Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
(III – Arbitrary selection of research papers) <- If time allows!
II – Plasma diagnostics
I – Solar radiation
Outline
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Nicolas Labrosse
School of Physics and Astronomy, University of Glasgow 0
Solar radiation and plasma diagnostics
particular features such as sunspots (appear dark)
I.1 Overview
observations: patchy microwave emission
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
X-rays: bright in localised areas (active regions)
X-rays: diffuse emission over solar disk except in coronal holes
 Hard
 Soft
 Radio
– Although the corona can be observed during eclipses, most of our knowledge
comes from
– Spectroscopy (late 1800s) allowed the chromosphere to be studied
 Has
– Optical telescopes show the visible surface (photosphere)
– Too many photons for your naked eyes!
• Basic facts
I.5 How do we detect it?
I.4 How is it formed?
I.3 Radiative transfer
I.2 Radiation basics
I. Solar radiation
I.1 Overview
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Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
From Rutten’s notes
• Radiation field in the solar atmosphere
I.2 Radiation basics
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
– 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.
Planck function
2¼hº 3
1
Iº =
´ Bº (T ) erg s-1 cm-2 sr-1 Hz-1
hº
c2 e kT
¡1
– If radiation field is in thermal equilibrium with surroundings (a closed cavity at
temperature T): blackbody radiation
– Amount of radiant energy flowing through unit area per unit time per unit
frequency and per unit solid angle: intensity Iº
• Radiation field in the solar atmosphere
I.2 Radiation basics
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cos ª = ¹
dh = dl cos ª
¿=
R
k¸ dx
dI¸
= ²¸ ¡ k¸ I¸
dh
cos ª = ¹
dh = dl cos ª
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
¹
– In the limit where dh! 0, we get
I¸(h + dh; ª) ¡ I¸(h; ª) = ²¸(h)dh sec ª ¡ I¸(h; ª)k¸dh sec ª
– Radiation propagating through the
slab along OA varies between h and
h+dh due to absorption and emission:
– More generally we have
• The interaction of the radiation field with the plasma is
described by the Radiative Transfer Equation
I.3 Radiative transfer
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
– If a beam of radiation with
intensity I¸(0) enters a uniform slab of linear
thickness x, the emergent radiation is then
I¸(x)=I¸(0) e-¿ , where ¿=k¸ x is the optical
depth of a uniform slab at wavelength ¸.
E.g. k¸=10-6 cm-1 around 5000 Å
– and absorbs radiant energy
k¸ is the linear absorption
coefficient in cm-1
– Medium emits radiant energy at rate
²¸ erg cm-3 s-1 sr-1 Å-1
• The interaction of the radiation field with the plasma is
described by the Radiative Transfer Equation
I.3 Radiative transfer
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dI¸
= ²¸ ¡ k¸ I¸
dh
h0
1
Z
k¸ dh
cos ª = ¹
dh = dl cos ª
¹
dI¸
= I¸ ¡ S¸
d¿¸
0
S(t) ¡t=¹
e
dt
¹
S(t) ¡t=¹
e
dt
¹
1
¿
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Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
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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.
S is constant at all depths: I(0; ¹+) = S
0
 If S is constant in only a small slab of optical thickness ¿0: I(0; ¹+) = S(1 ¡ e¡¿ =¹ )
emergent intensity not as large as S; reduced by optical depth term. If ¿0 is very
small, then I(0; ¹+) = S¿ 0=¹
 If
I(0; ¹+) =
1
– If ¿! 0 then
Z
I(¿; ¹+) = ¡e¿=¹
– The intensity of radiation flowing through the upper atmosphere (relative
to the point where
Z the optical depth is ¿) is given by
• Solutions to the Radiative Transfer Equation
I.3 Radiative transfer
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
¹
dI¸
= I¸ ¡ S¸ RTE
d¿¸
with the source function S¸ = ²¸=k¸
– The radiative transfer equation is then
¿¸ (h ) =
0
– Finally, in the solar atmosphere,
the optical depth at height h0 is
¹
• The interaction of the radiation field with the plasma is
described by the Radiative Transfer Equation
I.3 Radiative transfer
darkening and EB also imply that T increases with ¿
Simple emission line
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
Simple absorption line
• From Rob Rutten’s notes
I.4 How is it formed?
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
 Limb
results in the Eddington-Barbier relationship:
the intensity observed at any value of ¹ equals the source
function at the level where the local optical depth has the
value ¿ = ¹.
It means that you see deeper in the atmosphere as you look
towards the centre (¹=1) than towards the limb (¹! 0).
 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
This solution matches the limb darkening of the Sun!
S is not constant at all depths: taking S(¿) = a + b¿
one finds I(0; ¹+) = a + b¹
 If
• Solutions to the Radiative Transfer Equation
I.3 Radiative transfer
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Simple emission edge
Doubly-reversed absorption line
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
Self-reversed absorption line
• From Rob Rutten’s notes
I.4 How is it formed?
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
Simple absorption edge
• From Rob Rutten’s notes
I.4 How is it formed?
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Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
– The continuum...
• The photosphere (in short)
I.5 How do we detect it?
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
– The line strengths depend on the column densities of these atoms / ions which
contain electrons in the lower state of the transition
– Many absorption lines (dark) superimposed on
continuum signal presence of atoms / ions in solar atmosphere absorbing radiation
coming from below.
– This happens in the visible around 5000 Å
– Take advantage of photons that have
optical depth unity at the surface of the Sun
• The photosphere (in short)
I.5 How do we detect it?
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submillimetre and millimetre continua
–
continuum
emission lines and no obvious sign of
-Soft X-ray spectrum shows strong
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
Parkinson (1973)
See Edlen (1945) on Fe X 6375 Å and Fe XIV 5303 Å
– Optical forbidden lines tell us it’s hot ~ 1-2 MK and tenuous (less than 109 cm-3)
• The corona (in short)
I.5 How do we detect it?
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
T decreases with ¿
– No limb darkening: rather, limb brightening!
the core of lines such as H® or Ca II K, or
–
– This means looking at
photons for which ¿»1 about 1000-2000 km above the photosphere
– Tune your instrument to detect
– Don’t wait for an eclipse!
• The chromosphere: most poorly understood layer
I.5 How do we detect it?
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II.1 Overview
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
– E.g., energy and momentum balance and transport
• What for?
in a specific (observed) region of the solar atmosphere at a
certain time.
– Chemical abundances
– Pressure
– Mass flow velocities
– Densities
– Temperatures
• What do we (I) mean by plasma diagnostics?
An empirical derivation of:
II.3 Imaging vs spectroscopy
II.2 Direct spectral inversion
II. Plasma diagnostics
II.1 Overview
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opacities and emissivities
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
– 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.”
– Observations of different lines give an idea of variation of T and », and so of
distribution of energy in different layers
– Line width yields ion temperature T and non-thermal (or microturbulent) velocity »
• Optically thin plasma emitting Gaussian-shaped line
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
with observed spectrum ... and adjust model to start over again
RTE to get the emergent spectrum
 Compare
 Solve
 Determines
excitation and ionisation balance for all species
with given spatial distribution of T, p, n
 Solve
 Start
– Semi-empirical models
– Necessary for optically thick plasma
• Forward approach
– Yields spatially averaged values
– For optically thin plasma (all emitted photons leave freely without interaction)
• Direct inversion of spectral data
II.1 Overview
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pressure-sensitive lines (or line intensity ratios)
from density and temperature measurements
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
– See work of Feldman et al (1977), Mariska (1992), Mason and Monsignori Fossi
(1994), ...
– Techniques described now applicable to plasma with ne < 1013 cm-3 in ionization
equilibrium
– A lot of data: SOHO/SUMER, SOHO/CDS, SOHO, UVCS, Hinode/EIS, and then
IRIS (?)
• Application to XUV / EUV / UV lines
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
 Using
 Derived
– Gas pressure
requires good photometric calibration and accurate atomic data
strengths, or absorption of radiation
 Often
 Line
– Neutral and ion densities; abundances
measure methods
scattering measurements
 Thompson
 Emission
depolarization
broadening (generally yields upper limits)
 Collisional
 Stark
– Electron density estimated by
• Optically thin plasma emitting Gaussian-shaped line
II.2 Direct spectral inversion
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~1
~ 0.8
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
Carole Jordan’s work
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
Abundance of element with respect to H
– Now the population of the g level can be written as:
– Now balance excitation from ground level with spontaneous radiative decay
– Under the coronal approximation, only the ground level (g) and excited level (j)
are responsible for the emitted radiation. The statistical equilibrium reduces to:
– Emissivity of b-b transition
• Line emission from optically thin plasma
II.2 Direct spectral inversion
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Collision strength
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
Contribution functions for lines belonging to O III – O VI ions, CHIANTI v.5.1
http://www.chianti.rl.ac.uk/
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
where we have introduced the contribution function G(T)
– Finally...
– Collisional excitation coef:
(assuming Maxwellian
velocity distribution)
Statistical weight
• Line emission from optically thin plasma
II.2 Direct spectral inversion
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, with
the fact that contribution function is peaked to write
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
(see Hannah & Kontar, A&A 539, 146, 2012)
inversion is tricky, using observed line intensities, through calculating
G(T), assuming elemental abundances, and is sensitive to uncertain atomic data
 The
DEM contains information on the processes at the origin of the temperature
distribution, BUT
 The
and thus
– Differential Emission Measure:
yields distribution in temperature of plasma along LOS
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
also yields the electron density
• Electron temperature
 EM
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can be directly inferred from the observation of spectral lines
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 It may be defined also as EM = ne Vc [cm-3], with Vc the coronal volume emitting
the line
 EM
 Use
– Emission measure: yields amount of plasma emissivity along LOS
• Electron temperature
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
fV » EM=n2e
– Measures the fraction of the volume filled by material
• What is the volume filling factor?
II.2 Direct spectral inversion
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
– Intensity ratio yields ne averaged along LOS at line formation temperature
This is because of the density dependence of
the population of level m
, so
– For such a pair of lines from the same ion:
– Allowed transitions have I / n2e
– Forbidden and intersystem transitions, with a metastable (long lifetime) upper
state m, can be collisionally de-excited towards level k
• Electron density from line ratios
II.2 Direct spectral inversion
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–
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
Still issues about what lines contribute (and to what extent) to observed emission
– Narrow-band imaging getting close to spectroscopic imaging
– High cadence, high temporal resolution
– No detailed line profile, no Doppler shifts
• Imaging
– Integrated intensities should not be affected by instrumental profile
• Spectra are still useful even without detailed profiles
II.3 Imaging vs spectroscopy
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
– Line identification and blends can cause headaches!
– Data analysis relies on complex atomic data with high uncertainties
– It takes time to acquire spectra on rather limited field of views
• Issues
– Line profile shape: optical thickness
– Line intensity: densities, temperature
– Line position: Doppler shifts, mass flows
– Line width: thermal and non-thermal processes
• Line profiles give us key information on plasma
parameters
II.3 Imaging vs spectroscopy
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SUMER Measurements of Nonthermal Motions: Constraints on Coronal Heating Mechanisms
XUV spectra of the 1973 June 15 solar flare observed from Skylab. II - Intersystem and forbidden
transitions in transition zone and coronal ions
The solar transition region
Spectroscopic diagnostics in the VUV for solar and stellar plasmas
CHIANTI - an atomic database for emission lines - Paper XII: Version 7 of the database
Differential emission measures from the regularized inversion of Hinode and SDO data
Probing the solar wind acceleration region using spectroscopic techniques
Hα Doppler Brightening and Lyman-α Doppler Dimming in Moving Hα Prominences
EUV lines observed with EIS/Hinode in a solar prominence
Diagnostics of active and eruptive prominences through hydrogen and helium lines modelling
Effect of motions in prominences on the helium resonance lines in the extreme ultraviolet
On the Lyman α and β lines in solar coronal streamers
...
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Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
New Observations of Fe XVII in the Solar X-ray Spectrum
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• Bibliography
Further reading
Solar radiation and plasma diagnostics – STFC Advanced Summer School in Solar Physics – Nicolas Labrosse – 4/9/2012
– Solar Astrophysics, by Foukal, Wiley-vch
– Physics of the Sun: A first course, by D. Mullan, CRC Press
– Rob Rutten’s lectures: http://www.astro.uu.nl/~rutten/Lectures.html
– Nuggets (UKSP, EIS, RHESSI, ...)
– ADS (see some suggestions next page)
• Where can I look to learn more about solar radiation and
plasma diagnostics?
Further reading
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