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C. “Nick” ArgeC. “Nick” ArgeSpace Vehicles Directorate/Air Force Research Laboratory

SHINE Workshop

Aug. 2, 2007

Comparing the Observed and Modeled Comparing the Observed and Modeled Global Heliospheric Magnetic FluxGlobal Heliospheric Magnetic Flux

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OutlineOutline

• Overview of the Potential Field Source Surface (PFSS) Model.

• PFSS model results over the solar cycle and comparisons with observations.

• Overview of the Potential Field Source Surface + Schatten Current Sheet Model (PFSS+SCS).

• Comparison of modeled global magnetic flux with in situ observations in and out of the ecliptic.

• Summary

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PFSS Coronal SolutionPFSS Coronal Solution

Derived Coronal Holes (1.0 R)

“Source Surface” or Coronal Field (2.5 R)

Open Field Footpoint

Source Surface

Closed Field Footpoint

Predicted Solar Wind Speed (2.5 R)

MODEL INPUT:MODEL INPUT: Observed Photospheric Field

MODEL OUTPUTMODEL OUTPUT

MODEL OUTPUTMODEL OUTPUT

MODEL OUTPUTMODEL OUTPUT

fs = (R/Rss)2[BP(R)/B

P(Rss)]

V ~ fs-n

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Long-Term Comparison of Observed & Predicted Long-Term Comparison of Observed & Predicted Coronal Hole Sizes & LocationsCoronal Hole Sizes & Locations

Wang et al., Science, 271, p464-469, 1996See also……………….

Neugebauer et al.,1998

Henney & Harvey, 2005

Jones, 2005

de Toma, Arge, and Riley, 2005

Wilcox Magnetograms NSO HE Synoptic Maps

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Long-Term Comparison of Observations and Long-Term Comparison of Observations and PFSS Predictions of Radial IMF StrengthPFSS Predictions of Radial IMF Strength

Spacecraft Measurements

Model Calculation

Wang and Sheeley JGR, 2002

See also … Zhao & Hoeksema, JGR, 1995 Successfully predict Bx over a ~10 year interval using their CSSS model.

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Total (unsigned) photospheric flux varies by Total (unsigned) photospheric flux varies by a factor of ~5-8 over the solar cyclea factor of ~5-8 over the solar cycle

Total (Unsigned) Photospheric Field Flux for Total (Unsigned) Photospheric Field Flux for Three Solar Observatories Over Two Solar CyclesThree Solar Observatories Over Two Solar Cycles

Arge, Hildner, Pizzo, & Harvey, 2002

Sunspot

Minimum

Maximum

See also Wang & Sheeley, 2000 & 2002

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With Selected, Pre-1992 NSO-Kitt Peak Photospehric Field With Selected, Pre-1992 NSO-Kitt Peak Photospehric Field Values Corrected for Known BiasesValues Corrected for Known Biases

Arge, Hildner, Pizzo, Harvey, 2002

Total Open Magnetic Flux for Three Solar Total Open Magnetic Flux for Three Solar Observatories Over Two Solar CyclesObservatories Over Two Solar Cycles

Sunspot

Minimum

Maximum

See also Wang & Sheeley, 2000 & 2002Total (unsigned) Open flux varies by a factor of Total (unsigned) Open flux varies by a factor of 2-3 over the solar cycle2-3 over the solar cycle

Max Max MaxMin Min Min

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Wang & Sheeley, 2002

Relationship Between Solar Dipole and Quadrupole Relationship Between Solar Dipole and Quadrupole Moments and “Open” Flux Over the Solar CycleMoments and “Open” Flux Over the Solar Cycle

Variation of Open flux approximately follows Variation of Open flux approximately follows that of the Dipole strength except near solar that of the Dipole strength except near solar

maximum when Quadrupole also contributes.maximum when Quadrupole also contributes.

nT

Open Flux (nT)

Dipole (nT)

Quadrupole

(nT)

Min Max Min Max MaxMin

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Source Regions of the Open Flux Over the Source Regions of the Open Flux Over the Solar CycleSolar Cycle

Solar Minimum Solar MaximumSource of Open Flux over the Solar CycleWang & Sheeley,

2002

Luhmann et al., 2002

Near Ecliptic Solar Wind Sources

Open Flux Originates Open Flux Originates

- Primarily from polar coronal holes - Primarily from polar coronal holes Near Near MinimumMinimum

- Small, strong-field regions in activity - Small, strong-field regions in activity zones zones Near MaximumNear Maximum

: Lat > 45°

: Lat < 45°

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Fraction of Photosphere with Open FieldsFraction of Photosphere with Open Fields

Sunspot

Minimum

Maximum

Fraction of Photosphere with Open Magnetic Flux

Total Photospheric Magnetic Flux (1014 Wb)

Arge, Hildner, Pizzo, & Harvey, JGR 2002

See also Wang & Sheeley, 2000 & 2002

Fractional area of Fractional area of photosphere with Open flux photosphere with Open flux varies by a factor of ~4varies by a factor of ~4

• 25% 2-3 years before 25% 2-3 years before solar minimum.solar minimum.

• 5-10% near solar 5-10% near solar maximum.maximum.

Smaller variation of Open Smaller variation of Open flux over solar cycle flux over solar cycle explained by explained by

• Offset in the phasing of Offset in the phasing of total open area and |total open area and |BBphotophoto| strength.| strength.

• Fact that < |BFact that < |Bphotophoto|> in |> in

open regions ~ 4 times open regions ~ 4 times smaller during min. than smaller during min. than max. (i.e., ~5G vs. ~20G). max. (i.e., ~5G vs. ~20G).

Wang & Sheeley, 2002

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Percentage of Total Photospheric Flux Percentage of Total Photospheric Flux Open to the HeliosphereOpen to the Heliosphere

(Total Open Flux)/(Total Photospheric Flux)

Total Photospheric Magnetic Flux (1014 Wb)

• 40-50% of total 40-50% of total photospheric flux open photospheric flux open during minimum.during minimum.

• ~10% open during ~10% open during maximum.maximum.

Sunspot

Minimum

Maximum

Arge, Hildner, Pizzo, & Harvey, JGR 2002

See also Wang & Sheeley, 2000 & 2002

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PFSS+Schatten Coronal ModelPFSS+Schatten Coronal Model

Source Surface

PFSS Model

Schatten Current Sheet Model

5 Rs

2.5 Rs

Outer Coronal Boundary

Carrington Longitude

PFSS MODEL (R = 2.5 PFSS MODEL (R = 2.5 RR))

PFSSPFSS++SCS MODEL (R = 5.0 SCS MODEL (R = 5.0 RR))

Model Coronal Field

Carrington Longitude

Magnetic field more uniform using PFSS+SCS model

→ More consistent with ULYSSES Observations

Plot courtesy of Sarah McGregor

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Modeled Open

Flux (NSO)

Year

Tot

al F

lux

(1014

Wb

)Comparison of Modeled Flux Using MWO Comparison of Modeled Flux Using MWO

and NSO Carrington Maps as Input and NSO Carrington Maps as Input

Modeled Open

Flux (MWO)

Solar

Minimum

Solar

Maximum

MWO = Mount Wilson

NSO = Kitt Peak

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ULYSSES finds that r2|Br| is independent

of latitude.

4πr2|Br| “at any latitude provides

an accurate estimate of the

total open flux from the Sun.”

Smith et al. (2001 & 2003)

(At least true near ~1AU?)

Results From ULYSSES Observations Results From ULYSSES Observations

Br

Br

r1

r2

Br

Θ =Heliographic Lat.

Fixed R but different latitudes (Θ)

|Br| (r1,Θ =0°) = |Br|(r1,Θ≠ 0°)

For different R and Θ

|Br|(r1,Θ=0°) r12 = |Br| (r2,Θ≠ 0°) r2

2 = |Br|(r1,Θ≠0°) r12

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Modeled Open

Flux (NSO)

Year

Tot

al F

lux

(1014

Wb

)Comparison of Modeled Flux & Comparison of Modeled Flux &

1AU “Observations” in the Ecliptic1AU “Observations” in the Ecliptic

Modeled Open

Flux (MWO)

Solar

Minimum

Solar

Maximum

“Observed” Flux

Near Earth

16Year

Tot

al F

lux

(1014

Wb

)Comparison of Modeled Flux with In SituComparison of Modeled Flux with In Situ

Observations In and Out of the EclipticObservations In and Out of the Ecliptic

Solar

Minimum

Solar

Maximum

“Observed” Flux

At ULYSSES

Modeled Open

Flux (MWO)Modeled Open

Flux (NSO)

“Observed” Flux

Near Earth

17Year

Tot

al F

lux

(1014

Wb

)Comparison of In Situ Observations Comparison of In Situ Observations

In and Out of the EclipticIn and Out of the Ecliptic

“Observed” Flux

Near Earth

Solar

Minimum

Solar

Maximum

“Observed” Flux

At ULYSSES

Heliographic

Latitude of

ULYSSES

Heliographic

Distance of

ULYSSES

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Summary of Long-Term, Global Behavior of Summary of Long-Term, Global Behavior of Solar and Heliospheric FluxSolar and Heliospheric Flux

Over the solar cycle, Total (unsigned) photospheric magnetic flux varies by up to a factor of ~5-8. Total open/heliospheric magnetic flux varies only by a factor of ~2-3. The smaller variation of heliospheric (compared to photospheric) flux over the solar cycle can be

explained by the Offset in the phasing of total open area and |Bphoto| strength.

Fact that < |Bphoto|> in open regions is ~ 4 times smaller during minimum than maximum (~5G vs. ~20G).

Variation of Open flux approximately follows that of the Dipole strength except near solar maximum when the Quadrupole also contributes.

Open Flux Originates Primarily from polar coronal holes Near Minimum. In small, strong-field regions in activity zones Near Maximum.

The fractional area of photosphere with open flux varies by a factor of ~4, from 25% 2-3 years before solar minimum. 5-10% near solar maximum

The percentage of total photospheric flux open to the heliosphere varies from 40-50% during minimum. ~10% during maximum.

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1) From 1971-2001 the PFSS model reproduces the observed radial magnetic field strength near Earth relatively well (overall).

- Some notable exceptions (e.g., ~1984-1990).

2) From 1990-98, the PFSS+SCS model open flux results agree reasonably well with observations near Earth but underestimate the observed values by as much as 30-40% after that.

• Magnetic field data from two different solar observatories are used as model input.

• Agree with each other rather well.

• Observations and model results appear to be converging again.

3) Compared the total “open” flux derived from in situ measurements made near 1AU with those from the ULYSSES spacecraft for the period 1990 to present.

Fluxes derived from near Earth observations differ significantly from those calculated using ULYSSES when R gets large.

• Due to fluctuations in Bφ at large R?

• Bφ ~ 1/R while Br ~ 1/R2 Bφ » Br as R → large.

• Technique assumes that total (unsigned) magnetic flux can be deduced from single point in situ observations.

• How reasonable is this at large R?

SummarySummary

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BACKUP SLIDESBACKUP SLIDES

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ULYSSES Observations ULYSSES Observations Over the Solar Cycle Over the Solar Cycle

Solar Minimum Solar Minimum

22Year

Tot

al F

lux

(1014

Wb

)Comparison of In Situ Observations Comparison of In Situ Observations

In and Out of the EclipticIn and Out of the Ecliptic

“Observed” Flux

Near Earth

Solar

Minimum

Solar

Maximum

“Observed” Flux

At ULYSSES

Heliographic

Latitude of

ULYSSES

Heliographic

Distance of

ULYSSES

Bφ/Br

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Global Coronal Field: Observations & ExtrapolationsGlobal Coronal Field: Observations & Extrapolations

Comparison of photospheric field extrapolations (left) to white light (pB) image (right) indicate a degree of qualitative correlation between closed field lines and streamers

White light (pB) data HAO/MLSO/Mk3Photospheric field extrapolation (MWO)

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Validating Coronal Models Using Coronal HolesValidating Coronal Models Using Coronal Holes

Solar Minimum (CR1913)

Solar Maximum(CR1970)

Short After Solar Maximum(1978)

MAS/SAIC

de Toma, Arge, and Riley (2005)

See also Henney & Harvey [2005]And Jones [2005]

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750

Mount Wilson Solar Observatory (MWO)

650

550

450

350

250

750

650

550

450

350

250

Predicted and Observed Coronal HolesPredicted and Observed Coronal Holes

CR1988 CR1987 CR1986

National Solar Observatory at Kitt Peak (NSO)

de Toma and Arge

26Schatten, Cosmic Electrodynamics, 2, 232, 1971.

Potential Field Source Surface (PFSS) Potential Field Source Surface (PFSS) Model of the CoronaModel of the Corona

j = 0

Required because coronal magnetic fields are too weak to measure directly.

),(YrB + rA = ),(r, lm1)+-(l

lml

lm

l

-l=m0 = l

where,

0 = 2

Coefficients Alm and Blm are determined

from the boundary conditions.

= 4 JB c

0 = B

J = 0 B = -

Outward Directed Field

Inward Directed Field