Non-Local Thermodynamic Equilibrium
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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.

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Basic Outline

  • Introduction

  • Spectral Line Formation

  • Non-LTE Effects

  • Atmospheric Inhomogeneities

  • Effects On Stellar Abundances

  • Summary


  • 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


Aij=Radiative Emission

Bij=Radiative Absorption/Stimulated Emission

Cij=Collisional Excitation/De-excitation

  • What is meant by NLTE?


  • Radiation fields or level populations do NOT vary with time

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

NLTE Effects: Overionization

  • If Jυ>Bυwith 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)



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 Line


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



3D Solar Model

Integrated Line Profile



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: Carbon

Onset of Type Ia SNe

  • 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

Invoking Pop. III nucleosynthesis of C and O may be incorrect!

Rate C~Rate O

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

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



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


  • 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