chapter 13 cont’d – pressure effects more curves of growth how does the cog depend on excitation...
TRANSCRIPT
Chapter 13 Cont’d – Pressure Effects
• More curves of growth• How does the COG depend on excitation potential,
ionization potential, atmospheric parameters (temperature and gravity), microturbulence
• When/why does line strength depend on pressure?
• Mg b lines• Hydrogen lines
Line Strength Depends on Pressure
• For metal lines, pressure (gravity) affects line strength in two ways:– Changing the line-to-
continuous opacity ratio (by changing the ionization equilibrium)
– Pressure dependence of damping constant
– Pressure dependence of Stark broadening
• Pressure effects are much weaker than temperature effects
The Fe II 4508 line weakens with increasing pressure because the continuous opacity decreases (less H- - WHY?)
The Mg I b lines
• Why are the Mg I b lines sensitive to pressure?
Hydrogen lines
depend on pressure
• If Teff > 7500, hydrogen lines becomes sensitive to pressure (why, and why are they less sensitive at lower temperature?)
• Lines get stronger with increasing pressure
H- Profiles
• H lines are sensitive to temperature because of the Stark effect
The high excitation of the Balmer series (10.2 eV) means excitation continues to increase to high temperature (max at ~ 9000K).
Most metal lines have disappeared by this temperature. Why?
Pressure Effects on Hydrogen Lines
• When H- opacity dominates, the continuous opacity is proportional to pressure, but so is the line abs. coef. in the wings – so Balmer lines in cool stars are not sensitive to pressure
• When Hbf opacity dominates, is independent of Pe, while the line absorption coefficient is proportional to Pe, so line strength is too
• In hotter stars (with electron scattering) is nearly independent of pressure while the number of neutral H atoms is proportional to Pe
2. Balmer profiles are very pressure dependent
Rules of Thumb for Weak Lines
• When most of the atoms of an element are in the next higher state of ionization, lines are insensitive to pressure – When H- opacity dominates, the line and the continuous
absorption coefficients are both proportional to the electron pressure
– Hence the ratio line/continuous opacity is independent of pressure
• When most of the atoms of an element are in the same or a lower state of ionization, lines are sensitive to pressure– For lines from species in the dominant ionization state, the
continuous opacity (if H-) depends on electron pressure but the line opacity is independent of electron pressure
• Lines from a higher ionization state than the dominant state are highly pressure dependent
– H- continuous opacity depends on Pe
– Degree of ionization depends on 1/Pe
Examples of Pressure Dependence
• Sr II resonance lines in solar-type stars
• 7770 O I triplet lines in solar-type stars
• [O I] in K giants• Fe I and Fe II lines in solar-type
stars• Fe I and Fe II lines in K giants• Li I lines in K giants
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/
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
– Line strength depends (approximately) on the square root of the abundance
The Effect of Temperature on the COG
• Recall:
– (under the assumption that F comes from a characteristic optical depth )
• Integrate over wavelength, and let l=N
• Recallthat the wavelength integral of the absorption coefficient is
• Express the number of absorbers in terms of hydrogen
• Finally,
l
constant
c
c
F
FF
Nf
cmc
ew
22
constant
kTH
E
r eTu
gN
N
NAN
)(
logloglog)(
loglog2
2
gfAN
Tu
NN
mc
ewH
Er
The COG for weak lines
logloglog)(
loglog2
2
gfAN
Tu
NN
mc
ewH
Er
Changes in log A are equivalent to changes in log gf, ,or
For a given star curves of growth for lines of the samespecies (where A is a constant) will only be displaced along the abcissa according to individual values of gf,, or .
A curve of growth for one line can be “scaled” to beused 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 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 that makes the abundance independent of line strength.
Microturbulence in the COG
-7
-6
-5
-4
-3
-13 -12 -11 -10 -9 -8 -7 -6
Log A + Log gf
Lo
g w
/la
mb
da
0 km/sec
1 km/sec
2 km/sec
3 km/sec
5 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?
0 km/sec
5 km/sec