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!