introduction to daytime astronomical polarimetry - … · introduction to daytime astronomical...
TRANSCRIPT
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Introduction to Daytime Astronomical Polarimetry
Sami K. Solanki
Max Planck Institute for Solar System Research
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Introduction to Solar Polarimetry
Sami K. Solanki
Max Planck Institute for Solar System Research
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Overview Solar polarimetry covers a very broad range of
wavelengths, from X-rays (e.g. in flares) to radio waves (coming from corona), including UV, visible and IR
Most polarimetric observations have been made in the visible, followed by the IR and radio waves
A range of processes have been proposed as sources of the polarization: Zeeman effect Scattering polarization Bremsstrahlung Gyroresonance radiation
I won’t talk much about processes
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Never look directly into the Sun with
unprotected eyes!
Never ever with a Telescope that doesn’t have a blocking filter!
The Sun, a Boring Star?
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The Dynamic Sun
Active region loops
(1 million degrees)
Prominence (gas at 10000 C)
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The Violent Sun
Flare Coronal mass ejection
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The dynamics and activity of the Sun are driven by
its Magnetic Field
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Zeeman diagnostics Direct detection of magnetic field by obs. of magnetically
induced splitting and polarisation of spectral lines
Clear Zeeman splitting seen in sunspots. Outside spots often subtle effect in intensity Use unique polarisation signature
Measurement of polarization is central to measuring solar magnetic fields
Zeeman effect: by far most common way of measuring solar B field
Dis
tanc
e al
ong
slit
Wavelength
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Zeeman diagnostics Direct detection of magnetic field by obs. of magnetically
induced splitting and polarisation of spectral lines
Clear Zeeman splitting seen in sunspots. Outside spots often subtle effect in intensity Use unique polarisation signature
Measurement of polarization is central to measuring solar magnetic fields
Zeeman effect: by far most common way of measuring solar B field
Dis
tanc
e al
ong
slit
Wavelength Direction of slit
Direction of slit
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Zeeman diagnostics Direct detection of magnetic field by obs. of magnetically
induced splitting and polarisation of spectral lines
Clear Zeeman splitting seen in sunspots. Outside spots often subtle effect in intensity Use unique polarisation signature
Measurement of polarization is central to measuring solar magnetic fields
Zeeman effect: by far most common way of measuring solar B field
Wavelength
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Zeeman diagnostics Direct detection of magnetic field by obs. of magnetically
induced splitting and polarisation of spectral lines
Clear Zeeman splitting seen in sunspots. Outside spots often subtle effect in intensity Use unique polarisation signature
Measurement of polarization is central to measuring solar magnetic fields
Zeeman effect: by far most common way of measuring solar B field
Dis
tanc
e al
ong
slit
Wavelength
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Zeeman splitting of atomic levels & lines
Transitions between Zeeman split upper and lower atomic levels lead to spectral lines that are split in wavelength
Transitions are allowed between levels with ∆J = 0, ±1 & ∆MJ = 0 (π), ±1 (σb, σr) (for the most common types of transitions: electric dipole radiation)
J = 0
J = 1
B = 0 B > 0 MJ +1 0 −1
0
λ λ
I
Ene
rgy
σb π σr
𝜆𝜆0 𝜆𝜆0
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Stokes profiles produced by the Zeeman effect
𝐼𝐼/𝐼𝐼𝑐𝑐 𝑄𝑄/𝐼𝐼𝑐𝑐
𝑈𝑈/𝐼𝐼𝑐𝑐
𝑉𝑉/𝐼𝐼𝑐𝑐
Stokes 𝐼𝐼 = intensity; complex dependence on 𝐵𝐵
Stokes 𝑄𝑄 = net linear polarisation; samples transverse component of 𝐵𝐵
Stokes 𝑈𝑈 = net linear polarisation, rotated by 45∘ relative to 𝑄𝑄; also samples transverse component of 𝐵𝐵. 𝑄𝑄 & 𝑈𝑈 give azimuth of 𝐵𝐵
Stokes 𝑉𝑉 = net circular polarisation; samples longitudinal component of 𝐵𝐵
Wavelength
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Effect of changing field strength: typical solar absorption line
Formula for Zeeman splitting (for B in G, λ in Å): Δ𝜆𝜆𝐻𝐻 = 4.67 10−13 𝑔𝑔eff
𝐵𝐵 𝜆𝜆2 [Å] Splitting between observed 𝜎𝜎-peaks = Δ𝜆𝜆𝐻𝐻 only if
Zeeman splitting Δ𝜆𝜆𝐻𝐻 > Δ𝜆𝜆𝐷𝐷 = Doppler width of line
B=1600 G
𝐼𝐼/𝐼𝐼𝑐𝑐
𝑉𝑉/𝑉𝑉𝑐𝑐 Stokes 𝑉𝑉 shows splitting = Δ𝜆𝜆𝐻𝐻 only for 𝐵𝐵 > 1000 G
Δ𝜆𝜆𝐻𝐻 Δ𝜆𝜆𝐻𝐻
B=200 G
Δ𝜆𝜆𝐷𝐷
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Stokes profiles: dependence on B, γ, and φ for Zeeman split line
Juanma Borrero
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Zeeman splitting ~ λ2
𝐼𝐼 𝑉𝑉
Fe I 1564.8 nm
𝐼𝐼 𝑉𝑉
Fe I 630.2 nm
𝐵𝐵 cut along slit
𝐵𝐵 in a snapshot of 3D MHD simulation of a
piece of Sun A
rtificial slit
Dis
tanc
e al
ong
slit 𝐵𝐵
Magnetic feature
No magnetic feature
Magnetic feature
No magnetic feature
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Magnetograms Mangetogram: Roughly speaking, a map of the (LOS) magnetic field
Useful when star can be resolved, e.g. Sun
Magnetograph: Instrument to make maps of Stokes 𝑉𝑉 in wing of Zeeman sensitive line
Conversion of polarization into magnetic field requires a careful calibration
positive polarity
negative polarity
Magnetogram obtained by MDI on SOHO
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What does a magnetogram show? Plotted at left:
Top: Stokes V along a spectrograph slit
Bottom: Sample Stokes V profile
Red bars: example of a spectral range used to make a magnetogram, which shows longitudinal component of B
sign of V flips for 𝛾𝛾 > 90∘
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What does a magnetogram show? Plotted at left:
Top: Stokes V along a spectrograph slit
Bottom: Sample Stokes V profile
Red bars: example of a spectral range used to make a magnetogram, which shows longitudinal component of B
sign of V flips for 𝛾𝛾 > 90∘
In practice a combination of multiple 𝜆𝜆 ranges is used to counter effects of Doppler shifts and large Zeeman splitting
Nowadays also vector magnetograms, providing maps of full magnetic vector
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Sequence of Magneto-grammes
over a Solar rotation
MDI/SOHO
The Sun’s Measured Magnetic
Field
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Spectrograph-polarimeters vs. Filter-polarimeters
Sun is an extended object in the sky make images 2D
Zeeman effect needs spectral information 3D
Sun changes rapidly make movies 4D
4-D data hyper-cube needed, but current instruments only allow 2-D recordings at any one time
Give priority to either instantaneous spatial or 𝜆𝜆 coverage
Spectrograph: 1 spatial + spectral dimension simultaneously scan to get 2nd spatial dimension 3D data cube
Filtergraph: record 2 spatial dimensions simultaneously scan to get spectral dimension 3D data cube
Repeat with time to get information on evolution 4D
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Spectropolarimeter data
V U
I Q
Time needed to scan this region: roughly 20 min
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Filtergraph data
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Sequence of Magneto-grammes
over a Solar rotation
MDI/SOHO
The Sun’s Measured Magnetic
Field
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The Sun’s Measured Magnetic
Field
Sequence of Magneto-grammes
over a Solar rotation
MDI/SOHO Spatial resolution approx. 3000 km
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Higher Resolution Shows More Details
Sunspot: Magnetogram & Ca II K image by Hinode
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Sunspot: Magnetogram & Ca II K image by Hinode
Higher Resolution Shows More Details
Spatial resolution approx. 200 km
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Structure and dynamics at small spatial scales
Radiation-MHD Simulations of small-scale magnetic fields
Magnetic field Vögler et al. Intensity .
Spatial resolution 10 km
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Cancellation of Stokes 𝑽𝑽 signals
𝑖𝑖
𝑗𝑗
𝑘𝑘 Spatial resolution element
= positive polarity magnetic field = negative polarity magnetic field
Unresolved magnetic features with magnetic flux Φ𝑖𝑖 = 𝐵𝐵𝑖𝑖𝐴𝐴𝑖𝑖 , where 𝐵𝐵𝑖𝑖 = 𝐵𝐵 in element 𝑖𝑖 𝐴𝐴𝑖𝑖 = area of elem. 𝑖𝑖
Stokes V
Field pointing towards
observer Field pointing
away from observer
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Stokes V signal cancellation
+ =
negative polarity positive polarity (within spatial magnetic flux magnetic flux resolution element) =
Stokes 𝑉𝑉 signal only samples the net magnetic flux Extreme case:
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Scattering polarization
Solar surface
Scattering atom
Incident light (unpolarized)
Scattered light (polarized || solar surface)
Atoms scatter light resonantly, if collisions are rare
Atoms sitting in the atmosphere, scatter radiation from solar surface
If incoming light is anisotropic (i.e. mainly from one direction) scattered light is linearly polarized parallel to limb
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Scattering polarisation at Sun’s limb
Atoms high in atmosphere: Scatter radiation since
collisions are rare (low density)
Produce linearly polarized radiation because of anisotropic illumination
Limb darkening (dT/dz < 0, where T = temp.)
High location of atom
Scattering + anisotropy linear polarisation || limb
Linearly polarized scattered photon
Direction . of linear .
polarization
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Hanle effect Hanle effect: Modification of scattering polarisation by magnetic field. 2 effects:
Depolarisation depends on field orientation depends on B (complete
depolarisation if Δ𝜆𝜆𝐻𝐻 ≫ natural line width; i.e. radiative width)
also present for unresolved mixed polarity fields !
Rotation of polarisation plane depends on B, γ, χ only if field is spatially resolved Works for weak fields, where
Zeeman is ineffective (corona)
Signature of Hanle effect for spatially resolved field ↔ polarisation for 𝐵𝐵 = 0 ↔ polarisation for 𝐵𝐵 ≠ 0
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When does the Hanle effect work?
Needs scattering polarisation. Scattering of radiation takes place when collisions between the scattering atom and electrons are weak, i.e. where the density is low
Best in upper photosphere and chromosphere (on disk), in corona (off limb)
Works if Zeeman splitting is comparable to natural line width: 0.1 ... 100 G
Important: Hanle effect samples a regime in which Zeeman effect is insensitive, e.g. in corona (most Zeeman measurements are restricted to the lower-middle photosphere)
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Now you have the data, then what?
If you torture the data long enough, they will confess!
Gerard Piel
Which method of torture is the most effective for analysing solar Sokes data?
For simplicity, I’ll only consider Zeeman-effect
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Zeeman effect: information content
Intensity line profile Stokes 𝐼𝐼 has information on 𝐁𝐁(𝑧𝑧), but
this info is hidden if splitting incomplete. Stokes 𝐼𝐼 is also affected by elemental abundances, 𝑇𝑇(𝑧𝑧),𝑃𝑃(𝑧𝑧), 𝑣𝑣turb(𝑧𝑧), 𝑣𝑣LOS(𝑧𝑧), etc.
Polarization line profiles Stokes 𝑉𝑉 ⇒ ⟨𝐵𝐵long⟩(𝑧𝑧) Stokes 𝑄𝑄,𝑈𝑈 ⇒ ⟨𝐵𝐵trans⟩(𝑧𝑧) Stokes 𝑄𝑄,𝑈𝑈,𝑉𝑉 ⇒ 𝐁𝐁(z) (full vector) 𝑄𝑄,𝑈𝑈,𝑉𝑉 also react to 𝑇𝑇,𝑃𝑃, 𝑣𝑣turb, 𝑣𝑣LOS ...
Physical quantities often effect Stokes profiles non-linearly & non-uniquely
Hinode/SP Lites et al.
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Inversions: automated extraction of physical parameters
Slide by M. van Noort
Technique pioneered by Bruce Lites
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Inversions: automated extaction of physical parameters
Slide by M. van Noort
The Sun More or less simple model: stratification of
various physical quantities at one position on Sun. 𝛼𝛼 = Set of free
parameters
Solution of polarized radiative transfer equations
Observations at a telescope with a spectro-polarimeter
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Inversions: automated extaction of physical parameters
Slide by M. van Noort
The Sun
Solution of polarized radiative transfer equations
Observations at a telescope with a spectro-polarimeter
Determine differences Δ𝑆𝑆 between computed and observed Stokes spectra
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Inversions: automated extaction of physical parameters
Slide by M. van Noort
The Sun
Solution of polarized radiative transfer equations
Observations at a telescope with a spectro-polarimeter
Use Δ𝑆𝑆 to find a better set of free params 𝛼𝛼
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Inversion of a 3D data set:
Temperature
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Sunspot fine structure
Magnetic field strength
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Sunspot fine structure
Inclination of magnetic field
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Sunspot fine structure
Azimuth of magnetic field
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Sunspot fine structure
Line-of-sight velocity
Modern inversions allow such maps to be determined over
a range of heights (the heights
sampled by the inverted spectral
lines)
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