Chapter 14

1
Chapter 14 Chemical Analysis

• Review of curves of growth
• How does line strength depend on excitation
  potential, ionization potential, atmospheric
  parameters (temperature and gravity),
  microturbulence
• Differential Analysis
• Fine Analysis
• Spectrum Synthesis

2
The Curve of Growth

• The curve of growth is a mathematical relation
  between the chemical abundance of an element and
  the line equivalent width
• The equivalent width is expressed independent of
  wavelength as log W/l

Wrubel COG from Aller and Chamberlin 1956
3
Curves of Growth

• Traditionally, curves of growth are described
  in three sections
• The linear part
• The width is set by the thermal width
• Eqw is proportional to abundance
• The flat part
• The central depth approaches its maximum value
• Line strength grows asymptotically towards a
  constant value
• The damping part
• Line width and strength depends on the damping
  constant
• The line opacity in the wings is significant
  compared to kn
• Line strength depends (approximately) on the
  square root of the abundance

4
The Effect of Temperature on the COG

• Recall
• (under the assumption that Fn comes from a
  characteristic optical depth tn)
• Integrate over wavelength, and let lnrNa
• Recall that the wavelength integral of the
  absorption coefficient is
• Express the number of absorbers in terms of
  hydrogen
• Finally,

5
The COG for weak lines
Changes in log A are equivalent to changes in log
gfl, qc, or kn For a given star curves of growth
for lines of the same species (where A is a
constant) will only be displaced along the
abcissa according to individual values of gfl, c,
or kn. A curve of growth for one line can be
scaled to be used for other lines of the same
species.
6
A Thought Problem

• The equivalent width of a 2.5 eV Fe I line in
  star A, a star in a star cluster is 25 mA. Star
  A has a temperature of 5200 K.
• In star B in the same cluster, the same Fe I line
  has an equivalent width of 35 mA.
• What is the temperature of star B, assuming the
  stars have the same composition
• What is the iron abundance of star B if the stars
  have the same temperature?

7
The Effect of Surface Gravity on the COG for Weak
Lines

• Both the ionization equilibrium and the opacity
  depend on surface gravity
• For neutral lines of ionized species (e.g. Fe I
  in the Sun) these effects cancel, so the COG is
  independent of gravity
• For ionized lines of ionized species (e.g Fe II
  in the Sun), the curves shift to the right with
  increasing gravity, roughly as g1/3

8
Effect of Pressure on the COG for Strong Lines

• The higher the damping constant, the stronger the
  lines get at the same abundance.
• The damping parts of the COG will look different
  for different lines

9
The Effect of Microturbulence

• The observed equivalent widths of saturated lines
  are greater than predicted by models using just
  thermal and damping broadening.
• Microturbulence is defined as an isotropic,
  Gaussian velocity distribution x in km/sec.
• It is an ad hoc free parameter in the analysis,
  with values typically between 0.5 and 5 km/sec
• Lower luminosity stars generally have lower
  values of microturbulence.
• The microturbulence is determined as the value of
  x that makes the abundance independent of line
  strength.

10
Microturbulence in the COG
5 km/sec
0 km/sec
Questions At what line strength do lines
become sensitive to microturbulence? Why is it
hard to determine abundances from lines on
the flat part of the curve of growth?
11
Determining Abundances

• Classical curve of growth analysis
• Fine analysis or detailed analysis
• computes a curve of growth for each individual
  line using a model atmosphere
• Differential analysis
• Derive abundances from one star only relative to
  another star
• Usually differential to the Sun
• gf values not needed
• Spectrum synthesis
• Uses model atmosphere, line data to compute the
  spectrum

12
Jargon

• m/H log N(m)/N(H)star log N(m)/N(H)Sun
• Fe/H -1.0 is the same as 1/10 solar
• Fe/H -2.0 is the same as 1/100 solar
• m/Fe log N(m)/N(Fe)star log N(m)/N(Fe)Sun
• Ca/Fe 0.3 means twice the number of Ca atoms
  per Fe atom

13
Solar Abundances from Grevesse and Sauval
14
Basic Methodology for Solar-Type Stars

• Determine initial stellar parameters
• Composition
• Effective temperature
• Surface gravity
• Microturbulence
• Derive an abundance from each line measured using
  fine analysis
• Determine the dependence of the derived
  abundances on
• Excitation potential adjust temperature
• Line strength adjust microturbulence
• Ionization state adjust surface gravity

15
Projects!

• You may work in teams (1, 2 or 3 students)
• Perform an analysis of the spectrum
• Confirm the atmospheric parameters
• (optional) Measure the abundance of the atomic
  species in homework 3
• Use Moog
• Chris Sneden MOOG
• or use the computers in Rm 311 with Moog already
  installed

16
Data

• Select one of the data archives
• FTS archive
• Wallace Hinkle 1996, APJS, 107, 312
• DPP NOAO Digital Library
• ELODIE archive
• Prugniel Soubiran 2001, AA, 369, 1048
• The ELODIE archive
• Others?
• Work with published EQW data
• Select a sample of stars, at least one per team
  member

17
Whats known?

• Review the literature for your selected object
• extant photometry
• 2MASS, ISO data?
• radial velocity measurements?
• IUE/STIS spectra?
• previous atmospheric analyses?
• metallicity determinations? (see Catalogue of
  Fe/H (Cayrel de Strobel, 1997)

18
Step 3

• Measure equivalent widths/detailed COG
• Spectrum Synthesis?
• Use Thevenin line data
• wavelength
• e.p.
• gf
• may work differentially to Arcturus (optical or
  IR) or the Sun if needed