Transcript Slide 1

Model Construction
The atmosphere connects the star to the
outside world. All energy generated in the
star has to pass through the atmosphere
which itself usually does not produce
additional energy.
The photosphere is the region of the
atmosphere where most of the radiation
escapes from the star.
What needs to be done?
Parameters
There are many ways to construct model
atmospheres. Using a fixed optical depth
grid helps avoid pre-specifying the physical
extension of the atmosphere.
Minimum independent parameters:
Effective temperature Teff
Gravity g(r) = G M / r2
Mass, Radius or Luminosity L= 4πR2  Teff4
Abundances of all elements i = ni / nT
Hydrostatic Equilibrium
When mass loss is negligible, the total gas
pressure in the atmosphere is:
dP/dr = -g(r) 
With the optical depth:
d = - dr = -( + ) dr
where , ,  are the extinction,
absorption and scattering coefficients, we
get:
dP/d = g(r)  / 
Energy Conservation
In plane-parallel geometry, we have:
Frad + Fconv = ∫ F d =  Teff4 = cte
Each volume element has emission = absorption:
∫  (J - S ) d = 0
with J the mean intensity (direction averaged)
S the source function (simplest: B(T) )
The energy conservation determines
essentially the T() structure!
Model Flow Chart
Départ avec:
T()= grey model
(T4=3/4 Teff4 (+2/3))
Pout= 10-4 dyne/cm2
15 to 30 iterations
Spectrum:
∫Frad d =  Teff4
> 30,000 pts
UV  sbmm
 = 0.01 Å
Opacities
Absorption and scattering coefficients
∑  i j ni j
j: ionization stage
i: energy level within each ionization stage
ij: cross-section (cm2)
nij: population density (cm-3)
∑ over all elements, processes, ionization
stages, level.
ij from QM, measurements
LTE
TE = thermodynamic Equilibrium
= detailed balance of all process
= state described by Pgas,T
If:
- Collisions dominate radiation
- Radiation field is Planckian
- No scattering of radiation
 Local Thermodynamic Equilibrium (LTE)
Not the case in exospheres of all stars and planets
(radiation dominates) and in lines such as the Lyman
series of hydrogen (scattering is important).
Comparison of Opacity Calculations
Equation
of state
Molecular
opacity
Dust
opacity
# of
frequencies
A75
AJR 83
AF 94
Phoenix
Supersaturation
ratio
Straight
mean
Decoupled
gas & dust
Decoupled
gas & dust
Gas & dust
in
equilibrium
~8x108 lines
1 species
Rayleigh
50
3 species
Mie
900
2x105 lines + 3x107 lines
straight mean
water
4 species
CDE
9,000
31 species
EMT
25,000
CO & CH4 are dominant molecules
CO
CH4
-5
6
-5
-10
-10
-15
4
6
-5
2
-15
-5
-10
-15
-10
-5
4
-10
-15
-10
log P
0
2
-5
-2 -5
-15
-15
0
log P
-5
-10
-4
-10
-2
-5
-6
-15
-4
-15
-5
-8
-10
-10
-6
2.6
2.8
3.0
3.2
3.4
log T
3.6
3.8
4.0
-15
-8
2.6
2.8
3.0
3.2
3.4
log T
3.6
3.8
4.0
Beware of extrapolating polynomials beyond
their intended temperature range
Tsuji (1973)/JANAF
Sharp & Huebner (1990)/JANAF
6
difference log K p
5
4
3
CO
2
1
0
-1
1
difference log K p
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.2
3.4
3.6
0
-1
-2
-3
CH4
-4
-5
-6
2.4
2.6
2.8
3.0
log T
(m)
-2
1
2
3
4
5
T = 10000 K
-4
log 
-6
-8
-10
Atoms
-12
log 
-6
-8
-10
-12
-14
-16
-18
-6
-8
-10
-12
-14
-16
-18
log 
The role of
atomic and
molecular opacity
increases at lower
temperatures
log 
-14
-6
-8
-10
-12
-14
-16
-18
-20
T = 8000 K
Molecules
T = 6000 K
T = 4000 K
H & H1
2
3
(m)
4
5
H2O Abundance
6
-5
-10
-15
4
2
-5
-10
-15
log P
0
-2
-10
-5
-15
-4
-6
-10
-5
-15
-8
2.6
2.8
3.0
3.2
3.4
log T
3.6
3.8
4.0
Temperature Dependence of
H2O Opacity
log 
-10
-12
2000 K
-14
1000 K
-16
500 K
-18
3000 K
-20
-22
-24
1
2
3
 (m)
4
5
Sources of H2O opacities
Empirical ‘02
Theoretical ‘90s
Empirical ‘90s
Lab. ‘70s
Line density varies
among different molecules
-5
-5
CO
H2O
-10
-15
-15
log 
log 
-10
-20
-20
-25
-25
-30
-30
2
4
6
 (m)
8
10
2
4
6
 (m)
8
10
TiO only exists over a narrow
temperature range
6
4
log P(i) (dynes cm-2)
2
-7.0
0
-8.0
-7.5
-7.0
-8.0
-7.5
-2
-4
-6
-7.0
-8
-7.5
2.6
2.8
3.0
3.2
3.4
log T
3.6
3.8
4.0
Temperature Dependence of TiO
Opacity
-16
log /ni
-18
-20
3000 K
2000 K
-22
-24
1000 K
-26
0.5
1.0
1.5
 (m)
2.0
2.5
3.0
Temperature Dependence of TiO
Opacity
-10
-15
2000 K
log 
3000 K
-20
-25
1000 K
-30
0.5
1.0
1.5
 (m)
2.0
2.5
3.0
Even scarce molecules can affect
model spectra
5.5
no TiO
log F
5.0
4.5
Teff = 3100 K
log L/Lsun = 3.0
4.0
5.5
log F
5.0
0.6
0.8
1.0
1.2
1.4
1.2
1.4
 (m)
no VO
4.5
4.0
0.6
0.8
1.0
 (m)
Line density is also important
in the visual spectrum
-6
-6
-8
-8
-10
-10
-12
-12
log 
log 
FeH
-14
TiO
-14
-16
-16
-18
-18
-20
-20
0.4
0.6
0.8
1.0
 (m)
1.2
1.4
0.4
0.6
0.8
1.0
 (m)
1.2
1.4
Hydrides can be important in dwarfs
-15
6
-10
4
2
FeH abundance
and spectrum
-10
-10
-15
-10
-15
-15
0
log P
-6
-2
-15
-15
-8
-4
-10
log 
-15
-6
-8
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
-12
-14
-16
log T
-18
-20
0.4
0.6
0.8
1.0
1.2
 (m)
1.4
1.6
1.8
2.0
Conclusions
Models rely upon only a few basic equations
and several simplifying assumptions
(hydrostatic eq., energy eq., LTE), valid
only for the photospheres objects (Gas giant
planets, brown dwarfs, stars older than 1
Myr).
Improvements over the past 15 yrs: computer
capacities  better opacities !
Complete atmosphere course online:
http://www.hs.uni-hamburg.de/~stcd101/
References