Future Directions of Magnetic
Field Measurements
Christoph U. Keller
Utrecht University

Outline• Key Science Questions• Key Observations• Key Measurements
KeyProblemsandPossibleSolutions•

Key Science Questions• How is magnetic flux generated?
• How is magnetic flux removed?
• How is energy transported and transformed?

Key Observations• magnetic field and its connectivity• velocity field• temperature, density, composition
all from below the photosphere to the corona andbeyond as a function of time at spatial and temporal
resolutions compatible with the underlying physicalprocesses

Key Measurements• Sound speed and velocity vector fields in the solar
interior → helioseismology• Sensitive, precise photospheric magnetic and velocity
vector field measurements → spectropolarimetry• Sensitive and precise chromospheric magnetic andvelocity vector field measurements →spectropolarimetry• Coronal magnetic and velocity vector fields →spectroscopy, spectropolarimetry, radio, extrapolations• Temperature, density, composition from photosphere tocorona → spectroscopyKey Problem 1: Where
Want to measure magnetic fields in a volume, but noteasy to know where we measure• optically thick → 2-D (corrugated) ‘surface’• optically thin → integral along line of sight• response functions with respect to magnetic field may
not be what one wants• → spatial derivatives of magnetic field incorrect

Na I D1 optical depth unity (Uitenbroek 2006)

Na I D2 response function to B (Uitenbroek 2006)

Possible Solutions I• translate between optical depth at different
wavelengths and geometrical height• empirical 3-D models with physical constraints (semiempirical) that reproduce all measurements• observe with different lines of sight (stereoscopy)Key Problem 2: Filling Factor• filling factor α, field strength B, inclination γ:• Stokes V ~ α B cos γ (line of sight flux)• Stokes Q, U ~ α B sin γ• ‘3 unknowns, 2 equations’• difficult to distinguish between α and B• influences inclination determination• proportionality influenced by temperature
22InputME-Inversion

Possible Solutions 2• be aware of limitations in derived magnetic field vectormaps• go to infrared where Zeeman effect is larger →precise vectors at smaller field strengths• use several (>2) spectral lines• use different mechanism of spectral line polarization:
Zeeman, Hanle, hyperfine structureKey Problem 3: 180°Ambiguity• linear polarization cannot distinguish between

transverse component with opposite directions• cannot solve it in ‘interesting’ regions

SOLIS/VSM, inversion courtesy Catherine Fischer

Possible Solutions 3• observe at several heights to see geometrical changes• observe with different lines of sight (stereoscopy)• make use of temporal information

Key Problem 4: Photons• polarimetry is photon-starved because of rapid solar
evolution at small spatial scales• slit-spectrographs and tunable filters discard mostphotons of interest• time scales of scans need to be faster than typicaldynamic time scales of solar evolution

Possible Solutions 4• need to measure many spectral and spatial pixels
simultaneously• Integral Field Units (IFU)• all-reflective image slicer• multi-slit• microlens arrays• fiber bundles• multi-wavelength filters• combine information from many spectral lines

Image Slicer IFU

The Chromosphere• magnetic fields gain dominance over gas dynamics• flares/CMEs defined and triggered by topologicalcomplexity of magnetic field that permeates throughchromosphere• fine-scale structuring, highly dynamic nature ofchromosphere due to continuously evolving magnetic
fields make this regime the hardest to diagnose, modeland understand• harbors key processes that convey energy, mass, andmomentum fluxes to corona and beyond

DOT G-band, Ca II H, Hα-0.8A, Hα coreKey Problem 5: Chromospheric
Magnetic Field Measurements• strong spectral lines (e.g. Ca IR triplet)• only a few spectral lines• requires NLTE radiative transfer• He I 1083.0 nm, weak in quiet sun• UV lines• Zeeman effect/Doppler width ~ λ• require full NLTE radiative transfer• field-strength, filling factor difficult to determineLarge-scale Chromospheric Magnetic Fields

NSO/KPVT
photosphericmagnetogram
chromospheric
NSO/KPVT
chromosphericminus
photosphericmagnetogram
magnetogram

courtesy Jack Harvey

Small-scale Chromospheric Magnetic Fields
FeI 853.8 nm

photosphere

CaII 854.2 nm

chromosphere

NSO/KPVT, original data courtesy Karen Harvey

Possible Solutions 5• chromospheric field might be less dynamic than what
intensity images indicate• be aware of limitation of chromospheric vector fieldmeasurements (line-of-sight flux and azimuth ‘good’)• extrapolations from photosphere as additional
constraint• Hanle effect as additional constraint (limb only?)• radio observations provide excellent temperature
measurements from chromosphere to coronaalong limb

height above limb

Scattering Polarization in CaII 854.2 nm

wavelength

Key Problem 6: Coronal
Magnetic Field• difficult to measure directly• in dark parts of corona• when connectivity down to photosphere is•importantextrapolations:photosphere is not force-freephotospheric field inclination often not welldetermined
180° ambiguity not solved in interesting regions•••

Possible Solutions 6• coronal polarimetry at limb from different point ofview• extrapolations:• line-of-sight flux and azimuth well determined• chromosphere more force-free than photosphere• use temporal information

Observing Systemcoronaspace

groundtransition region
chromospheregroundphotospherespaceGamma-ray

X-rayEUVUVVisibleNear-IR

Thermal IRRadio
0.02”

0.2”

Spatial Scales

Solar-C

2”

HinodeRHESSI

20”

SDO
ATST/EST200”

HinodeSDO

SOLIS
Wavelength

FASR

2000”

Conclusions• need to observe magnetic fields in time-dependent
3-D volumes by measuring polarization of many,
carefully selected spectral lines• need 3-D semi-empirical models to translatemeasurements into 3-D magnetic field observations• understanding requires numerical simulations• operate at suitable part of solar cycle