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Force-free magnetic field modeling based onSDO/HMI and Hinode SOT/SP data:
Instrumental and resolution effects
J. K. Thalmann
in collaboration with:
T. Wiegelmann, S. K. Tiwari and B. Inhester
MPI for Solar System Research, Katlenburg-Lindau, GermanySolar Group Seminar, 19 Feb 2013
Supported by DFG-grand WI 3211/1-1
Motivation
Direct measures of magneticfield vector in outer atmosphereof Sun: not routinely available
↓
Use routinely delivered surface(photospheric) magnetic fieldvector: model the magneticfield above
↓
“force-free” field models
Existing:
comparative studies of different force-free model algorithms basedon the same lower boundary conditions(e. g., Schrijver et al., 2008; DeRosa et al., 2009; Gilchrist et al., 2012)
Most studies of the coronal magnetic structure above ARs:
force-free models based on photospheric vector magnetic field datainferred from polarization measurements from
Hinode SOT/SP (e. g. Hao et al., 2012; Inoue et al., 2012)
or
SDO/HMI (e. g., Sun et al., 2012b,a)
Missing:
comparative study of the same reconstruction algorithm based ondata from different instruments (SDO/HMI and SOT/SP)
Motivation
Models accommodating
– large fields-of-view– sufficient spatial resolution– measurement uncertainties
might be reliable.
Existing:
comparative studies of different force-free model algorithms basedon the same lower boundary conditions(e. g., Schrijver et al., 2008; DeRosa et al., 2009; Gilchrist et al., 2012)
Most studies of the coronal magnetic structure above ARs:
force-free models based on photospheric vector magnetic field datainferred from polarization measurements from
Hinode SOT/SP (e. g. Hao et al., 2012; Inoue et al., 2012)
or
SDO/HMI (e. g., Sun et al., 2012b,a)
Missing:
comparative study of the same reconstruction algorithm based ondata from different instruments (SDO/HMI and SOT/SP)
Motivation
Sun et al. (2012b)
Hao et al. (2012)
Existing:
comparative studies of different force-free model algorithms basedon the same lower boundary conditions(e. g., Schrijver et al., 2008; DeRosa et al., 2009; Gilchrist et al., 2012)
Most studies of the coronal magnetic structure above ARs:
force-free models based on photospheric vector magnetic field datainferred from polarization measurements from
Hinode SOT/SP (e. g. Hao et al., 2012; Inoue et al., 2012)
or
SDO/HMI (e. g., Sun et al., 2012b,a)
Missing:
comparative study of the same reconstruction algorithm based ondata from different instruments (SDO/HMI and SOT/SP)
Motivation
How accurate are model-relatedestimates?()
Existing:
comparative studies of different force-free model algorithms basedon the same lower boundary conditions(e. g., Schrijver et al., 2008; DeRosa et al., 2009; Gilchrist et al., 2012)
Most studies of the coronal magnetic structure above ARs:
force-free models based on photospheric vector magnetic field datainferred from polarization measurements from
Hinode SOT/SP (e. g. Hao et al., 2012; Inoue et al., 2012)
or
SDO/HMI (e. g., Sun et al., 2012b,a)
Missing:
comparative study of the same reconstruction algorithm based ondata from different instruments (SDO/HMI and SOT/SP)
Active Region Selection
Selection criteria:
– close to disk-center
– co-temporal observations ofHMI and SP
AR 11382 on 22 Dec 2011:
centered at ∼S19W07
SP scan: 04:46 – 05:29 UT
spatial resolution ∼ 440 km
HMI measurement at 05:00 UT
spatial resolution ∼ 720 km
Data preparation:
– transformation to heliographiccoordinates (Gary & Hagyard, 1990)
Blos → Bz , Bt → Bh
– alignment of the data sets
– determine HMI-subfield
– bin SP data to resolution of HMI
SPores → SPrebin
Active Region Selection
Selection criteria:
– close to disk-center
– co-temporal observations ofHMI and SP
AR 11382 on 22 Dec 2011:
centered at ∼S19W07
SP scan: 04:46 – 05:29 UT
spatial resolution ∼ 440 km
HMI measurement at 05:00 UT
spatial resolution ∼ 720 km
Data preparation:
– transformation to heliographiccoordinates (Gary & Hagyard, 1990)
Blos → Bz , Bt → Bh
– alignment of the data sets
– determine HMI-subfield
– bin SP data to resolution of HMI
SPores → SPrebin
Active Region Selection
Selection criteria:
– close to disk-center
– co-temporal observations ofHMI and SP
AR 11382 on 22 Dec 2011:
centered at ∼S19W07
SP scan: 04:46 – 05:29 UT
spatial resolution ∼ 440 km
HMI measurement at 05:00 UT
spatial resolution ∼ 720 km
Data preparation:
– transformation to heliographiccoordinates (Gary & Hagyard, 1990)
Blos → Bz , Bt → Bh
– alignment of the data sets
– determine HMI-subfield
– bin SP data to resolution of HMI
SPores → SPrebin
Why binning?
– keep computational expenses low
– investigate effect on model result
Force-free Magnetic Field Modeling
Solve the boundary value problem:
(∇ × B ) × B = 0 ∇ · B = 0 B = Bz=0 on Sz=0
Preprocessing: (Wiegelmann & Inhester, 2006)
approximate force-free chromosphere Bobs → Bprepro
transform non force-free photospheric field to achromospheric-like, nearly force-free one
Force-free modeling: (Wiegelmann, 2004; Wiegelmann & Inhester, 2010)
model 3D magnetic field above Bprepro =Bz=0
calculate potential field Bpot from Bz ,prepro
replace bottom boundary by Bprepro
iteratively solve for force- and divergence free field Bnlff
Force-free fields obey:
(∇ × B ) × B = 0
which can be fulfilled by
∇ × B = 0
(“current-free”, “potential”)
or
∇ × B ‖ B
(“force-free”)
↓
∇ × B = α(r)B(“nonlinear force-free”)
Force-free Magnetic Field Modeling
Solve the boundary value problem:
(∇ × B ) × B = 0 ∇ · B = 0 B = Bz=0 on Sz=0
Preprocessing: (Wiegelmann & Inhester, 2006)
approximate force-free chromosphere Bobs → Bprepro
transform non force-free photospheric field to achromospheric-like, nearly force-free one
Force-free modeling: (Wiegelmann, 2004; Wiegelmann & Inhester, 2010)
model 3D magnetic field above Bprepro =Bz=0
calculate potential field Bpot from Bz ,prepro
replace bottom boundary by Bprepro
iteratively solve for force- and divergence free field Bnlff
original lower boundary
↓preprocessed lower boundary
Force-free Magnetic Field Modeling
Solve the boundary value problem:
(∇ × B ) × B = 0 ∇ · B = 0 B = Bz=0 on Sz=0
Preprocessing: (Wiegelmann & Inhester, 2006)
approximate force-free chromosphere Bobs → Bprepro
transform non force-free photospheric field to achromospheric-like, nearly force-free one
Force-free modeling: (Wiegelmann, 2004; Wiegelmann & Inhester, 2010)
model 3D magnetic field above Bprepro =Bz=0
calculate potential field Bpot from Bz ,prepro
replace bottom boundary by Bprepro
iteratively solve for force- and divergence free field Bnlff
original lower boundary
↓preprocessed lower boundary
↓extrapolated 3D force-free field
Magnetic Field Related Quantities
2D lower |φz | <Bh>
boundary [× 1022 Mx ] [ mT ]
HMI 1.279 20.9SPrebin 2.338 33.5
3D model Enlff Epot⋆∆Enlff
pot ∆Enlffpot
volume [× 1025 J ] [ % of Enlff ]
HMI 3.45 2.80 0.65 19SPrebin 7.44 5.80 1.64 22
⋆∆Enlffpot = Enlff − Epot
– absolute estimates differ
HMI model hosts ∼ half of energy
lower boundary hosts ∼ half the flux
– relative estimates very similar
excess energy ∼ 20% of total energy
Magnetic Field Related Quantities
2D lower |φz | <Bh>
boundary [× 1022 Mx ] [ mT ]
HMI 1.279 20.9SPrebin 2.338 33.5
3D model Enlff Epot⋆∆Enlff
pot ∆Enlffpot
volume [× 1025 J ] [ % of Enlff ]
HMI 3.45 2.80 0.65 19SPrebin 7.44 5.80 1.64 22
⋆∆Enlffpot = Enlff − Epot
– absolute estimates differ
HMI model hosts ∼ half of energy
lower boundary hosts ∼ half the flux
– relative estimates very similar
excess energy ∼ 20% of total energy
Magnetic Field Structure
Look at same topological feature:
localize strong gradients in magneticconnectivity (Q large)
– clear pattern of high Q inboth models
more diffuse in SPmodel
– relative displacement ofseveral Mm y
HMI SPrebin
Magnetic Field Structure
Look at same topological feature:
localize strong gradients in magneticconnectivity (Q large)
– only consider field linesoriginating from Q ≥ 100
outline two neighboringmagnetic flux domains
– clearly different (height)extension y
HMI SPrebin
Magnetic Field Structure
Look at same topological feature:
localize strong gradients in magneticconnectivity (Q large)
– different locations of yfield-line endpoints
– relative shared fluxcomparable
∼ 1% of unsigned verticalflux on lower-boundary
HMI SPrebin
Magnetic Field Structure
Look at overall connectivity:
consider all field lines originatingfrom (60 Mm ≤ x, y)
– similar statistical properties offield lines
well-defined relation of lengthand apex height
– SP model field lines on yaverage higher
HMI SPrebin
Magnetic Field Structure
Look at overall connectivity:
consider all field lines originatingfrom (60 Mm ≤ x, y)
– similar statistical properties offield lines
well-defined relation of lengthand apex height
– similar range of field linescarrying most flux
HMI SPrebin
Magnetic Field Structure
Look at overall connectivity:
consider all field lines originatingfrom (60 Mm ≤ x, y)
– similar statistical properties offield lines
well-defined relation of lengthand apex height
– no preferred range of fieldlines carrying most current
HMI SPrebin
Shown so far:
Similarities:
– relative B-related estimates
excess energy (% of total energy)
– recovery of magnetic flux domains
relative shared flux & current comparable
– similar statistical properties of field lines
well-defined relation of length and apex height
similar range of field lines carrying most flux
Differences:
– absolute B-related estimates
– (height) extension of flux domains
and on overall
Are these caused by binning the
SP data to the resolution of HMI
(SPores → SPrebin)?
Shown so far:
Similarities:
– relative B-related estimates
excess energy (% of total energy)
– recovery of magnetic flux domains
relative shared flux & current comparable
– similar statistical properties of field lines
well-defined relation of length and apex height
similar range of field lines carrying most flux
Differences:
– absolute B-related estimates
– (height) extension of flux domains
and on overall
Are these caused by binning the
SP data to the resolution of HMI
(SPores → SPrebin)?
Effect of Binning – Magnetic Field Related Quantities
2D lower |φz | <Bh>
boundary [× 1022 Mx ] [ mT ]
HMI 1.279 20.9SPrebin 2.338 33.5SPores 2.364 30.3
3D model Enlff Epot⋆∆Enlff
pot ∆Enlffpot
volume [× 1025 J ] [ % of Enlff ]
HMI 3.45 2.80 0.65 19SPrebin 7.44 5.80 1.64 22SPores 7.31 5.85 1.46 20
⋆∆Enlffpot = Enlff − Epot
– absolute estimates very similar
HMI model hosts ∼ half of energy
lower boundary hosts ∼ half the flux
– relative estimates very similar
excess energy ∼ 20% of total energy
– effect of binning < instrumental effect
dESPoresSPrebin
<< dESPoresHMIhmi
Effect of Binning – Magnetic Field Related Quantities
2D lower |φz | <Bh>
boundary [× 1022 Mx ] [ mT ]
HMI 1.279 20.9SPrebin 2.338 33.5SPores 2.364 30.3
3D model Enlff Epot⋆∆Enlff
pot ∆Enlffpot
volume [× 1025 J ] [ % of Enlff ]
HMI 3.45 2.80 0.65 19SPrebin 7.44 5.80 1.64 22SPores 7.31 5.85 1.46 20
⋆∆Enlffpot = Enlff − Epot
– absolute estimates very similar
HMI model hosts ∼ half of energy
lower boundary hosts ∼ half the flux
– relative estimates very similar
excess energy ∼ 20% of total energy
– effect of binning < instrumental effect
dESPoresSPrebin
<< dESPoresHMIhmi
Effect of Binning – Magnetic Field Related Quantities
2D lower |φz | <Bh>
boundary [× 1022 Mx ] [ mT ]
HMI 1.279 20.9SPrebin 2.338 33.5SPores 2.364 30.3
3D model Enlff Epot⋆∆Enlff
pot ∆Enlffpot
volume [× 1025 J ] [ % of Enlff ]
HMI 3.45 2.80 0.65 19SPrebin 7.44 5.80 1.64 22SPores 7.31 5.85 1.46 20
⋆∆Enlffpot = Enlff − Epot
– absolute estimates very similar
HMI model hosts ∼ half of energy
lower boundary hosts ∼ half the flux
– relative estimates very similar
excess energy ∼ 20% of total energy
– effect of binning < instrumental effect
dESPoresSPrebin
<< dESPoresHMIhmi
Effect of Binning – Magnetic Field Structure
Look at overall connectivity:
consider all field lines originatingfrom (60 Mm ≤ x, y)
– identical statistical propertiesof field lines
well-defined relation of lengthand apex height
– similar range of field linescarrying most flux
HMI
SPrebin SPores
Effect of Binning – Magnetic Field Structure
Look at overall connectivity:
consider all field lines originatingfrom (60 Mm ≤ x, y)
– identical statistical propertiesof field lines
well-defined relation of lengthand apex height
– no preferred range of fieldlines carrying most current
HMI
SPrebin SPores
Conclusions
Similarities:
– relative B-related estimates
– recovery of magnetic flux domains
– statistical properties of field lines
Differences:
– absolute B-related estimates
– (height) extension of flux domains
and on overall
Possibly reliable.
Are not caused by binning the SP data.
To be taken with caution.
References I
DeRosa, M. L., Schrijver, C. J., Barnes, G., et al. 2009, Astrophys. J., 696, 1780
Gary, G. A., & Hagyard, M. J. 1990, Sol. Phys., 126, 21
Gilchrist, S. A., Wheatland, M. S., & Leka, K. D. 2012, Sol. Phys., 276, 133
Hao, Q., Guo, Y., Dai, Y., et al. 2012, Astron. Astrophys., 544, L17
Inoue, S., Shiota, D., Yamamoto, T. T., et al. 2012, Astrophys. J., 760, 17
Schrijver, C. J., DeRosa, M. L., Metcalf, T., et al. 2008, Astrophys. J., 675, 1637
Sun, X., Hoeksema, J. T., Liu, Y., Chen, Q., & Hayashi, K. 2012a, Astrophys. J., 757, 149
Sun, X., Hoeksema, J. T., Liu, Y., et al. 2012b, Astrophys. J., 748, 77
Wiegelmann, T. 2004, Sol. Phys., 219, 87
Wiegelmann, T., & Inhester, B. 2006, Sol. Phys., 236, 25
—. 2010, Astron. Astrophys., 516, A107
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