Lecture 7 Element abundances

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Lecture 7Element abundances

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Origin of the Elements

• Hydrogen (H) formed in the Big Bang fireball,
  which lasted 3 minutes.
• Then helium (He) was also formed in the Big
  Bang, when the Universe was 3 20 minutes old.
  The temperature was then just right (107 K) for
  this, and the density was not too large for He
  to be broken up again.
• All other elements were formed in the cores of
  1st-generation massive stars Burbidge,
  Burbidge, Hoyle, Fowler (1957 Rev. Mod. Phys.).
  (A. G. W. Cameron also had a 1957 paper then on
  this subject.)

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B2FH
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B, F of B2FH
150th anniversary dinner of the UK Royal
Astronomical Society, Dorchester Hotel, London,
1970
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G. Burbidge
F. Hoyle
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Chemical composition of the Sun

• The Sun is a second-generation star made up of
  material from first-generation stars undergoing
  supernova explosions.
• Suns composition (by number) 90 H, nearly 10
  He, and lt1 heavier elements.
• Of heavy elements, C, N, O are most abundant,
  followed by even-Z elements like Ne, Mg, Si, S,
  Ar, Ca, Fe. These are formed in He-burning in
  stars . An up-down pattern in abundances.
• Odd-Z elements like Cl and K are also present.

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Element abundances in the solar photosphere
H
He
CNO
Fe
Element abundance values from Foukal (Solar
Astrophysics, 2nd ed, 2004)
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Tolstoys view in 1889

• .... If it is a question of whether there is a
  lot of iron or other metals in the Sun or the
  stars, they soon find out .....
• In the Kreutzer Sonata.
• This was written before it was known how spectral
  lines were formed.
• All that was known in 1889 was that there was
  iron (etc.) in the Sun, not how much!

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Russell (1929)
Dont let your paper abstracts be this long!!
H. N. Russell, ApJ (1929), 70, 11
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How do we estimate solar element abundances in
the photosphere?

• For elements like C, N, O, Mg, Si, S, Ca, Fe,
  solar photospheric abundances from
  curve-of-growth analysis using Fraunhofer
  (absorption) lines in visible or infra-red
  spectrum.
• The total absorption in a Fraunhofer line depends
  on number of absorbing atoms and oscillator
  strength f (related to transition probability).
• It can be measured by the Fraunhofer lines
  equivalent width.

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Theory of curve of growth

• Theoretical line equivalent width is
• W? ? (Fcont F?)/Fc d?
• where Fcont continuum flux, F? line flux at
  wavelength ?, Fc the flux at line centre, the
  integral being across the line profile.
• Total number of absorbing atoms N their
  absorbing power X(?)
• X(?) atomic constants f parameter depending
  on line profile .
• Curve of growth is the relation between W? and
  X(?).
• It describes how an absorption (Fraunhofer) line)
  grows with increasing number of absorbing
  atoms.

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Typical curve of growth
Fraunhofer line profiles
Optically thin lines
Optically thick lines
Lines grow through their wings
Curve of growth
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Abundances from curve of growth

• N number of absorbing atoms
• Nelement excitation factors ionization
  factors
• where Nelement is the total number of atoms of a
  particular element, e.g. Fe.
• Normally a Boltzmann distribution for the states
  can be assumed, with excitation temperature an
  average temperature of the solar atmosphere (but
  it will slightly depend on the element/ion
  concerned).
• So the abundance of the element can be found.

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Empirical curve of growth
Curve of growth for Fe I and Ti I solar lines (K.
Wright 1948)
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Confusions in the past

• With some elements like Fe (iron), there are many
  spectral lines throughout the Suns visible
  spectrum.
• We must measure the line oscillator strengths f
  (i.e. transition probabilities) to get good
  abundance estimate.
• This used to be done with high-temperature arc
  spectra in the laboratory.
• Because of temperature variations in the arc, the
  measurements gave misleading results, leading to
  Fe abundance estimates that were (up to 1960s)
  too small by a factor 10!

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Model solar atmosphere calculations

• Nowadays, we can improve on curve-of-growth
  methods.
• We know more about spectral lines than equivalent
  widths we can get accurate spectral line
  profiles (i.e. shape of line with wavelength ?).
• There are now also model solar atmosphere
  calculations (i.e. density, temperature with
  height in the atmosphere).
• Often it is OK to assume local thermodynamic
  equilibrium LTE.

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Recent developments

• Now improved calculations take into account the
  dynamic nature of the photosphere, in particular
  solar granulation 3D calculations.
• Solar granules are tops of small-scale convection
  currents hot material from deep layers comes to
  the surface, cool material sinks in the
  intergranular lanes.
• This is important for spectral lines formed at
  the higher temperature.
• Calculations have been done by Nordlund, Asplund
  et al. over the past 10 years.

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Hinode movie of solar granulation

Solar granulation observed in quiet Sun region,
2006 Nov. 10
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Photospheric Fe lines observed theoretical
line profiles
Asplund et al. (2000)
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Some recent changes to solar abundances

• C and O have smaller abundances than before
• N(C)/N(H) is now 2.5 10-4 (previously 3.6
  10-4 Anders Grevesse 1989)
• N(O)/N(H) is now 4.6 10-4 (previously 9.3
  10-4 Grevesse et al. 1989)
• See Asplund et al. AA 318 (2005), 521 AA 417
  (2004), 751.
• Models etc. Are described by Asplund AA 318
  (1997), 521

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Photospheric abundances of the noble gases He,
Ne, Ar

• There are no known Fraunhofer lines formed in the
  photosphere due to He, Ne, or Ar.
• Their spectral lines can only be excited at very
  high Ts gtgt T of the photosphere (6400 K).
• So abundances cannot be determined directly.
• Meteorites (CI carbonaceous chondrites) also do
  not tell us their abundances because these
  elements have evaporated.
• Meyer (1985 ApJS), Feldman Laming (2000 Phys
  Scripta), Grevesse Sauval (1998) use nearby
  stars as proxies for photospheric abundance.

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Solar coronal abundances

• Emission lines emitted by quiet corona, active
  regions or flares available for abundance
  analysis.
• Emission line flux from a volume V is  
•   
• where
• So we can get the relative element abundance
• NE /NH knowing excitation and ionization
  parameters for the line (these depend on Te).

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How do we get coronal element abundances?

• From X-ray and UV spectroscopy e.g. SMM/FCS and
  BCS, SOHO/SUMER etc.
• Most reliable instruments are those that see
  continuum which is formed (mostly) by H.
• So RESIK is important as the instrumental
  background can be eliminated or taken account of.
  
• RHESSI is also good even though the spectral
  resolution is broad-band it sees the Fe line
  complex at 2 Å (6.7 keV) and nearby continuum.
• An X-ray spectrometer (1.5-15 keV) on Mars
  Messenger sees continuum and line groups of
  several elements, so we can get abundances.
• SphinX observing this region now (JS writing
  Nature paper!)

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Example RESIK determination of Ar abundance
From Sylwester et al. (2008) ASR 42, 838.
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Abundance determinations for K, Ar, Si, S
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RHESSI observations of the Fe line at 1.9 Å
6.7 keV
We can analyze RHESSI count rate spectra to get
the Fe line flux.
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RHESSI observations of the Fe line at 1.9 Å
6.7 keV
Observed equivalent width similar to theory
curve, calculated for Fe abundance 4 x
photospheric Fe abundance.
From Phillips, Chifor, Dennis (2006) ApJ, 647,
1480
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Not always a good result!
Eq. Width (keV)
T (MK)
9 flares sometimes measured Fe equivalent
width agreed with theory curve, sometimes not!
Depends on the flare and on attenuator state.
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Coronal, SEP abundances different from
photospheric

• For elements with well-measured abundances,
  coronal SEP abundances often gt photospheric.
• Meyer (1985 ApJS), Feldman Laming (2000 Phys
  Scripta) and others say that the difference is
  related to first ionization potential (FIP) of
  each element.
• This is the FIP effect.
• Why? Maybe its because elements with low FIP (lt
  9 eV) are partly ionized in photosphere and may
  therefore be accelerated into the corona, and so
  enrich it.

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A possible FIP mechanism Rising magnetic loop
Neutral atoms

Photo-sphere
Ions
A
B
Rising magnetic loop
Ions now attached to rising magnetic field line
Neutral atoms remain in photosphere
C
Ions enrich the corona
DIAGRAM FOR A LOW-FIP ELEMENT
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FIP effect for solar energetic particles /
photosphere

Based on U. Feldmans plot Chap. 11 of Phillips
et al. book (2008).
FIP bias abundance in corona/abundance in
photosphere. FIP bias appears to be x 4 for
low-FIP elements, and 1 for high-FIP elements.
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FIP effect for corona/photosphere
So the FIP effect looks like a step function
BUT....
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Theoretical mechanisms dont explain a FIP bias
of x 4

• To explain why coronal abundances 4 x
  photospheric abundances, somehow enrichment
  process must be 4 x more efficient.
• Its hard to find any such mechanism.

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Some thoughts on the FIP effect

• There is certainly an enhancement of the coronal
  abundance of many elements compared with the
  photospheric abundance.
• But is there a step-function dependence on first
  ionization potential (FIP)?
• I think there is too much uncertainty (especially
  with the photospheric abundances of He, Ne, Ar)
  to say this as yet.
• Does this depend on flare abundances? Sylwester
  et al. (Nature 1984) thought that abundances were
  variable with time. This would greatly affect the
  picture.