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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Non-Local Thermodynamic Equilibrium

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Non local thermodynamic equilibrium

Non-Local Thermodynamic Equilibrium

By: Christian Johnson


Non local thermodynamic equilibrium

Basic Outline

  • Introduction

  • Spectral Line Formation

  • Non-LTE Effects

  • Atmospheric Inhomogeneities

  • Effects On Stellar Abundances

  • Summary


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

Spectral Line Formation

Pij=Aij+BijJυ+Cij

Aij=Radiative Emission

Bij=Radiative Absorption/Stimulated Emission

Cij=Collisional Excitation/De-excitation

  • What is meant by NLTE?

    • DEPARTURES FROM STATISTICAL EQUILIBRIUM!

  • Radiation fields or level populations do NOT vary with time


Non local thermodynamic equilibrium

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)


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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

LTE

NLTE

O I Triplet


Non local thermodynamic equilibrium

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)

1D, MARCS

τ=0


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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)

LTE

Na D Line

NLTE


Non local thermodynamic equilibrium

Atmospheric Inhomogeneities

  • Convection seen in the photosphere as a pattern of broad, warm upflows surrounded by narrow, cool downdrafts


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

Atmospheric Inhomogeneities

T>Tsurf

T<Tsurf

3D Solar Model

Integrated Line Profile

Downdraft

Updraft


Non local thermodynamic equilibrium

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.


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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]


Non local thermodynamic equilibrium

Effects on Stellar Abundances


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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”)


Non local thermodynamic equilibrium

Effects on Stellar Abundances: Oxygen

Center

Limb

  • 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


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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


Non local thermodynamic equilibrium

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

The End!


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