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Non-Local Thermodynamic Equilibrium. By: Christian Johnson. Basic Outline. Introduction Spectral Line Formation Non-LTE Effects Atmospheric Inhomogeneities Effects On Stellar Abundances Summary. Introduction. - PowerPoint PPT Presentation
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Non-Local Thermodynamic
Equilibrium
By: Christian Johnson
Basic Outline
Introduction
Spectral Line Formation
Non-LTE Effects
Atmospheric Inhomogeneities
Effects On Stellar Abundances
Summary
Introduction Model atmospheres and input parameters often limit abundance measurement accuracy
NLTE effects mostly unknown for low mass end (M stars and below); flux mostly carried via convection
NLTE effects for the hottest stars (A-type and above) are more well known; photospheric flux carried by intense radiation field (e.g., review by Hubeny, Mihalas, & Werner 2003)
Most F-K stellar abundances employ 1D, hydrostatic LTE models for atmospheres and line formation mechanisms
Spectral Line Formation
What is meant by NLTE?
DEPARTURES FROM STATISTICAL EQUILIBRIUM!
N
ijijiji
N
ijjdt
rdn rPrnrPrni 0)()()()()(
Radiation fields or level populations do NOT vary with time
Pij=Aij+BijJυ+Cij
Aij=Radiative Emission
Bij=Radiative Absorption/Stimulated Emission
Cij=Collisional Excitation/De-excitation
Spectral Line Formation Problem? Coupled level populations depend on the radiation field
…which depends on the populations
Everything depends on everything else, everywhere else!
Solution: solve rate equations simultaneously with radiative transfer equation at all relevant frequencies
Compare to LTE: local gas temperature gives excitation populations and ionization via Boltzmann and Saha equations
Caution: major assumption in NLTE codes…LTE departures do NOT feedback into the model atmosphere!
Problem for opacity contributors and electron donors? (think low I.P. metals)
Spectral Line Formation Important NLTE contributors: e- collisions with (1) other e- and (2) neutral H
Estimates of nH/ne given by classical Drawin (1968, 1969) and van Regemorter (1962) formulae
What does this suggest? Collisions with neutral H may dominate the collision rates in metal-poor stars
(1) ignore them
(2) use Darwin formula as is (classical)
(3) apply scaling factor SH
Important: LTE is NOT a middle ground and often falls on either end of NLTE calculations
NLTE Effects
Line formation in atmospheres is intrinsically out of equilibrium due to nonlocality of radiative transfer
Line strength can differ from LTE in two ways:
(1) line opacity has changed
(2) line source function departs from the Planck function
NLTE Effects: Resonance Scattering
In strong lines, only relevant formation process is the line itself
Outward photon losses cause Jυ<Bυ
Pronounced when scattering dominates over absorption
Line becomes stronger in NLTE
Resonance scattering not important when continuum processes dominate
O I Triplet
LTE
NLTE
NLTE Effects: Overionization
If Jυ>Bυ with radiative bound-free transitions, photoionization rates will exceed LTE values
Ions in minority stage will thus be “overionized”
This can weaken the lines significantly by changing the line opacity
Occurs more in the UV (Bυ drops faster than Jυ with height) and metal-poor stars (larger ionizing radiation field for a given height)
τ=01D, MARCS
NLTE Effects: Photon Pumping
Bound-bound equivalent of overionization
Jυ-Bυ excess in a transition overpopulates the upper level compared to LTE
Weakens the line by increasing Sυ
Ex: B I resonance line
NLTE Effects: Photon Suction
Sequence of high probability, radiative bound-bound transitions from close to the ionization limit down to lower levels
Combined photon losses can generate efficient flow of electrons downward
Can lead to flow from primary ionization state to minority state (also causes an overionization)
Na D LineLTE
NLTE
Atmospheric Inhomogeneities
Convection seen in the photosphere as a pattern of broad, warm upflows surrounded by narrow, cool downdrafts
Atmospheric Inhomogeneities
When the ascending isentropic gas nears the surface, photons leak out→cooling→HI photoionization opacity decreases→more photons leaving→more cooling
Causes rapid adjustment in a narrow atmospheric region for the Sun
Atmospheric Inhomogeneities
Integrated Line Profile
T>Tsurf
T<Tsurf
Updraft Downdraft
3D Solar Model
1D vs 3D Models Line strengths may differ between 1D and 3D for two reasons
(1) different mean atmospheric structures and (2) the existence of atmospheric inhomogeneities
[Fe/H]~0.0, the abundance of spectral lines generates sufficient radiative heating in optically thin layers so <T>~radiative equilibrium
Lower [Fe/H], paucity of lines gives much weaker coupling between the radiation field and gas
Near adiabatic cooling of upflowing material dominates over radiative heating and T considerably lower than rad. eq.
1D vs 3D Models
What problems does this cause?
Differences between 3D and 1D models can be larger than 1000 K in optically thin layers (bad for abundance determinations)
Steeper temperature gradients produce stronger Jυ/Bυ divergence→stronger NLTE effects
Effects on Stellar Abundances: Carbon
Aside from molecular bands, carbon abundances can be measured with the [C I] 8727 line or other high excitation (χex>7.5 eV) lines
Easy, Right? Not really, [C I] is very weak, even in the Sun
High E.P. lines have NLTE effects due to the source function falling below the local Planck function
[C I]
Effects on Stellar Abundances
Effects on Stellar Abundances: Carbon
In the metal-poor regime, only transitions from over-populated levels are available
Combination of increased optical depth (lower opacity in those stars) and previously mentioned source function effect gives NLTE corrections of perhaps -0.40 dex
This has important consequences for Carbon enrichment of the galaxy
Onset of Type Ia SNe
Rate C~Rate O
Invoking Pop. III nucleosynthesis of C and O may be incorrect!
Effects on Stellar Abundances: Nitrogen
Disregarding NH and CN, Nitrogen only has a few high excitation lines available for analysis (χex>10 eV)
NLTE departures similar to C I; near solar Teff, dominant effect is Sυ/Bυ<1
This comes from photons escaping, but at higher temperatures the NLTE driver is line opacity
Effects on Stellar Abundances: Nitrogen
Nitrogen abundances determined from NH can have NLTE corrections ranging up to almost -1 dex!
This could drastically alter the view of galactic Nitrogen production and have an impact on many stellar interiors problems such as the CNO cycle and s-process neutron capture (N is a “neutron poison”)
Effects on Stellar Abundances: Oxygen
Notoriously difficult to obtain accurate abundances
O I triplet at ~7770 Å likely not formed in LTE (seemingly proven by center-to-limb estimates)
The departures are mostly due to photon losses, so at least a two level atom can be used
Sυ<Bυ, so the line will be stronger in NLTE
CenterLimb
Effects on Stellar Abundances: Light and Fe-Peak Elements
Na I D resonance lines are quite strong in F-K stellar spectra
Combination of resonance scattering and photon suction should cause a flow to Na II (always negative NLTE correction)
However, Gratton et al. (1999) find for low metallicity giants, the correction should be positive
Discrepancy is currently unknown
Effects on Stellar Abundances: Light and Fe-Peak Elements
Mg I has several optical lines available for analysis
Photoionization cross sections for lower Mg I levels are large, which can cause substantial overionization; NLTE corrections of order +0.1-+0.2
Al also has a very large photoionization cross section in the ground state, making the situation conducive to significant overionization
Corrections range from ~+0.1 for solar resonance lines to ~+0.8 at [Fe/H]<-1
Effects on Stellar Abundances: Light and Fe-Peak Elements
Granulation effects for these and other light elements not well studied
LTE departures most pronounced in upflows
Upflow radiation fields produce overionization; downflows cause photon suction
Remember: integrated line profiles biased toward upflows
Effects on Stellar Abundances: Light and Fe-Peak Elements
Fe: ridiculous number of optical transitions available
Important for tracing metallicity and is a key opacity constituent
Fe I lines undoubtedly form in NLTE conditions; severity unknown
Main cause: overionization
Effects on Stellar Abundances: Light and Fe-Peak Elements
Things to consider for Fe overionization:
(1) Accurate photoionization cross sections important
(2) Collisional coupling of Fe I to Fe II
(3) Accurate estimate degree of thermalization by collision with electrons and hydrogen atoms
(4) Jυ/Bυ excess dependent on steepness of temperature profile
Effects on Stellar Abundances: Light and Fe-Peak Elements
Fe II lines possibly immune from NLTE
BUT, same process driving Fe I overionization causes photon pumping in UV resonance lines of Fe II
However, Fe II corrections are likely only of order +0.05-+0.1 dex
Fe I/II NLTE effects have significant impact on stellar abundance determination techniques
[Fe/H]=0.0 [Fe/H]=-3.0
Effects on Stellar Abundances: Neutron-Capture Elements
Overall low abundance and low E.P. leads to most elements being measured in a dominant ionization stage
Overionization typically not a problem
But, only resonance or low E.P. subordinate lines strong enough for detection (especially in metal poor stars)…the latter being more T sensitive
Not much work has been done, but given the fact that single resonance lines are quite often used, this could be a problem
Summary NLTE work is vitally important to line formation and abundance determinations; but calculations are difficult and require accurate input physics
LTE is good for comparison, but is rarely a middle ground
NLTE corrections are highly dependent on atmospheric parameters, line formation mechanisms, and metallicity
If some proposed corrections are valid, our view of the early universe and Pop. III stars may soon drastically change
The End!