Transcript Chapter 14 – Chemical Analysis

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
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
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
The Effect of Temperature on the COG
• Recall:
Fc  Fn
l
 constant n
Fc
kn
– (under the assumption that Fn comes from a
characteristic optical depth tn)
• Integrate over wavelength, and let lnr=Na
• Recall that the wavelength integral of the absorption
coefficient is
e2 l2 N
w  constant
mc c
f
kn
• Express the number of absorbers in terms of hydrogen
• Finally,
Nr
g 
NA
NH
e
NE
u (T )
kT
 e 2 N r N E

log  log 2
N H   log A  log gfl    logkn
l
 m c u (T )

w
The COG for weak lines
 e 2 N r N E

log  log 2
N H   log A  log gfl    logkn
l
 m c u (T )

w
Changes in log A are equivalent to changes in log gfl, ,
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,
, or kn.
A curve of growth for one line can be “scaled” to be
used for other lines of the same species.
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?
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
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
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.
Microturbulence in the COG
-3
5 km/sec
Log w/lambda
-4
0 km/sec
-5
0 km/sec
1 km/sec
-6
2 km/sec
3 km/sec
5 km/sec
-7
-13
-12
-11
-10
-9
-8
-7
Log A + Log gf
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?
-6
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
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
Solar Abundances from
Grevesse and Sauval
CNO
Log e (H=12)
8
Fe
5
Sr, Y, Zr
Sc
2
Ba
Li, Be, B
Eu
-1
10
20
30
40
50
Atomic Number
60
70
80
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
Projects!
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•
•
•
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
Data
• Select one of the data archives
– FTS archive
• Wallace & Hinkle 1996, APJS, 107, 312
• DPP: NOAO Digital Library
– ELODIE archive
• Prugniel & Soubiran 2001, A&A, 369, 1048
• The ELODIE archive
– Others?
– Work with published EQW data
• Select a sample of stars, at least one
per team member
What’s 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)
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