1 C. “Nick” Arge Space Vehicles Directorate/Air Force Research Laboratory SHINE Workshop Aug. 2, 2007 Comparing the Observed and Modeled Global Heliospheric Magnetic Flux

2 Outline 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

3 PFSS 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 OUTPUT f s = (R  /R ss ) 2 [B P (R  )/B P (R ss )] V ~ f s -n

4 Long-Term Comparison of Observed & Predicted Coronal Hole Sizes & Locations Wang et al., Science, 271, p , 1996 See also………………. Neugebauer et al.,1998 Henney & Harvey, 2005 Jones, 2005 de Toma, Arge, and Riley, 2005 Wilcox MagnetogramsNSO HE Synoptic Maps

5 Long-Term Comparison of Observations and PFSS Predictions of Radial IMF Strength Spacecraft Measurements Model Calculation Wang and Sheeley JGR, 2002 See also … Zhao & Hoeksema, JGR, 1995 Successfully predict B x over a ~10 year interval using their CSSS model.

6 Total (unsigned) photospheric flux varies by a factor of ~5-8 over the solar cycle Total (Unsigned) Photospheric Field Flux for Three Solar Observatories Over Two Solar Cycles Arge, Hildner, Pizzo, & Harvey, 2002 Sunspot Minimum Maximum See also Wang & Sheeley, 2000 & 2002

7 With Selected, Pre-1992 NSO-Kitt Peak Photospehric Field Values Corrected for Known Biases Arge, Hildner, Pizzo, Harvey, 2002 Total Open Magnetic Flux for Three Solar Observatories Over Two Solar Cycles Sunspot Minimum Maximum See also Wang & Sheeley, 2000 & 2002 Total (unsigned) Open flux varies by a factor of 2-3 over the solar cycle Max Min

8 Wang & Sheeley, 2002 Relationship Between Solar Dipole and Quadrupole Moments and “Open” Flux Over the Solar Cycle Variation of Open flux approximately follows that of the Dipole strength except near solar maximum when Quadrupole also contributes. nT Open Flux (nT) Dipole (nT) Quadrupole (nT) Min Max MinMax Min

9 Source Regions of the Open Flux Over the Solar Cycle Solar MinimumSolar Maximum Source of Open Flux over the Solar Cycle Wang & Sheeley, 2002 Luhmann et al., 2002 Near Ecliptic Solar Wind Sources Open Flux Originates - Primarily from polar coronal holes Near Minimum - Small, strong-field regions in activity zones Near Maximum : Lat > 45° : Lat < 45°

10 Fraction of Photosphere with Open Fields Sunspot Minimum Maximum Fraction of Photosphere with Open Magnetic Flux Total Photospheric Magnetic Flux (10 14 Wb) Arge, Hildner, Pizzo, & Harvey, JGR 2002 See also Wang & Sheeley, 2000 & 2002 Fractional area of photosphere with Open flux varies by a factor of ~4 25% 2-3 years before solar minimum.25% 2-3 years before solar minimum. 5-10% near solar maximum.5-10% near solar maximum. Smaller variation of Open flux over solar cycle explained by Offset in the phasing of total open area and |B photo | strength.Offset in the phasing of total open area and |B photo | strength. Fact that in open regions ~ 4 times smaller during min. than max. (i.e., ~5G vs. ~20G).Fact that in open regions ~ 4 times smaller during min. than max. (i.e., ~5G vs. ~20G). Wang & Sheeley, 2002

11 Percentage of Total Photospheric Flux Open to the Heliosphere (Total Open Flux)/(Total Photospheric Flux) Total Photospheric Magnetic Flux (10 14 Wb) 40-50% of total photospheric flux open during minimum.40-50% of total photospheric flux open during minimum. ~10% open during maximum.~10% open during maximum. Sunspot Minimum Maximum Arge, Hildner, Pizzo, & Harvey, JGR 2002 See also Wang & Sheeley, 2000 & 2002

12 PFSS+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 R  ) PFSS+SCS MODEL (R = 5.0 R  ) Model Coronal Field Carrington Longitude Magnetic field more uniform using PFSS+SCS model → More consistent with ULYSSES Observations Plot courtesy of Sarah McGregor

13 Modeled Open Flux (NSO) Year Total Flux (10 14 Wb) Comparison of Modeled Flux Using MWO and NSO Carrington Maps as Input Modeled Open Flux (MWO) Solar Minimum Solar Maximum MWO = Mount Wilson NSO = Kitt Peak

14 ULYSSES finds that r 2 |B r | is independent of latitude.  4πr 2 |B r | “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 BrBr BrBr r1r1 r2r2 BrBr Θ =Heliographic Lat. Fixed R but different latitudes (Θ) |B r | (r 1,Θ =0°) = |B r |(r 1,Θ≠ 0°) For different R and Θ | B r |(r 1,Θ=0°) r 1 2 = |B r | (r 2,Θ≠ 0°) r 2 2 = |Br|(r 1,Θ≠0°) r 1 2

15 Modeled Open Flux (NSO) Year Total Flux (10 14 Wb) Comparison of Modeled Flux & 1AU “Observations” in the Ecliptic Modeled Open Flux (MWO) Solar Minimum Solar Maximum “Observed” Flux Near Earth

16 Year Total Flux (10 14 Wb) Comparison of Modeled Flux with In Situ Observations 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

17 Year Total Flux (10 14 Wb) Comparison of In Situ Observations In 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

18 Summary of Long-Term, Global Behavior of Solar 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 |B photo | strength.  Fact that 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.

19 1)From the PFSS model reproduces the observed radial magnetic field strength near Earth relatively well (overall). - Some notable exceptions (e.g., ~ ). 2)From , 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 B φ at large R? B φ ~ 1/R while B r ~ 1/R 2  B φ » B r 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? Summary

20 BACKUP SLIDES

21 ULYSSES Observations Over the Solar Cycle Solar Minimum

22 Year Total Flux (10 14 Wb) Comparison of In Situ Observations In 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 B φ /B r

23 Global 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/Mk3 Photospheric field extrapolation (MWO)

24 Validating 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]

Mount Wilson Solar Observatory (MWO) Predicted and Observed Coronal Holes CR1988 CR1987 CR1986 National Solar Observatory at Kitt Peak (NSO) de Toma and Arge

26 Schatten, Cosmic Electrodynamics, 2, 232, Potential Field Source Surface (PFSS) Model of the Corona j = 0 Required because coronal magnetic fields are too weak to measure directly. where, Coefficients A lm and B lm are determined from the boundary conditions. J = 0  B = -  Outward Directed Field Inward Directed Field