More on contribution functions

1
More on contribution functions
Suppose we have a tiny active region on the Sun
with volume 1 cm3, electron density 1 cm-3,
and with a temperature T1 1.2 MK (let us
suppose). The flux of an emission line e.g. Fe
IX 171 Å from this tiny active region is
because the emission is only 1 cm-3
(extremely small).
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Then we look up G(T)...
We plot G(T) for this Fe IX line at 171 Å and
look up its value at 1.2 MK 1 x 10-24. So
this is the line flux (erg cm-2 s-1) coming from
this tiny active region F. In practice V
might be 1026 cm3 and Ne 1011 cm-3, so the
emission measure is (1011)2 x 1026 1048 cm-3.
Flux then 1048 x F x h? / 4p R2.

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Dont forget that....

• Emission measure is a property of the emitting
  region on the Sun which is assumed to be
  isothermal it is a measure of the amount of
  material in an emitting region in the corona Ne2
  V.
• It is just a number (e.g. 1049 cm-3).
• (It is not the same as the number of electrons or
  ions in the emitting region NeV or NionV.)
• Differential emission measure describes the
  temperature dependence of the emitting region if
  it is not isothermal f(T) Ne2 dV/dT.

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and that ...

• G(T) is a property of the emission spectral line
  and can be calculated from atomic physics (e.g.
  by CHIANTI).

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Lecture 6Diagnosing solar plasmas from their
spectra

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Spectroscopic diagnostics for studying the Suns
atmosphere

• We can study or diagnose laboratory
  high-temperature plasmas using probes inserted
  into the plasma.
• This is done for large tokamak devices which use
  high-power magnets to contain very hot plasmas
  for fusion research.
• The Joint European Torus (JET) tokamak at Culham
  Laboratory has a large array of such probes.
• To determine the temperature and number density
  of particles forming the 20 MK plasma during
  shots, monochromatic (i.e. narrow spectral
  line) laser beams are shone into the plasma.
• The scattered radiation is detected by
  spectrometers. The width of the spectral line
  determines the ion temperature and the intensity
  of the scattered radiation determines the
  particle density.

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The JET tokamak
Coils carrying current that forms containing mag.
field
Torus
High-temperature plasma formed in short shots
T20MK
Port holes in torus allow probes to view the hot
plasma
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Solar coronal plasmas remote sensing

• We cannot insert probes or shine lasers into the
  solar atmosphere, but we can use spectroscopic
  diagnostic techniques, using spectral lines in
  the extreme ultraviolet or X-ray region remote
  sensing.

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Plasma temperature diagnostics

• To determine the temperature of the corona ( 12
  MK) or active region within the corona ( 25
  MK), we may use spectral lines from adjacent
  ionization stages.
• E.g. for corona, Fe8 to Fe14 are abundant
  ionization stages. So we could use the ratio of
  these extreme ultraviolet lines to determine the
  coronas temperature
• Fe IX (171 Å) / Fe X (174.8 Å)
• Fe X (174.8 Å) / Fe XI (180.4 Å)
• This ratio is very suitable for Hinode EIS
  spectra
• Fe XI (180.4 Å) / Fe XII (195 Å)

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Hinode EIS spectrum of solar coronal spectrum,
175210 Å
Quiet Sun spectrum, 2006 Nov. 4

11
Another temperature diagnostic two lines from
same ionization stage
Consider two lines from same ionization stage,
excited from ground level (0) to upper levels 1
and 2. If the transitions 1?0 and 2?0 result in
strong (resonance) lines, then approximately N0Ne
C01 I1 and N0NeC02 I2 or
and
Hence
If energy difference (E2 E1) gtgt kT, I2/I1
sensitively depends on T.
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Dielectronic Satellite Lines in the X-ray
Spectrum of the Sun
In the solar X-ray spectrum, we observe lines
that are excited by hot active regions or flares
temperatures range from 25MK (non-flaring
active regions) to gt 20 MK (flares). We can use
lines formed in the dielectronic recombination
process satellite lines to get information
about temperature in such plasmas. Satellite
lines are so called because they occur just to
the long-wavelength side of associated
resonance (strong) lines.
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Dielectronic satellites close to the Fe XXV 1s2
1s2p resonance line
Spectra of Fe XXV and satellites during a flare
from the Hinotori spacecraft (K. Tanaka,
1981) Dielectronic satellites of Fe XXIV on the
long-wavelength side of the Fe XXV resonance
line (w) at 1.85 Å
Wavelength 1.85 1.86 1.87
1.88 Å
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Fe XXIV dielectronic recombination satellite
lines at 1.851.87 Å
Helium-like Fe has a strong resonance line at
1.850 Å. The transition is 1s2 1S0 1s2p 1P1.
This line is excited by electron collisions in
the usual way. But we can also have dielectronic
recombination of Fe24 ions, with an electron
being captured to form a doubly excited state 1s
2p2 Fe24 (1s2 1S0) e- ? Fe23 (1s
2p2) The doubly excited state 1s 2p2 could (a)
auto-ionize (or return to Fe24 (1s2) free
electron) or (b) stabilize by these transitions
1s 2p2 ? 1s2 2p h?DS Fe XXIV dielectronic
satellite line photon at 1.87Å 1s2 2p ? 1s2
2s (an EUV photon is emitted not
important)

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Temperature dependence of Fe sat. j / Fe XXV w
T dependence of Ca sat. k / Ca XIX w
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Solar flare spectra of Fe XXV lines and Fe XXIV
satellites observations by the SMM spacecraft
Te15.0MK Satellites intense compared with Fe
XXV resonance line w. Te17.5 MK Satellites
weaker compared with Fe XXV line w.
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Electron densities

• We can get very rough values of electron density
  Ne by imaging a flare or active region on the Sun
  and guestimating its temperature.
• Thus, if we had an X-ray image of a flare in
  RHESSI near the Fe line (mostly made up of Fe
  XXV lines at 1.85 Å 6.7 keV), we could get
  temperature T and emission measure Ne2V (from the
  continuum emission).
• From a RHESSI image we could get volume V.
• So Ne v(emission measure / V).

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Early estimates of flare densities

• This is what Pallavicini et al. (ApJ 1977) got
  from using this method for X-ray flares observed
  with Skylab Ne probably too small by x 10 or
  more.

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Plasma density spectral diagnostics

• It is more difficult to measure density with
  spectral line ratios than temperature.
• A few spectral lines have intensities that are
  density-dependent because there is in the energy
  level diagram of the emitting ion a metastable
  level a level that has a relatively long
  lifetime compared with other excited levels.
• In the (relatively) long time ions are in a
  metastable state, at high densities, collisions
  with free electrons may occur to raise it to
  another level.
• As a result, another line may appear or an
  already existing line may become more intense.

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The case of He-like ions

• The ground state of a He-like ion (e.g. O6) is
  1s2 1S0.
• When the He-like ion is excited by collision of
  the ion with a free electron to an n2 level,
  there are various possibilities the most
  probable is 1s2p 1P1.
• But excitation to 1s2p 3P1 and 1s2s 3S1 is
  possible.
• Radiative de-excitation of each of these levels
  is possible, resulting in these X-ray spectral
  lines
• 1s2 1S0 1s2p 1P1 the resonance line (w)
• 1s2 1S0 1s2p 3P1 the intercombination line
  (y)
• 1s2 1S0 1s2s 3S1 the forbidden line (z)

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Energy level diagram for He-like ion
Resonance line w unaffected by density.

1s2p 1P1 (3)
Resonance line w
1s2p 3P1 (2)
Metastable level (1) 1s2s 3S1
Inter- combination line y
Forbidden line z
1s2 1S0 (0)
As Ne increases, there is more collisional
excitation from level C to level B. Flux of line
y increases, flux of line z decreases.
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Solving equations for level populations

• To get theoretical density dependence, we have to
  solve equations that give the populations of the
  levels 0, 1, 2, 3.
• For level 3, this is simply Ne n0 C03 n3 A30
• where n0 is the population of level 0 ( number
  density of O6 ions in the ground state) and n3
  the population of level 3 (number density of O6
  ions in the 1s2p 1P1 state). C03 is the
  collisional rate coefficient 0?3 transitions, A30
  the transition rate 3?0.
• For levels 1, 2, this is much more complex. I
  will give you the final solution (but if youre
  interested I can give you the details! ?)

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Solution for He-like ion populations

• Let R Iz / Iy ratio of flux of line z to flux
  of line y
• n1 A10 / n2 A20
• Put F C01/C02 and B A20/(A20 A21).
• Then
• The low-density limit (Ne 0) is

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Density sensitivity of He-like O (O VII) lines
Density-sensitive ratio R ratio forbidden line
(z) / intercombination line (y).
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Observations of O VII lines during a solar flare
observed by the P78-1 spacecraft (1980)
Max. density spectrum
Low-density spectra
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Density measurements from O VII X-ray lines
during solar flares

• Repeated measurements of O VII X-ray lines for
  solar flare on 1980 April 8 (P78-1 X-ray
  spectrometer) gave
• Maximum density Ne 2 1012 cm-3
• Late in flare Ne 5 1011 cm-3.
• Temperature (Te) of O VII lines 2 MK.
• So gas pressure at maximum density was
• Ne kBTe 550 dyne cm-2
• Magnetic field needed to contain this plasma
  (pressure B2/8p) B 120 G.
• Based on a paper by Doschek et al. (ApJ 249, 372,
  1981)

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Density diagnostics in the EUV and soft X-ray
spectrum

• Several ions have ground configurations with more
  than 1 level e.g. C-like ions.
• C has ground configuration 1s2 2s2 2p2.
• 1s2 and 2s2 are complete shells, but 2p2 is not.
• There are 5 levels within the 2p2 configuration

1S0
1D2
1s2 2s2 2p2
3P2
3P1
3P0
Ground level
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The case of Mg VII (C-like Mg) lines

• Mg VII lines are at (1) 278.39 Å (2p2 3P2 2s2p3
  3S1) and (2) 280.75 Å (2p2 1D2 2s2p3 1P1).
• Collisional excitation occurs from 2p2 3P2 for
  line (1) and from 2p2 1D2 for line (2).
• The entire population of Mg6 ions is in the
  ground state 2p2 3P0 for low Ne, but as density
  increases, populations of 3P2 and 1D2 (and 3P1,
  1S0) levels increase.
• So I(278.39) / I (280.75) is a useful density
  diagnostic of active regions, accessible to
  Hinode EIS.

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Density maps using Hinode EIS
Tripathi et al. (2008, AA 481, L53) active
region density maps using Fe XII lines.
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Spectral line profiles

• A spectral line emitted by a gas or plasma with
  atoms or ions with Maxwell-Boltzmann distribution
  gives rise to a spectral line that is broadened
  into a Gaussian profile.
• The number of atoms or ions moving directly
  towards an observer is
• where v0v(2kT/M) most probable thermal
  velocity (M atom or ion mass kBoltzmann
  constant, Ttemperature).
• If the atoms or ions emit a spectral line with
  central wavelength ?0, then atoms or ions
  approaching and receding from the observer give
  rise to Doppler shifts (v/c) ?0.

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Spectral line profiles (contd.)

• The net result is a broadened spectral line that
  has a profile (shape) given by
• where
• The profile is a Gaussian.
• Its ½ - 1/e - width ??.
• Its full width half maximum intensity (FWHM)
  2v(loge2) ?? 1.665 ??.

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Spectral line profiles (contd.)

• For most cases in the solar atmosphere, spectral
  line profiles are Gaussian, but there may be a
  non-thermal component
• Sometimes there may be a component with
  Lorentzian shape,
• The combination of a Gaussian and Lorentzian
  profile gives a Voigt profile. If the Lorentzian
  and Gaussian widths are known, the Voigt profile
  can be found from tabulations or from the IDL
  VOIGT routine.

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Diagnostics of mass motions

• Spectral lines can give information about mass
  motions, e.g. flows of gas or plasma.
• This is done through the Doppler shifts of
  spectral lines.
• For example, during solar flares, X-ray lines
  indicate upflowing plasma flows at the flare
  onset phase, velocities of several hundred km/s.
  These are indicated by spectral line components
  on the short-wavelength side of the unshifted
  component.
• The upflowing plasma is thought to occur because
  non-thermal electron beams directed at the
  chromosphere cause the plasma to convect upwards
  the plasma cannot radiate fast enough in
  response to the energy dumped by the electron
  beam. This is chromospheric evaporation.

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Ca XIX X-ray lines during a flare
Ca XIX w, x, y, z lines observed with SMM (BCS)
at the flare impulsive stage. There is an
undisplaced line component plus a component
shifted to shorter (blue) wavelengths for disk
flares. The blue-shifted component disappears
after the impulsive stage.
Undisplaced component
Blue-shifted compt.
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Line broadening during flares

• X-ray line profiles are often broadened beyond
  the thermal Doppler width.
• This occurs for disk and limb flares.
• It is generally attributed to plasma turbulence,
  but it is hard to see how there can be eddy
  currents if the hot plasma is held by a magnetic
  field.
• Perhaps instead the line broadening arises by
  chromospheric evaporation flows along directions
  making different angles to the line of sight.

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Flare ion temperature gt electron temperature?

• The X-ray line broadening during flares might
  alternatively be due to ion temperatures raised
  above the electron temperature.
• This could occur if there are plasma waves that
  excite only ions and not electrons.
• Otherwise, the ions and electrons would very soon
  equilibrate and their temperatures would be
  practically equal.
• If say Tion 40 MK, Te20MK, the equilibration
  time teq
• is
• where N particle number density (cm-3).

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Diagnostic for flare nonthermal electrons

• At flare impulsive stage, there are huge numbers
  of nonthermal electrons accelerated by
  reconnection events in the pre-flare (active
  region) loops.
• The emission that we see is practically all
  thermal, and formed by evaporated and heated
  chromospheric material filling loops.
• However, there may still be a small number of
  nonthermal electrons left over from the
  acceleration phase.

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Dielectronic satellites as diagnostics

• For dielectronic satellite lines, we have
  transitions like
• 1s2 e- ? 1s 2p2 (n2 satellite)
• For Fe XXIV, transitions like this (forming
  satellites at 1.85 Å) are excited by electrons
  with energies 4.7 keV.
• Some transitions are like
• 1s2 e- ? 1s 2p3p (n3 satellite)
• and are excited by electrons with energies 5.8
  keV.
• The Fe XXV w line is excited by electrons with
  energies gt 6.7 keV.
• So the flux ratio I (n2 sat.) I (n3 sat.) I
  (w) should give the same temperatures. If not,
  the differences may indicate that there are
  nonthermal electrons (e.g. exciting the Fe XXV w
  line but not the satellites).

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Coronal magnetic field

• Although the Zeeman effect can be used to measure
  the photospheric magnetic field, it is almost
  impossible to get the coronal magnetic field
  using UV or visible lines.
• But infra-red lines do offer some prospect of
  measuring fields the best candidates are Fe
  XIII lines at 10747 Å and 10798 Å.
• They are using them at Sac Peak and elsewhere to
  do this, with limited success.

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Coronal magnetic field (contd.)
Small box on EIT 171 Å image shows region viewed
with coronagraph at NSO/Sac Peak the
polarimeter looking at the Fe XIII IR lines saw a
variation in the Stokes Q parameter indicating a
change of magnetic field strength across the
loop.