Spectroscopy

1
Spectroscopy Chemical Analysis

• Curve of Growth
• Results

2
Differential Analysis

• The abundances depend on a variety of stellar
  parameters (effective temperature, gravity, etc)
  as well as oscillator strength f. In particular
  the the product of Af is obtained, the product of
  the abundance and the oscillator strength.
• The uncertainties in the f value is what limits
  you in practice. These depend on laboratory
  measurements, and for many lines poor values are
  known.
• A differential analysis is usually employed.
  That is the ratio of abundances between stars
  (best if they have the same effective
  temperature). In this way the oscillator
  strengths cancel.
• The chemical analysis holds only for the
  atmosphere of the star! E.g. chemical analyses of
  peculiar stars give abundances of rare earth
  elements 1000 100.000 greater than the Sun.

3
Caveat
The observed spectral lines come from a layer of
the stellar atmosphere that is 500 km thick!
Depth (km)
Log t
4
For direct computation we use the equation for
the flux (LTE) and compute the flux for a series
of points spanning the line
We then integrate across the line to get the
equivalent width
Fc and Fn are the fluxes in the continuum and in
the line, respectively
Given the line absorption coefficient, ln, you
adjust the abundance A until you match the
observed equivalent width. Compters allow a
direct computation. Old way was to use the curve
of growth, i.e. the log-log plot of equivalent
width and the abundance.
5
Scaling relations
For weak lines
The equivalent width of the line becomes
lnr Na, r is the mass density, N is the number
of absorbers per unit volume, and a is the
absorption coefficient
6
a is the wavelength integrated absorption
coefficient
Introduce the number abundance relative to
hydrogen, A NE/NH, and the fraction in the rth
stage of ionization, Nr/NE (given by the
Boltzmann equation), you can write N as
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The equvialent width
Depends on
q 5040/T and division by l normalizes Doppler
dependent phenomena
?Depends on Teff, gravity, composition, etc.
A change in any one of these mimics a change in
the abundance
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This equation tell us that for a given star, the
curve of growth for the same species where A is
constant will differ only in displacements along
the abscissa by individual values of gfl, c, and
kn. We chose a line, this fixes gfl and c, our
stellar atmospheric model fixes q and kn. We can
then vary A and generate the curve of
growth Different lines of the same species have
different gfl and c but these have to have the
same abundance, A. This can be used to constrain
the equation.
The scaling with kn is usually small, especially
if lines are in the same wavelength region. For
example, between 4000 and 6000 Å, ? log kn/?l
0.1 cm2/gm per 1000 Å for T lt 7500 K
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The Curve of Growth
3 phases
Weak lines the Doppler core dominates and the
width is set by the thermal broadening DlD. Depth
of the line grows in proportion to abundance A
Saturation central depth approches maximum value
and line saturates towards a constant value
Strong lines the optical depth in the wings
become significant compared to kn. The strength
depends on g, but for constant g the equivalent
width is proportional to A½
10
The curve of growth shape looks the same, but is
shifted to the right for higher values of the
excitation potential. This is because fewer atoms
are excited to the absorbing level when c is
higher. The amount of each shift can be
interpreted as qexcc.
11
Curve of Growth Temperature Effects

• It is difficult to determine the temperature of a
  star to better than 50100 K. Temperature
  effects
• Nr/NE (ratio of populated states to total number
  of atoms)
• kn (continuous opacity)
• qex (i.e. Temperature)
• And all of these effect the abundance

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Curve of Growth Gravity Effects

• Gravity can effect line strength through
• Nr/NE
• kn
• Since both of these can be sensitive to the
  pressure, For neutral lines the effects cancel

There is a linear relationship between Dlog A and
Dlog g
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? log A/? log g
Teff Ca I Ca II Cr I Cr II Fe I Fe II
7200 0.02 0.33 0.02 0.33 0.01 0.33
5040 0.00 0.39 0.00 0.40 0.11 0.45
3870 0.06 0.43 0.26 0.53 0.35 0.60
As long as an element is mostly ionized, lines
neutral species are insensitive to gravity. The
equivalent width of ionized lines vary as g?
14
As long as the element is mostly ionized, lines
of neutral species are insensitive to gravity
changes. Lines of ions are sensitive to gravity
roughly as g?
A separate and independent analysis can be done
for the ions and neutrals of the same element.
Both should have the same abundance, A. Gravity
is a free parameter and you vary it until you
force both ions and neutrals to give the same
abundance.
Try to avoid strong lines in abundance analyses
because of errors due to saturation
15
Microturbulence
When people first started doing abundance
analyses the observed equivalent width of
saturated lines was greater than the predicted
values using thermal and natural broadening
alone. An extra broadening was introduced, the
micro-turbulent velocity x. This is a fudge
factor introduced just to make the observed line
strengths agree with the models. Its physical
interpretation is that it arises form turbulent
velocities in the atmosphere of the star.
16
Recall the combined absorption coefficient
a(total) a(natural)a(Stark)a(v.d.Waals)a(ther
mal)
Which is a combination of the convolution of 4
broadening mechanisms. Now we have to add a 5th
which is due to microturbulent broadening
a(total) a(natural)a(Stark)a(v.d.Waals)a(ther
mal)a(micro)
17

• Procedure for determining microturblent velocity
• Fit the equivalent widths to the weakest lines
  where the line strength does not change with x.
• This fixes A. You can now use the curve of
  growth for the saturated lines to compute x.
• Also can just determine x by trial and error
  until the derived abundance is independent of
  line strength.

But the saturation portion of the curve of
growth depends also on the temperature
distribution.Doh!
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Fitting the microturbulence
19

• The temperature distribution can vary from star
  to star because of
• Line blanketing so many lines that the line
  opacity affects the continuum opacity. This
  blocks flux which re-emerges in other regions of
  the spectrum
• Differences in the strength of convection
• Mechanical energy dissipation

This results in an ambiguity between T(t) and x
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Curve of Growth Analysis for Abundances
Advantage Simple, you measure the equivalent
width of a line and read the abundance off the
log W versus log A plot

• Disadvantage Lots of calculation and the
  difficulty in dealing with microturbulence and
  saturation effects.
• Make an initial guess of x
• The theoretical curves of growths are calculated
  for all measured equivalent widths of some
  element with lots of lines
• From each line an abundance A is obtained.
• Now plot A versus W
• We find that A is a function of W. x must be
  wrong.
• Chose a new x and start all over. Continue until
  you converge

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Curve of Growth Analysis for Abundances
To simply things, we can use the scaling
relations and just compute one reference curve of
growth rather than many.

• Simplified procedure
• W is entered into the standard curve of growth
  taken for standard values (c 0, log gf 0, l
  l0)

• This abundance is valid for the standard curves
  parameters A0

• The real abundance is obtained by

D log A log (gf/gf1 ) log (l/l0) log(kn/k1)
q(cc0)
log A log A0 D log A
So instead of plotting W versus A, we plot W
versus D log A
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A reference curve-of-growth for a solar model
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Reference curve-of-growth
DA
D log A log (gf ) log (l/l0) log(kn/k0) qc
0
2
6
2
4
4
D Log A
log A log A1 D log A
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Curve of Growth Analysis for Abundances
Abundance determinations with a graph and
calculator 1. Plot observed log (Wl/l) versus
log gfl log (kn/k0) qexc. If qex is wrong
there will be a lot of scatter. The best value of
qex minimizes the scatter.
q 5040/T
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Curve of Growth Analysis for Abundances
Procedure
2. Calculate the vertical shift between the
observed and theoretical curves. The vertical
shift is log xT/c where
x2T x2thermal x2micro
3. Move horizontally to get the abundance
Vertical shift ? turbulent velocities Horizontal
shift ? abundances
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Spectral Synthesis
In real life, one no longer does a
curve-of-growth analysis, but rather a full
spectral synthesis. This can be expanded to 3-D
models and includes true velocity fields on the
star.
28
Spectral synthesis programs can be obtained from
the internet. Most popular are the ATLAS9
routines of Kurucz and MOOG from Sneden
ATLAS ? http//kurucz.harvard.edu
MOOG ? http//verdi.as.utexas.edu/moog.html
SME ? Spectroscopy Made Easy GUI based IDL
routines for calculating synthetic
spectra (Valenti Piskunov, AA Supp, 1996, 118,
585 Tutorialhttp//tauceti.sfsu.edu
/Tutorials.html
All programs require a line list. This can be
obtained from the VALD (Vienna Atomic Line
Database) http//ams.astro.univie.ac.at/vald/
or http//www.astro.uu.se/vald/
29
Abundances Nomenclature
Fe/H the logarithm of the ratio of the iron
abundance of the star to that of the sun.
E.g. Fe/H 2 ? star has 1/100 solar abundance
of iron
Fe/H 0.5 ? star has 3.16 x solar abundance of
iron
30
1-D versus 3-D
And to complicate matters even further, most
spectral synthesis is for 1-D plane parallel
models with no true velocity fields. Work by
Apslund and collaborators (Collet, Asplund,
Trampedach, 2007, AA, 469, 687) indicated that
when one uses a 3-D hydrodynamic modeling, that
this can seriously affect the derived abundances.

• Improvements
• Better gf (oscillator strength values)
• Better treatment of convection
• Better opacities
• 3-D hydrodynamics
• Better observational data

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The hydrodynamic simulations show that the
abundance can have a strong effect on the
velocity pattern of the star, and the velocity
field has an effect on the derived abundances as
well as the temperature structure of the star.
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Recommended Values
3-D average /MARCS
1.07
0.93
1.0
0.93
1.00
1.0
0.72
0.93
1.02
1.17
0.81
0.87
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Major differences of 3-D results

• Chmielewski, Brault Müller (1975) reported
  that Beryllium was depleted by a factor of two.
  Be is now normal. This was because of poor UV
  opacities. Boron is also not depleted (UV
  opacities help)
• Carbon eventually revised down. Current
  abundance is a factor of 0.6 the earliest values
• Nitrogen is 0.6 0.8 earlier determinations
• Oxygen is the most abundant element not produced
  in the Big Bang, but its abundance is in dispute.
  In the past 20 years this value has dropped by
  0.57.
• Magnesium abundance is consistent with
  meteoritic value, but gf-values of Mg are
  notoriously uncertain

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The Solar Composition
An old figure from Grays book. Note that Be and
B are depleted, but this is no longer the case
with 3-D models
Massive stars can burn elements up to iron in the
core. Elements heavier than iron are formed by
rapid and slow capture of neutrons
r-process supernovae explosions s-process
Asymptotic Giant Branch Stars
38
Uranium in Stars
Frebel et al. 2007
In this star Uranium is due to r-processing of
elements
39
Abundances of Stars
40
Standard picture Universe started out with
Hydrogen and Helium, stars formed converting this
to heavier elements ? supernovae explosions
pollute the interstellar medium with heavier
elements. The next generation of stars have a
higher abundance of metals
So with time the mean abundance of stars in the
galaxy should increase.
41
Abundances of Stars Galactic Variations
Halo Mostly Pop II stars, metal poor, globular
clusters
Globular clusters
Disk Pop I stars, metal rich
Bulge Mostly Pop II stars, metal poor, some Pop
I stars
What does this tell us about the chemical
evolution of the galaxy?
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Abundances of Stars Galactic Variations
43
Abundances of Stars Galactic Variations
Globular clusters were the first to form, thus
metal poor.
Disk stars are the last to form, thus metal rich
t t2
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Abundances of Stars Metal Poor
After the Big Bang the universe was entirely
hydrogen and helium. This means that the first
stars were pure hydrogen and helium. So where are
all the Pop III stars (stars with no heavy
elements)
Observational Cosmologists Try to break the
record for the highest redshift quasar. This
pushes back the earliest time we can observe the
universe. ? z large (z is redshift)
Stellar Spectroscopists Try to break the record
for the lowest Fe/H. This pushes back to the
earliest time that stars formed. ? z small (z is
metal content in this case)
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Ultra Metal Poor Stars
46
And the current champion is HE 1327-2326 with an
Fe/H 5.4 or 0.000004 x solar metallicity
Frebel et al. 2007
Is this really one of the first stars?
47
Venn Lambert (2008) have argued that this may
not be the case. Peculiar stars such as post AGB
stars and l Boo stars have iron abundances as low
as Fe/H 5. These are thought to be due to
the separation of gas and dust beyond the stellar
surface followed by an accretion of the
dust-depleted gas. Thus the iron abundances are
artifically low, but the Carbon, Oxygen, and
Nitrogen abundance is only about X/Fe 2. So
this may not be one of the first stars, rather a
peculiar star like the l Boo class of objects.
Where are the Pop III stars? Current wisdom says
that pure H/He stars have to be very massive and
thus have very short lifetimes. They have long
since vanished
48
Abundances of Stars Super Metal Rich
These are stars with metallicity Fe/H 0.3
0.5
Valenti Fischer
There is believed to be a connection between
metallicity and planet formation. Stars with
higher metalicity tend to have a higher frequency
of planets.
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Endl et al. 2007 HD 155358 two planets and..
Hyades stars have Fe/H 0.2 and according to
VF relationship 10 of the stars should have
giant planets, but none have been found in a
sample of 100 stars
Fe/H 0.68. This certainly muddles the
metallicity-planet connection
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Abundances of Stars Lithium
Abundance variations can also be caused by
evolutionary changes in the stellar composition.
An example is Lithium
Lithium is destroyed at temperatures of T 2 x
106 K. The convection zone of the star brings Li
to the deeper, hotter layers of the star where it
is destroyed by conversion to He. It is used as
an indication of age, although it depends on the
depth of the convection zone, temperature
profile (convection zone), and age of star.
In the Sun Lithium is depleted with respect to
meteoritic composition by a factor of 150
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Abundances of Stars Lithium
Li in the sun
Li 6708 Å
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Abundances of Stars Lithium
The Lithium abundance depends on both the
temperature (depth of convection zone and
temperature profile) and age. Lithium is messy
and can only be used as an approximate age
indicator
Old Pop II stars of roughly the same age
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Abundances of Stars Lithium
Surprise, surprise even cool giant stars can have
high lithium
The presence of Li in giant stars is a mystery.
These stars have deep convection zones and are
old stars. They should have destroyed their
lithium long ago. One hypothesis pollution due
to swallowing a binary or even planetary
companion.
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Abundances of Stars Enigmas
Normal F0 star
Przybylskis star

• 50 of the spectral lines are unidentified
• Abundance of Lantanides 100.000 x solar
• Presence of radioactive elements, including Pm
  with a half life of 17.7 years

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Origin of the anomalous abundances
The Ap phenomenon must be a surface phenomenon
since the overabundance of rare earth elements
(e.g. Eu is overabundant by a factor of up to
104 ) is so great that a signficant fraction of
the supply of such elements in the Universe would
be contained in Ap stars if this abundance
extended throughout the star

• Explanations abnormal model atmosopheres,
  accretion of planetesimals, interior nuclear
  processes with mixing, surface nuclear processes,
  or magnetic accretion.

• Most accepted hypothesis Diffusion

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The Diffusion Theory of Michaud (1970)

• A stars have high effective temperatures (high
  radiation field)

• A stars have an outer radiative zone (stable).
  Magnetic field further stabilizes the atmosphere

• If an element has many absorption lines near
  flux maximum radiation pressure drives it
  outwards where it can accumulate and become
  overabundant

• If an element has few absorption lines near flux
  maximum radiation it sinks under its own weight
  and can become underabundant

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A bit of History

• Cecilia Payne-Gaposchkin (1900-1979).
• At Harvard in her Ph.D thesis on Stellar
  Atmospheres she
• Realized that Sahas theory of ionization could
  be used to determine the temperature and chemical
  composition of stars
• Identified the spectral sequence as a
  temperature sequence and correctly concluded that
  the large variations in absorption lines seen in
  stars is due to ionization and not abundances
• Found abundances of silicon, carbon, etc on sun
  similar to earth
• Concluded that the sun, stars, and thus most of
  the universe is made of hydrogen and helium.

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There remains one very much more serious
discrepancy, namely, that for hydrogen, helium
and oxygen. Here I am convinced that there is
something seriously wrong with the present
theory. It is clearly impossible that hydrogen
should be a million times more abundant than the
metals, and I have no doubt that the number of
hydrogen atoms in the two quantum state is
enormously greater than is indicated by the
theory of Fowler and Milne. Henry Norris
Russell in a letter to CPG
Later Russell reversed his position after seeing
new analysis of the sun an wrote a paper On the
Composition of the Suns Atmosphere where he
states that the sun is mostly hydrogen. He
acknowledged the work of Payne-Gaposchkin, but
Russell had the stature to convince the
community. A case where the person who persuades
the community is the one getting the credit!
Otto Struve undoubtedly the most brilliant Ph.D
thesis ever written in Astronomy
Youngest scientist to be listed in American Men
of Science !!!