force-free magnetic ﬁeld modeling based on sdo/hmi and hinode … · sdo/hmi and hinode sot/sp...

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:





or


Missing:


Motivation

Sun et al. (2012b)

Hao et al. (2012)

Existing:





or


Missing:


Motivation

How accurate are model-relatedestimates?()

Existing:





or


Missing:


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


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


HMI measurement at 05:00 UT


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”)



(∇ × B ) × B = 0 ∇ · B = 0 B = Bz=0 on Sz=0









original lower boundary

↓preprocessed lower boundary



(∇ × B ) × B = 0 ∇ · B = 0 B = Bz=0 on Sz=0









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 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




– only consider field linesoriginating from Q ≥ 100

outline two neighboringmagnetic flux domains

– clearly different (height)extension y

HMI SPrebin




– different locations of yfield-line endpoints

– relative shared fluxcomparable

∼ 1% of unsigned verticalflux on lower-boundary

HMI SPrebin


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






– similar range of field linescarrying most flux

HMI SPrebin






– 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)?

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



– identical statistical propertiesof field lines


– similar range of field linescarrying most flux

HMI

SPrebin SPores

Effect of Binning – Magnetic Field Structure



– identical statistical propertiesof field lines


– 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

force-free magnetic ﬁeld modeling based on sdo/hmi and hinode … · sdo/hmi and hinode sot/sp...

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