1. Non-Local Thermodynamic Equilibrium By: Christian Johnson

2. Basic Outline  Introduction  Spectral Line Formation  Non-LTE Effects  Atmospheric Inhomogeneities  Effects On Stellar Abundances  Summary

3. 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

4. Spectral Line Formation  What is meant by NLTE?  DEPARTURES FROM STATISTICAL EQUILIBRIUM!  Radiation fields or level populations do NOT vary with time P ij =A ij +B ij J υ +C ij A ij =Radiative Emission B ij =Radiative Absorption/Stimulated Emission C ij =Collisional Excitation/De-excitation

5. 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)

6. Spectral Line Formation  Important NLTE contributors: e - collisions with (1) other e - and (2) neutral H  Estimates of n H /n e 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 S H Important: LTE is NOT a middle ground and often falls on either end of NLTE calculations

7. 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

8. NLTE Effects: Resonance Scattering  In strong lines, only relevant formation process is the line itself  Outward photon losses cause J υ <B υ  Pronounced when scattering dominates over absorption  Line becomes stronger in NLTE  Resonance scattering not important when continuum processes dominate O I Triplet LTE NLTE

9. NLTE Effects: Overionization  If J υ >B υ 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 (B υ drops faster than J υ with height) and metal-poor stars (larger ionizing radiation field for a given height) τ=01D, MARCS

10. NLTE Effects: Photon Pumping  Bound-bound equivalent of overionization  J υ -B υ excess in a transition overpopulates the upper level compared to LTE  Weakens the line by increasing S υ  Ex: B I resonance line

11. 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 LTE NLTE

12. Atmospheric Inhomogeneities  Convection seen in the photosphere as a pattern of broad, warm upflows surrounded by narrow, cool downdrafts

13. 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

14. Atmospheric Inhomogeneities Integrated Line Profile T>T surf T<T surf Updraft Downdraft 3D Solar Model

15. 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 ~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.

16. 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 J υ /B υ divergence→stronger NLTE effects

17. Effects on Stellar Abundances: Carbon  Aside from molecular bands, carbon abundances can be measured with the [C I] 8727 line or other high excitation (χ ex >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]

18. Effects on Stellar Abundances

19. 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!

20. Effects on Stellar Abundances: Nitrogen  Disregarding NH and CN, Nitrogen only has a few high excitation lines available for analysis (χ ex >10 eV)  NLTE departures similar to C I; near solar T eff, dominant effect is S υ /B υ <1  This comes from photons escaping, but at higher temperatures the NLTE driver is line opacity

21. 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”)

22. 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  S υ <B υ, so the line will be stronger in NLTE Center Limb

23. 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

24. 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

25. 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

26. 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

27. 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) J υ /B υ excess dependent on steepness of temperature profile

28. 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

29. 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

30. 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

31. The End!