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“Insights” on Coronal Hole Magnetic Fields From a High-Order PFSS Model

D.J. Bercik and J.G. LuhmannSpace Sciences Lab, UC Berkeley

FEW 2011, Aug 24

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Introduction

• The two most viable models of solar wind energization both ultimately appeal to convective granular flows– “wave/turbulence” models (e.g. Hollweg 1986; Matthaeus et al. 1999;

Cranmer et al. 2007): energy is in the form of Alfvén waves driven by the buffeting of open flux by granular-scale convection

– “reconnection/loop-opening” models (e.g. Axford & McKenzie 1997; Fisk et al. 1999; Schwadron & McComas 2003; Fisk & Zurbuchen 2006): energy is released and mass and momentum are transferred by means of stochastic, intermittent reconnection between open and closed magnetic flux systems, driven by the constant shuffling of small-scale fields by granulation

• Reconnection models are more relevant in the context of flux emergence

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Introduction (2)

• Two approaches that can be taken to investigate these phenomena:– Simulations

• pros: dynamical solution, known physical quantities• cons: large-scale, potentially non-local problem, high resolution

– Photospheric data• pros: it's reality, high resolution• cons: no full-Sun data available, must extrapolate field,

instantaneous solutions• Small scales require high-order extrapolations. As a first step,

need to determine the consequences of this requirement.

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PFSS Model Description

• Uses potential field solution of Wang & Sheeley 1992

• If necessary, interpolate input photospheric data to Gauss-Legendre grid.

• Take the spherical harmonic transform of Br. SHT based on technique from geodesy (Holmes & Featherstone 2002) . Capable of transforms up to order 2700 using double precision.

• Trace stream/field lines. Focus on accuracy*:– High-order adaptive integration– Calculate magnetic field at each integration step

* This is code-speak for “I want my code to run really, really slowly”

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MDI

Lmax = 30

Lmax = 120

Lmax = 480

Lmax = 720

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Input Data

• Choose MDI synoptic map of CR 2068• Represents the conditions on the photosphere and in the

corona typical of the cycle 23 late declining phase and minimum

• Exhibited significant area low-mid latitude coronal holes and a large, complex southern polar coronal hole extension that survived for a number of months in 2008

• Lee et al. (2011) demonstrated that the near-solar minimum EUV coronal hole images and interplanetary flux alike were both most consistent with 1.8 R⊙ source surface for the period leading up to and around the cycle 23 minimum rather than the typically used 2.5 R⊙.

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More T720 examples from CR 1979

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Open Field Areas & FluxesFractions of open area and flux for CR 2068 decrease with cutoff order, but only change by a few percent from order 150 to 720.

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Open Field Boundaries0.25 stream line grid

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Open Field Boundaries0.10 stream line grid

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Open Field Boundaries0.25 stream line grid

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Low-order modes map to the “envelopes” of coronal hole regions. Here T10 stream lines are traced up to source surface. These endpoints are then traced back down to the photosphere with T720 stream lines.

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Footpoint Locations that Intersect the Source Surface Equator

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Footpoint Locations that Intersect the Source Surface Equator

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Footpoint Latitude Separation0.25 stream line grid

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Footpoint Longitude Separation0.25 stream line grid

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Footpoint Angular Separation0.25 stream line grid

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• High-order PFSS models show open field regions to be increasingly fragmented into “swiss cheese” patterns. The holes are often filled by small-scale bipolar flux systems.

• The holes may provide sites for reconnection with surrounding open field. The model also predicts that the surrounding open field expands more radially than open field near the “envelope” boundaries.

• Still need to determine how much altering the height of the source surface affects the results, and any solar-cycle dependencies.

Summary

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