Non-Local Thermodynamic Equilibrium

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 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

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 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

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 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

9. 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

10. 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

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) LTE Na D Line 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 T>Tsurf T<Tsurf 3D Solar Model Integrated Line Profile Downdraft Updraft

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 <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.

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 Jυ/Bυ 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 (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]

18. Effects on Stellar Abundances

19. 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

20. 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

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 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

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) Jυ/Bυ 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!