The magnetic flux budgetof the polar regions
Karel Schrijver
Lockheed Martin
Advanced Technology CenterSources of polar-cap fields
Local sources (mixed-polarity field): Proximate: High-latitude ephemeral
regions (here: all small spotless
bipolar regions).
 Ultimate: Local dynamo source or
global dynamo decay?

Distant sources (large-scale field): Proximate: All bipolar regions on thesolar surface, dominated by largest
regions near the equator.
 Ultimate: Global dynamo

Sinks of polar-cap fields
Local sources (mixed-polarity field): Subduction
 (Near-)surface fragmentation anddissipation
 Expulsion

Distant sources (large-scale field): Subduction
 Interaction with the small-scale field

What do horizontal fields tell us about all this?
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“Local” sources: where/how do ephemeral regions form?
Ephemeral regions––––

form a continuous extension of the AR frequency-flux spectrum, but vary much less (andperhaps in anti-phase) with ARs.
display a butterfly pattern that broadens with decreasing flux.
have an increasingly random orientation relative to the E-W direction with decreasing size.
are less frequent in environments with larger flux imbalance (fewer in “unipolar” regions and thus indirectly fewer under coronal holes). Effect not yet measured for polar regions.

N.B. Stellar observations show that the least active stars have at most internetwork-level emissions.
Instrument
cutoffEphemeral
regions

Activeregions

Composite distribution function of bipoles
emerging on the Sun per day, per flux
interval of 1018 Mx. The distribution for
active regions (defined as regions larger
than 2.5 deg2) taken from the literature(K. Harvey, 1994) varies by about a factorof 8 through a typical cycle; the extremesof that variation bound the dark shaded
area on the right. The much smaller
variation for the smallest ephemeral
regions—shown by the darkest shading—is likely weakly in antiphase with thesunspot cycle; full histograms are shownfor 1997 October (black) and 2000 August(gray). The turnover below 1018 Mx likely
reflects the detection threshold of MDI.
The lightly shaded area between thesmallest ephemeral regions and the active
regions is an approximation that still
awaits confirmation. Figure fromHagenaar et al. 2003

2000
2001
2002
2003
2004
2005

From Hagenaar et al. (2008; ApJ 678, 541)
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Simulations of activity: surface-flux transport

Simulated “Sun” from 40°N

B

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Polar fields in an assimilation-simulation modelN









5

Much of the time, polar
fields consist of strongfield “unipolar” network
field, and horizontal
internetwork field.
Large-scale polar fields
build up as a result oflarge-scale surface flux
transport.
Role of ephemeral
regions and 3D transportremain to be determined.
Shown are polar views
from a movie on thenext page …

1SN

2

3

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Polar fields in an assimilation-simulation modelMovie showing 12 years (@12h steps) of hybrid SOHO/MDI andassimilation flux-dispersal model:

See http://www.lmsal.com/forecast for ongoing daily assimilation.
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Polar fields in an assimilation-simulation modelMovie showing 30d (@6h) of hybrid SOHO/MDI and assimilation fluxdispersal model for polar regions (within 10 degrees of pole). This run
does not incorporate the Hagenaar et al. (2008) findings.

Movie at 1” pixels; gray scale saturation at 1 kG.
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Modeling surface flux dispersal
The diffusion approximation:
If field is always normal to the surface, the MHD induction equation yields adiffusion equation for a signed scalar, subject to:• Flux emergence• From AR to ER; butterfly pattern; tilts; clustering; ….
• Diffusion by the (super-)granular random walk• Magnetoconvective coupling; nonlinear behavior• Meridional advection• Weak flow, close to detection limit• Differential rotation
Yields a fair quantitative approximation of flux behavior on large scales andfor long time scales. The role of ‘intranetwork field’ is unclear…
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Sensitivity of polar fields to component processes
A few sample experiments:

baseline model:
simulated Sunvary diffusion
coefficient(DIFF)

truncate emergence
spectrum(EMER)

vary linearity ofdiffusion(LIN)

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Sensitivity of polar fields to component processes- polar view From J. Cirtain.

baseline

EMERDIFFEMERDIFFcycle phaseA

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Sunspot cycles: history and approximation
Successive cycles often differ strongly:

B

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Polar-cap (>60°) absolute flux

(1022 Mx)

And the polar-cap flux “capacitor” does not simply
alternate in strength or even polarity:

No polarpolarity
inversion?

B

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What if flux “decayed” by, e.g., 3D transport?
The polar-cap flux behavior signals something is missing
from our understanding:[Schrijver et al. 2002 (ApJ 577, 1006)]

B

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Alternative: modulation of flux transport
Changing meridional advection [Wang et al. 2002 (ApJL 577, 53)],
can cause cycle strength and advected polar flux to be nearly
the same from cycle to cycle:

B

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Detailed modeling of cycle 23
The flux dispersal model can be combined with observational data:• Direct insertion of magnetic fluxes from SOHO/MDI or SOLIS;• Use data only within ~60 degrees from disk center• Initial configuration: from ‘best-fit’ run since 1643

N.B. In this model the high-latitude field results from advection of flux fromthe assimilation zone between ±60 degrees in latitude.

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Detailed modeling of cycle 23
Simulations (color)
compared to (black)assimilation run.

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Axial dipole moments: obs. and model
Whole Sun

Polar regions
reference level3 runs of reference model
Polar regions

Whole Sun

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Axial dipole moments and meridional flow
Axial
Whole Sun

Lower-latitude gradient

A steeper/shallower meridional
flow profile near the equator
weakens/strengthens the polar caps
and delays/hastens polarity
reversal.

D

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Detailed modeling of cycle 23
Axial
Whole Sun
Assimilation

Simulation

Polar regions
Assimilation

Simulation

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‘Best-fit’ meridional flow profile
tracking
Komm et al.

‘reference curve’
Van Ballegooijen‘best fit’

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Conclusions:H21The surface flux dispersal model reproduces large-scale properties ofthe solar photospheric field to within current uncertainties. The moststringent test is based on a comparison with decade-long MDI records.

Modeling based on historical records suggest something is missing fromour surface flux transport models: 3D diffusive transport appears
unavoidable. Modulation of meridional flow has been observed, but notdirectly over multiple cycles. Perhaps tracers like limb faculae (Sheeleyand Warren 2006) or historical filament observations can be used to infer
any meridional flow changes.

Modeling of the current cycle suggests changes in average strength or
profile of the meridional circulation from cycle to cycle, but themagnitude may be close to observational uncertainties.

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Understanding the polar flux budgetTo understand the net polar-cap flux requires–long-term (>11 y), continuous (<1 min.), highly-sensitive (<1 Mx/cm2)
measurements of
 the evolving full-sphere vector-magnetic field, and the evolving meridional advection, in comparison with
 a high-fidelity 3-D flux-transport model;–and a high-fidelity, high-resolution convective-MHD model of the Sun.

To understand mixed-polarity component of the (polar) quiet
Sun requires–

detailed study of statistical properties of the ensemble of ephemeral
regions, as function of cycle phase and environment (flux balance, latitude, …);–22

and a high-fidelity, high-resolution convective-MHD model of the Sun.

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Issues for a science definition exercise:––––––––Is there really a significant and important problem with the polar flux budgetthat we must (and can) address at high latitudes, or do observations of lower
latitudes suffice to learn what the Sun can tell us?
Are the (high-latitude) surface phenomena telling enough about the deepseated field?
How would we differentiate local from global dynamo action, and why arehigh latitudes important to answering that question?
High-fidelity modeling of field transport is important for definition of themission and critical for the interpretation of the results.
Polar-field reversal is a multi-year process, starting in cycle-rise phase.
Telemetry will be an important limitation: minute-cadence, high-resolution
magnetograms appear to be needed, exceeding telemetry available by >10x-100x[TBD] for field measurements only.
Measurements depend on resolution – impact of elliptical orbits on science
return TBD.
“Calibration” dependence on latitude (on Sun and in orbit) will need to be ahigh priority [can probably be addressed now as function of longitude].