more solar wind predictions using coronal extrapolation modelsbpoduval/psfiles/bsd2016.pdf · solar...
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Bala Poduval Boulder Solar Day 14 March 2016
More Solar Wind Predictions Using
Coronal Extrapolation models
BALA PODUVAL SPACE SCIENCE INSTITUTE, BOULDER, CO
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SOLAR WIND
Parker 1958 — solar wind model
above a reference height, radially directed solar wind totally controls the magnetic field
determine this reference height to quantitatively model background IMF and solar wind speed
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SOLAR WIND ORIGINFast wind: coronal holes - open magnetic field region (> 450 km/s)
Slow: near streamers – closed magnetic field (< 450 km/s)
Y. M. Wang & N. R. Sheeley, 1990s
All the solar wind originate from coronal holes (CH)
fast wind – center slow wind – near the boundaries
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SOLAR WIND ORIGIN
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WHY CORONAL MODELS?Direct observations of coronal magnetic field — challenging and limited (e. g. using CoMP: Dove et al., ApJ, 731, 2011;
Bak-Steslicka et al., ApJL, 770, 2013)
Models that extrapolate observed photospheric magnetic field into the corona and beyond
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TWO MODELS
Potential Field Source Surface (PFSS) model Schatten et al., 1969; Altschuler & Newkirk, 1969 coronal magnetic field - computed from scalar
potential obeying LaPlace’s law
Current Sheet Source Surface (CSSS) model
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CSSS MODEL
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BOGDAN & LOW 1986 obtained solution to magnetostatic equilibrium — electric currents flowing
perpendicular to gravity (1/r2) everywhere
J =1
µ0r[1� ⌘(r)]
2
4 1
sin(✓)
@2�
@�@r�̂� @2�
@✓@r�̂
3
5 (1)
and
B = �⌘(r)@�
@rr̂ � 1
r
@�
@✓✓̂ � 1
sin(✓)
@�
@��̂ (2)
where, µ0 is the magnetic permeability, ⌘(r) = 1 + (a/r)2
and �(r, ✓, �) is a scalar function determined by the bound-ary conditions at the photosphere and corona (Zhao andHoeksema, 1995).
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CSSS MODELusing spherical harmonic expansion and source surface technique
Zhao & Hoeksema, (JGR, 100, 99, 1995) developed CSSS model
includes - volume & sheet currents
- source surfaceBala Poduval Boulder Solar Day 14 March 2016
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CSSS MODEL - GEOMETRY
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inner region
middle region
outer region extrapolate computed B out into the heliosphere because
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SOLAR WIND PREDICTION
used CSSS and PFSS models to compute FTE
used the speed-FTE relationship of Wang & Sheeley to predict solar wind speed
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DATA
• Daily averaged solar wind data 1996-2010 solar cycles 23, 24
• Photospheric synoptic maps
SOHO/MDI 1° lat-lon
MDI data not available outside of this period
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METHOD-Step 1
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METHOD-Steps 2-4Step 2: map coronal location back to photosphere along open field lines using CSSS & PFSS models
Step 3: compute FTE at each solar wind source location
Step 4: predicted solar wind speed using WS relationship
Speed FTE
> 750 < 4.5
650 – 750 4.5 – 8 550 – 650 8 – 10
450 – 550 10 – 20
< 450 > 20 Bala Poduval Boulder Solar Day 14 March 2016
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QUADRATIC FUNCTION
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WSO a = 110.3
b = -416.0 c = 676.6
NSO/Kitt Peak a = 113.9
b = 466.6 c = 763.4
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SOLAR WIND PREDICTION
the quadratic function is used for all the subsequent solar wind speed predictions
used the same functional form for both PFSS and CSSS models
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RMSE
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Evaluate performances of PFSS and CSSS models
Root Mean Square Error (RMSE) between observed and predicted speeds
RMSE ratio = RMSEPFSS/RMSECSSS
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RMSE increases as solar cycle progresses —> (1) difficulty modelling complex magnetic field. (2) Optimization of free parameters: RSS = 15 Rsun or closer? Rcp = 2.5 Rsun? Height of cusp varies over wide range (see, e.g. Cranmer et al., 2007 Zhao & Hoeksema, 1995)
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CONCLUDING REMARKS
Investigation of the controlling influence of magnetic field on
solar wind outflow. FTE = Br(pho)/Br(ss) * (R/Rss)2
Br(pho); R: photospheric magnetic field & radius Br(ss), Rss: source surface magnetic field & radius
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CONCLUDING REMARKS
-solar cycle variation - quadratic term in the best fit to speed-FTE
-nearly disappearing during certain solar rotations,
- giving rise to an almost linear fit -
-this variation is significant in CSSS model
-nearly negligible in PFSS model
How this information can be used to deduce the influence of magnetic field on solar wind outflow is being investigated further.
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CONCLUDING REMARKS
Solar Orbiter & Solar Probe Plus provide information on coronal
conditions within 40 Rsun — CSSS predictions will be useful in interpreting the results …
Bala Poduval Boulder Solar Day 14 March 2016