Solar radiation and plasma diagnostics
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Nicolas LabrosseSchool of Physics and Astronomy, University of Glasgow
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
III – Arbitrary selection of research papers
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I. Solar radiation
I.1 OverviewI.1 Overview
I.2 Radiation basics
I.3 Radiative transfer
I.4 How is it formed?
I.5 How do we detect it?2
• 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
I.1 Overview
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– 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)
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• 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
I.2 Radiation basics
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
closed cavity at temperature T): blackbody radiation
Planck function erg s-1 cm-2 sr-1 Hz-1
– 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.
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Iν =2πhν3
c2
1
ehν
kT − 1≡ Bν(T)
• Radiation field in the solar atmosphere
I.2 Radiation basics
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 5
From Rutten’s notes
• The interaction of the radiation field with the plasma is described by the Radiative Transfer Equation
– Medium emits radiant energy at rateελ erg cm-3 s-1 sr-1 Å-1
– and absorbs radiant energyk is the linear absorption
I.3 Radiative transfer
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
dh = dl cosΨ
cosΨ = µ
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 thenIλ(x)=Iλ(0) e-τ , where τ=kλ x is the opticaldepth of a uniform slab at wavelength λ.E.g. kλ=10-6 cm-1 around 5000 Å
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• The interaction of the radiation field with the plasma is described by the Radiative Transfer Equation
– More generally we have
– Radiation propagating through the
I.3 Radiative transfer
τ =∫kλdx
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
dh = dl cosΨ
cosΨ = µ
– Radiation propagating through the slab along OA varies between h and h+dh due to absorption and emission:
– In the limit where dh→ 0, we get
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Iλ(h+ dh,Ψ)− Iλ(h,Ψ) = ελ(h)dh secΨ− Iλ(h,Ψ)kλdh secΨ
µdIλdh
= ελ − kλIλ
• The interaction of the radiation field with the plasma is described by the Radiative Transfer Equation
– Finally, in the solar atmosphere,
I.3 Radiative transfer
µdIλdh
= ελ − kλIλ
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
dh = dl cosΨ
cosΨ = µ
– Finally, in the solar atmosphere,the optical depth at height h′ is
– The radiative transfer equation is then
with the source function
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τλ(h′) =
∫ h′
∞
kλdh
Sλ = ελ/kλ
µdIλdτλ
= Iλ − Sλ RTE
• Solutions to the Radiative Transfer Equation
– The intensity of radiation flowing through the upper atmosphere (relative to the point where the optical depth is τ) is given by
– If 0 then
I.3 Radiative transfer
µdIλdτλ
= Iλ − Sλ
I(τ, µ+) = −eτ/µ∫ τ
∞
S(t)
µe−t/µdt
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
I(0, µ+) = S(1− e−τ′/µ)
– If τ→ 0 then
� If S is constant at all depths:
� If S is constant in only a small slab of optical thickness τ′:emergent intensity not as large as S; reduced by optical depth term. If τ′ is very small, then
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.
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I(0, µ+) =
∫∞
0
S(t)
µe−t/µdt
I(0, µ+) = S
I(0, µ+) = Sτ ′/µ
• Solutions to the Radiative Transfer Equation
� If S is not constant at all depths: taking one finds
This solution matches the limb darkening of the Sun!
�This particular form of the source function is actually a naturalconsequence of the assumption of a Gray atmosphere, where
I.3 Radiative transfer
I(0, µ+) = a+ bµ
S(τ ) = a+ bτ
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
consequence of the assumption of a Gray atmosphere, wherethe opacity is independent of wavelength.
�This results in the Eddington-Barbier relationship:the intensity observed at any value of µ equals the sourcefunction at the level where the local optical depth has thevalue τ = µ.It means that you see deeper in the atmosphere as you looktowards the centre (µ=1) than towards the limb (µ→ 0).
�Limb darkening and EB also imply that T increases with τ
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• From Rob Rutten’s notes
I.4 How is it formed?
Simple absorption line Simple emission line
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 11
• From Rob Rutten’s notes
I.4 How is it formed?
Simple absorption edge Simple emission edge
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 12
• From Rob Rutten’s notes
I.4 How is it formed?
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
• The photosphere (in short)
– Take advantage of photons that haveoptical depth unity at the surface of the Sun
– This happens in the visible around 5000 Å
– Many absorption lines (dark) superimposed on the continuum
I.5 How do we detect it?
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– 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
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• The photosphere (in short)
– The continuum...
I.5 How do we detect it?
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 15
• The chromosphere (in short)
– Don’t wait for an eclipse!
– Tune your instrumentto detect photons for whichτ∼1 about 1000-2000 km above the photosphere
I.5 How do we detect it?
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
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.
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• 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
I.5 How do we detect it?
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 17
– Soft X-ray spectrum showsstrong emission lines and no obvious sign of continuum
Parkinson (1973)
II. Plasma diagnostics
II.1 OverviewII.1 Overview
II.2 Direct spectral inversion
II.3 Imaging vs spectroscopy
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• What do we (I) mean by plasma diagnostics?An empirical derivation of:
– Temperatures– Densities– Mass flow velocities
II.1 Overview
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– 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
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• Direct inversion of spectral data
– For optically thin plasma (all emitted photons leave freely without interaction)– Yields spatially averaged values
• Forward approach
II.1 Overview
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
• 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
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• 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,
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– 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 ofSOHO/SUMER observations.“The isotropic and small-scale nature of the
nonthermal motions appear to be suited for
MHD turbulence.”
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• Optically thin plasma emitting Gaussian-shaped line
– Electron density estimated by�Stark broadening (generally yields upper limits)�Collisional depolarization �Thompson scattering measurements
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
�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)
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• 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
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
in ionization equilibrium
– See work of Feldman et al (1977), Mariska (1992), Mason and Monsignori Fossi (1994), Phillips et al (2008), ...
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• 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:
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
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:
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~ 1 ~ 0.8
Abundance of element with respect to H
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 25
Carole Jordan’s work
• Line emission from optically thin plasma
– Collisional excitation coef:(assuming Maxwellianvelocity distribution)
– Finally...
II.2 Direct spectral inversion
Statistical weight Collision strength
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– Finally...
where we have introduced the contribution function G(T)
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II.2 Direct spectral inversion
http://www.chianti.rl.ac.uk/
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 27
Contribution functions for lines belonging to O III – O VI ions, CHIANTI v.5.1
• 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
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
EM = n2eVc
�EM can be directly inferred from the observation of spectral lines
�It may be defined also as [cm-3], with Vc the coronal volume emitting the line
�EM also yields the electron density
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• Electron temperature
– Differential Emission measure: yields distribution in temperature of plasma along LOS
and thus
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
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
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• Electron density from line ratios
– Allowed transitions have
– 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:
II.2 Direct spectral inversion
I ∝ n2e
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– For such a pair of lines from the same ion:
, so
This is because of the density dependence ofthe population of level m
– Intensity ratio yields ne averaged along LOS at line formation temperature
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• What is the volume filling factor?
– Measures the fraction of the volume filled by material
II.2 Direct spectral inversion
fV ∼ EM/n2
e
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 31
• 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
II.3 Imaging vs spectroscopy
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– 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!
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• Spectra are still useful even without detailed profiles
– Integrated intensities should not be affected by instrumental profile
• Imaging
II.3 Imaging vs spectroscopy
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– No detailed line profile, no Doppler shifts
– High cadence, high temporal resolution
– Narrow-band imaging getting close to spectroscopic imaging
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III. Arbitrary selection of research papers
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• 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
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– 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
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• Plasma diagnostics in the solar wind acceleration region
– Solar wind velocities by the Doppler dimming effect (Hyder & Lites1970)�Intensity of resonantly scattered component of spectral line depends on
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 36
∫∞
∞−
− νννφν
dJw)(
mean intensity of disk radiation
normalised absorption profile
Doppler shift introduced by wind velocity
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 37
Kohl & Withbroe 1982
III. Arbitrary selection of research papers
Labrosse et al (2006)Labrosse et al (2007, 2008)
Ly-β
Ly-α
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 38
Ly-α
Ly-α (SOHO/UVCS)
• 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,
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– 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)
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• 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
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 40
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 41
Correspondence between asymmetry and downflows
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 42
Correspondence between line reversals and magnetic field
Flatter profiles (reduced opacity) cluster along the network lane
• 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
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– 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
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• Graham et al., 2011
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 44
• Graham et al., 2011
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 45
• Graham et al., 2011
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 46
• 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
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– Used optically thick He II 256 Å line and non-LTE models
– Infer H column density of 1020 cm-2
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• Labrosse et al., 2011
III. Arbitrary selection of research papers
EIS
fiel
d of
vie
w
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 48
SOT XRT
Prominence observed on 26 April 2007 by HinodeE
IS fi
eld
of v
iew
• Labrosse et al., 2011
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 49
Line formed in the PCTR Line formed in the corona
• Labrosse et al., 2011
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 50
6.03.0195 −=τ
• Labrosse et al., 2011
– Prominence plasma parameters obtained by comparison between inferred intensities and computed intensity at 256 Å
III. Arbitrary selection of research papers
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011 51
• 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
Further reading
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 1/9/2011
– 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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