1. Solar radiation and plasma diagnostics
Nicolas Labrosse
School of Physics and Astronomy, University of Glasgow 0
2. Outline
I – Solar radiation
II – Plasma diagnostics
III – Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 1
3. I. Solar radiation
I.1 Overview
I.2 Radiation basics
I.3 Radiative transfer
I.4 How is it formed?
I.5 How do we detect it?
2
4. I.1 Overview
• Basic facts
– Too many photons for your naked eyes!
– Optical telescopes show the visible surface (photosphere)
Has particular features such as sunspots (appear dark)
– Spectroscopy (late 1800s) allowed the chromosphere to be studied
– Although the corona can be observed during eclipses, most of our
knowledge come from
Radio observations: patchy microwave emission
Soft X-rays: diffuse emission over solar disk except in coronal holes
Hard X-rays: bright in localised areas (active regions)
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 3
5. I.2 Radiation basics
• Radiation field in the solar atmosphere
– Amount of radiant energy flowing through unit area per unit time
per unit frequency and per unit solid angle: intensity Iν
– If radiation field is in thermal equilibrium with surroundings (a
closed cavity at temperature T): blackbody radiation
2πhν 3 1
Planck function Iν = ≡ Bν (T ) erg s-1 cm-2 sr-1 Hz-1
c2 e kT − 1
hν
– Deep in the solar atmosphere, local thermodynamic equilibrium
holds, and mean free path of photons is short (a few km): photons
within a small volume can be considered to be contained in a cavity
where the temperature is ~ constant.
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 4
6. I.2 Radiation basics
• Radiation field in the solar atmosphere
From Rutten’s notes
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 5
7. I.3 Radiative transfer
• The interaction of the radiation field with the plasma is
described by the Radiative Transfer Equation
– Medium emits radiant energy at rate
λ erg cm s sr Å
-3 -1 -1 -1
– and absorbs radiant energy
kλ is the linear absorption
coefficient in cm-1
– If a beam of radiation with
intensity Iλ(0) enters a uniform slab of linear
thickness x, the emergent radiation is then
Iλ(x)=Iλ(0) e-τ , where τ=kλ x is the optical dh = dl cos Ψ
depth of a uniform slab at wavelength λ. cos Ψ = µ
E.g. kλ=10-6 cm-1 around 5000 Å
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 6
8. I.3 Radiative transfer
• The interaction of the radiation field with the plasma is
described by the Radiative Transfer Equation
– More generally we have τ = kλ dx
– Radiation propagating through the
slab along OA varies between h and
h+dh due to absorption and emission:
Iλ (h + dh, Ψ) − Iλ (h, Ψ) = λ (h)dh sec Ψ − Iλ (h, Ψ)kλ dh sec Ψ
– In the limit where dh→ 0, we get dh = dl cos Ψ
dIλ cos Ψ = µ
µ = λ − kλ Iλ
dh
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 7
9. I.3 Radiative transfer
• The interaction of the radiation field with the plasma is
described by the Radiative Transfer Equation
dIλ
µ = λ − kλ Iλ
dh
– Finally, in the solar atmosphere,
the optical depth at height h is
h
τλ (h ) = kλ dh
∞
– The radiative transfer equation is then
dIλ dh = dl cos Ψ
µ = Iλ − Sλ RTE
dτλ cos Ψ = µ
with the source function Sλ = λ /kλ
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 8
10. I.3 Radiative transfer
dIλ
• Solutions to the Radiative Transfer Equation µ = Iλ − S λ
dτλ
– The intensity of radiation flowing through the upper atmosphere (relative
to the point where the optical depth is τ) is given by
τ
τ /µ S(t) −t/µ
I(τ, µ+) = −e e dt
∞ µ
– If τ→ 0 then
∞
S(t) −t/µ
I(0, µ+) = e dt
0 µ
If S is constant at all depths: I(0, µ+) = S
If S is constant in only a small slab of optical thickness τ : I(0, µ+) = S(1 − e−τ /µ )
emergent intensity not as large as S; reduced by optical depth term. If τ is very
small, then I(0, µ+) = Sτ /µ
In the case of constant source function, the emergent intensity from a slab cannot be
greater than S, but may be much smaller than S if the optical depth is small.
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 9
11. I.3 Radiative transfer
• Solutions to the Radiative Transfer Equation
If S is not constant at all depths: taking S(τ ) = a + bτ
one finds I(0, µ+) = a + bµ
This solution matches the limb darkening of the Sun!
This particular form of the source function is actually a natural
consequence of the assumption of a Gray atmosphere, where
the opacity is independent of wavelength.
This results in the Eddington-Barbier relationship:
the intensity observed at any value of µ equals the source
function at the level where the local optical depth has the
value τ = µ.
It means that you see deeper in the atmosphere as you look
towards the centre (µ=1) than towards the limb (µ→ 0).
Limb darkening and EB also imply that T increases with τ
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 10
12. I.4 How is it formed?
• From Rob Rutten’s notes
Simple absorption line Simple emission line
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 11
13. I.4 How is it formed?
• From Rob Rutten’s notes
Simple absorption edge Simple emission edge
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 12
14. I.4 How is it formed?
• From Rob Rutten’s notes
Self-reversed absorption line Doubly-reversed absorption line
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 13
15. I.5 How do we detect it?
• The photosphere (in short)
– Take advantage of photons that have
optical depth unity at the surface of the Sun
– This happens in the visible around 5000 Å
– Many absorption lines (dark) superimposed on the continuum
signal presence of atoms / ions in the solar atmosphere absorbing
radiation coming from below.
– The line strengths depend on the column densities of these atoms
/ ions which contain electrons in the lower state of the transition
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 14
16. I.5 How do we detect it?
• The photosphere (in short)
– The continuum...
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 15
17. I.5 How do we detect it?
• The chromosphere (in short)
– Don’t wait for an eclipse!
– Tune your instrument
to detect photons for which
τ∼1 about 1000-2000 km above the photosphere
– This means looking at the core of lines such as Hα or Ca II K
– No limb darkening: rather, limb brightening!
So T decreases with τ.
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 16
18. I.5 How do we detect it?
• The corona (in short)
– Optical forbidden lines tell you that it’s hot ~ 1-2 MK and tenuous
(less than 109 cm-3)
See Edlen (1945) on Fe X 6375 Å and Fe XIV 5303 Å
– Soft X-ray spectrum shows
Parkinson (1973)
strong emission lines and no
obvious sign of continuum
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 17
20. II.1 Overview
• What do we (I) mean by plasma diagnostics?
An empirical derivation of:
– Temperatures
– Densities
– Mass flow velocities
– Pressure
– Chemical abundances
in a specific (observed) region of the solar atmosphere at a
certain time.
• What for?
– Energy and momentum balance and transport
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 19
21. II.1 Overview
• Direct inversion of spectral data
– For optically thin plasma (all emitted photons leave freely without
interaction)
– Yields spatially averaged values
• Forward approach
– Necessary for optically thick plasma
– Semi-empirical models
Start with given spatial distribution of T, p, n
Solve excitation and ionisation balance for all species
Determines opacities and emissivities
Solve RTE to get the emergent spectrum
Compare with observed spectrum ... and adjust model to start over again
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 20
22. II.2 Direct spectral inversion
• Optically thin plasma emitting Gaussian-shaped line
– Line width yields ion temperature T and non-thermal (or
microturbulent) velocity ξ
– Observations of different lines give an idea of variation of T and ξ,
and so of distribution of energy in different layers
– See e.g. Chae et al (1998) analysis of
SOHO/SUMER observations.
“The isotropic and small-scale nature of the
nonthermal motions appear to be suited for
MHD turbulence.”
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 21
23. II.2 Direct spectral inversion
• Optically thin plasma emitting Gaussian-shaped line
– Electron density estimated by
Stark broadening (generally yields upper limits)
Collisional depolarization
Thompson scattering measurements
Emission measure methods
– Neutral and ion densities; abundances
Line strengths, or absorption of radiation
Often requires good photometric calibration and accurate atomic data
– Gas pressure
Derived from density and temperature measurements
Using pressure-sensitive lines (or line intensity ratios)
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 22
24. II.2 Direct spectral inversion
• Application to XUV / EUV / UV lines
– A lot of data: SOHO/SUMER, SOHO/CDS, SOHO, UVCS,
Hinode/EIS, and then IRIS (?)
– Techniques described now applicable to plasma with ne < 1013 cm-3
in ionization equilibrium
– See work of Feldman et al (1977), Mariska (1992), Mason and
Monsignori Fossi (1994), Phillips et al (2008), ...
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 23
25. II.2 Direct spectral inversion
• Line emission from optically thin plasma
– Emissivity of b-b transition
– Under the coronal approximation, only the ground level (g) and
excited level (j) are responsible for the emitted radiation. The
statistical equilibrium reduces to:
– Now only have to balance excitation from ground level with
spontaneous radiative decay, which yields
– Now the population of the g level can be written as:
Abundance of element with respect to H
~1 ~ 0.8
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 24
26. II.2 Direct spectral inversion
Carole Jordan’s work
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 25
27. II.2 Direct spectral inversion
• Line emission from optically thin plasma
– Collisional excitation coef:
(assuming Maxwellian
velocity distribution) Statistical weight Collision strength
– Finally...
where we have introduced the contribution function G(T)
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 26
28. II.2 Direct spectral inversion
http://www.chianti.rl.ac.uk/
Contribution functions for lines belonging to O III – O VI ions, CHIANTI v.5.1
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 27
29. II.2 Direct spectral inversion
• Electron temperature
– Emission measure: yields amount of plasma emissivity along LOS
Use the fact that contribution function is peaked to write
, with
EM can be directly inferred from the observation of spectral lines
It may be defined also as EM = n2 Vc [cm-3], with Vc the coronal volume
e
emitting the line
EM also yields the electron density
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 28
30. II.2 Direct spectral inversion
• Electron temperature
– Differential Emission measure: yields distribution in temperature of
plasma along LOS
and thus
The DEM contains information on the processes at the origin of the
temperature distribution, BUT
The inversion is tricky, using observed line intensities, through calculating
G(T), assuming elemental abundances, and is sensitive to uncertain
atomic data
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 29
31. II.2 Direct spectral inversion
• Electron density from line ratios
– Allowed transitions have I ∝ n2
e
– Forbidden and intersystem transitions, with a metastable (long
lifetime) upper state m, can be collisionally de-excited towards level k
– For such a pair of lines from the same ion:
, so
This is because of the density dependence of
the population of level m
– Intensity ratio yields ne averaged along LOS at line formation
temperature
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 30
32. II.2 Direct spectral inversion
• What is the volume filling factor?
– Measures the fraction of the volume filled by material
fV ∼ EM/n2
e
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 31
33. II.3 Imaging vs spectroscopy
• Line profiles give us key information on plasma
parameters
– Line width: thermal and non-thermal processes
– Line position: Doppler shifts, mass flows
– Line intensity: densities, temperature
– Line profile shape: optical thickness
• Issues
– It takes time to acquire spectra on rather limited field of views
– Data analysis relies on complex atomic data with high
uncertainties
– Line identification and blends can cause headaches!
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 32
34. II.3 Imaging vs spectroscopy
• Spectra are still useful even without detailed profiles
– Integrated intensities should not be affected by instrumental profile
• Imaging
– No detailed line profile, no Doppler shifts
– High cadence, high temporal resolution
– Narrow-band imaging getting close to spectroscopic imaging
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 33
36. III. Arbitrary selection of research papers
• Plasma diagnostics in the solar wind acceleration region
– Uses ratio of collisional and radiative components of pairs of
strong resonance lines (e.g., O VI 1032/1037; Ne VIII 770/780; Mg X
610/625; Si XII 499/521; Fe XVI 335/361)
– Kinetic temperatures and deviations from Maxwellian distributions
can be determined from line shapes and widths (mass or charge-to-
mass dependent processes)
– Mass-independent broadening can also be produced by bulk
motions of coronal plasma
– Measurements provide key tests for models
See Kohl & Withbroe (1982); Withbroe et al. (1982); UVCS papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 35
37. III. Arbitrary selection of research papers
• Plasma diagnostics in the solar wind acceleration region
– Solar wind velocities by the Doppler dimming effect (Hyder & Lites
1970)
Intensity of resonantly scattered component of spectral line depends on
∞
∫ J φ (ν −ν )dν
−∞
ν w
Doppler shift introduced by wind velocity
mean intensity of disk radiation
normalised absorption profile
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 36
38. III. Arbitrary selection of research papers
Kohl & Withbroe 1982
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39. III. Arbitrary selection of research papers
Labrosse et al (2007, 2008) Labrosse et al (2006)
Ly-β
Ly-α
Ly-α (SOHO/UVCS)
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 38
40. III. Arbitrary selection of research papers
• The TR and coronal downflows
– Net redshift in all TR emission lines, peaking at log T=5, explained
by material draining down on both sides of TR loops towards
footpoints (Brekke et al., 1997; Dammash et al., 2008).
– Similar observations in coronal lines (e.g. EIS: del Zanna 2008,
Tripathi et al 2009)
– Also observed in optically thick Lyman lines by SOHO/SUMER
(see Curdt et al., 2011)
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 39
41. III. Arbitrary selection of research papers
• Lyman-α is one of the most important lines
– 1216 Å
– Transition between atomic levels 1 and 2 of hydrogen
– Key role in radiative energy transport in solar atmosphere
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 40
42. III. Arbitrary selection of research papers
Correspondence between asymmetry and downflows
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43. Correspondence between line reversals and magnetic field
Flatter profiles (reduced opacity) cluster along the network lane
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 42
44. III. Arbitrary selection of research papers
• Plasma diagnostics in the flaring solar chromosphere
(Graham et al., 2011)
– Combined EIS, RHESSI, XRT and TRACE data covering a wide
range of temperatures
– Evidence for T~7 MK in footpoints from XRT
– and ne~a few 1010 cm-3 at T~1.5-2 MK
– Small downflows at T<1.6MK; upflows up to 140 km s-1 above
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 43
45. III. Arbitrary selection of research papers
• Graham et al., 2011
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46. III. Arbitrary selection of research papers
• Graham et al., 2011
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 45
47. III. Arbitrary selection of research papers
• Graham et al., 2011
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 46
48. III. Arbitrary selection of research papers
• Solar prominence diagnostics with Hinode (Labrosse et
al., 2011)
– Used EIS data covering a wide range of temperatures
– Evidence for absorption and volume blocking
– Used optically thick He II 256 Å line and non-LTE models
– Infer H column density of 1020 cm-2
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 47
49. III. Arbitrary selection of research papers
• Labrosse et al., 2011
EIS field of view
SOT XRT
Prominence observed on 26 April 2007 by Hinode
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50. III. Arbitrary selection of research papers
• Labrosse et al., 2011
Line formed in the PCTR Line formed in the corona
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51. III. Arbitrary selection of research papers
• Labrosse et al., 2011
τ 195 = 0.3 − 0.6
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52. III. Arbitrary selection of research papers
• Labrosse et al., 2011
– Prominence plasma parameters obtained by comparison between
inferred intensities and computed intensity at 256 Å
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 51
53. Further reading
• Where can I look to learn more about solar radiation and
plasma diagnostics?
– ADS
– Nuggets (UKSP, EIS, RHESSI, ...)
– Rob Rutten’s lectures: http://www.astro.uu.nl/~rutten/Lectures.html
– Physics of the Sun: A first course, by D. Mullan, CRC Press
– Solar Astrophysics, by Foukal, Wiley-vch
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