrijver
• ? ? ?
• Lockheed Martin Solar and Astrophysics Laboratory
• Palo Alto, CA
• ? ? ?
• 9 November 2006
• LoHCo Meeting, Boulder, CO

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Solar Surface-Flux Evolution

• Appearance and evolution of surface-flux provides
  many constraints on (and many clues toward
  understanding) the solar dynamo.
• All scales are important! For example, active
  regions would evolve differently if magnetic
  carpet were absent.
• MDI has enabled detailed studies of the evolution
  of surface flux (especially small-scale ephemeral
  population). Can we build an idealized model
  based on their characteristics? What can we
  learn about the dynamo from such models?

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Evolving Surface-Flux Transport Model
Research areas Dynamo, alpha effect 3D
magnetoconvection Global field-flow
coupling Sub-resolution dynamics 3D flux transport

• This model includes
• active to ephemeral region flux, atomic
  description (no grid)
• bipole strengths, emergence latitudes, tilts
  chosen from empirically determined statistical
  distribution functions
• nonlinear magnetoconvective coupling nesting,
  andflux-dependent dispersal coefficient

Schrijver (2001)
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Consistency Check
cycle maximum
cycle minimum
Schrijver (2001)
model magnetogram
(Mx cm-2)

• Histograms of model flux match histograms of flux
  observed from magnetograms very well.

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Model Activity Cycles

• Formation of polar caps occurs naturally, arising
  from the tilt of emergent bipoles, combined with
  the convective dispersal and poleward meridional
  flows.

pure simulated Sun(from 40 corotating frame)
Schrijver (2001)
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Model Activity Cycles
for fun simulated star that is 30? more active
than sun
pure simulated Sun(from 40 corotating frame)
Schrijver (2001)
Schrijver (2001)
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Historical Sunspot Cycles
Schrijver, DeRosa Title (2002)
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Model Surface Flux
(1022 Mx)
Schrijver, DeRosa Title (2002)
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Net Flux Poleward of North-60
(1022 Mx)
Schrijver, DeRosa Title (2002)
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What If Flux Decayed with a Half-Life Set to 5
yrs?
(1022 Mx)
Schrijver, DeRosa Title (2002)
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Possible Solution to the ConundrumActive Region
Inflows

• Helioseismic inferences of subsurface and
  near-surface flows indicate that many active
  regions seem to be surrounded by horizontal
  inflows on the order of 20-50 m/s very near the
  surface.
• Additionally, there is evidence that the
  magnitude of the inflow velocities scales with
  the amount of flux contained within the active
  region.
• What effects do these inflows have on the
  transport and evolution of surface magnetic
  fields? Can these inflows help to solve the
  polar-flux paradox?

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Measurements of Active Region Inflows

• Below are shown surface flows inferred from
  f-mode time-distance analysis for part of CR1949
  (in 1999), as an example of this phenomenon.

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Measurements of Active Region Inflows

• Inflows surrounding active regions are also found
  in ring-diagram analyses of active regions.

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What effects can these active-region inflows have
on surface fields?

• Inflows affect the appearance and evolution of
  active regions.
• Inflows affect the amount of flux transported
  poleward during each sunspot cycle.
• Polar-cap flux is the source of much of the
  heliospheric field (especially during solar
  minimum).
• Polar-cap flux might eventually be recycled into
  the convection zone, and appear as emergent flux
  during future sunspot cycles.

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MDI Assimilation Model
Schrijver DeRosa (2003)
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Adding Inflows to the Model

• Model inflows scale with the gradient in absolute
  flux density, after 15? smoothing v ??? ?? ?
  .
• Model inflows are time-invariant.

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Adding Inflows to the Model
MDI assimilation model
? ? v 0 m/s
DeRosa Schrijver (2007)
? ? v 10 m/s
? ? v 30 m/s
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Inflow Model Results

• For v ??? ?? ? and a range of values of ? and
  ?, we compute correlation coefficients for
  synoptic maps of our assimilation model run with
  and without the active-region inflows.
• Results for 6-rotation intervals are averaged
  over ten starting times 1996.8, 1997.3, 1997.8,
  1999.3, 1999.8, 2000.3, 2000.8, 2001.3, 2001.8,
  2002.3.

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Decorrelation Rates

• Dashed line No inflow model
• Solid line Best-fit inflow model (average of
  ten runs, shown by diamonds)
• Dotted line Assimilation model

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Relative correlations

• Correlations relative to the assimilation model
• C 0.95
• C 0.90
• Dotted contours 90th percentile of flow norm
  (m/s)

ß
a
(darker colors indicate better correlation)
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Concluding Remarks

• Inflows faster than 10 m/s are needed to resolve
  the polar-flux conundrum. However,
• Inflows faster than 10 m/s markedly affect the
  evolution of active-region flux. The flows are
  either not as fast, not as persistent, or not
  uniformly converging around the active region as
  modeled here (or some combination of all three).
• We have assumed that active-region inflows and
  magnetic fields couple as efficiently all other
  observed surface flows.
• We have also assumed that the inflows are not
  dependent on the evolutionary stage of the active
  region. (The time dependence of the measured
  inflows is not well known.)
• Maybe too there is a selection effect in the
  helioseismic analyses? Looking forward to
  results of forward modeling efforts