1 AGB - Asymptotic Giant Branch wykład III Atmosphers of AGB stars Ryszard Szczerba Centrum Astronomiczne im. M. Kopernika, Toruń (56) ext. 27

2 „Asymptotic Giant Branch” Harm Habing, Hans Olofsson (Eds.) A&A Library, 2004 Springer-Verlag

3 AGB Stars: how to define atmosphere? Difficult to define the lower and outer boundary:  atmosphere – stellar region visible from outside;  Outer boundary - the outer stellar region where the outflow velocity is higher than the escape velocity. There is a close coupling between: 1)the stellar interior; 2)the atmosphere; and 3)the wind. Unified models: different regions are given a consistent treatment. Understanding of wind must be rooted in the physics of the stellar interior. Proper analysis of a stellar spectrum (e.g. for abundance determination) requires a model of the spectrum-forming regions (for which: knowledge about transfer of mass, momentum & energy is necessary).EVERTHING is COUPLED!!!

4 AGB Stars: how to define atmosphere? atmosphere – a transition region between the relatively SIMPLE interior and the COMPLEXITY of interstellar matter.  The stellar interior is SIMPLE (LTE conditions hold – e.g. T and  are enough); => star = f(M i ; age; initial chem. comp.)  ISM is COMPLEX (e.g. time-dependent non-equilibrium chemistry is necessary to consider). COMPLEXITY of the atmosphere grows up closer to the ISM we are!!!  deviations from LTE;  time-dependent non-equilibrium chemistry;  complexity of the geometrical structures;  strong radiation flux; .....

5 AGB Stars: characteristic „atmospheric” phenomena? low gravity – assumption of spherical symmetry less realistic. instability against convection in deeper layers – due to H disociation and absorption (giant granular cells). instability against pulsations – generation of shock fronts (complex dynamics) Molecule and dust formation - complex radiation transfer & wind generation. Interaction between: 1.) convection, 2.) pulsations, 3.) radiation, 4.) molecular and dust formation and absorption, 5.) acceleration of the stellar wind.

6 AGB Stars: why to study their atmospheres? To understand stellar spectra – in terms of: 1.) mass; 2.) age; 3.) chemical composition. To understand elements „production” – C, F and s-process elements are mainly produced by AGB stars. To understand their complexity! – Physics.

7 AGB Stars: observational constraints - optical. The most important spectral classes of AGB stars are M, S and C. MS –top: dominated by TiO (VO – in very cold stars); C- bottom: C 2 and CN molecules dominate. S-stars have ZrO; Zr is s-process element.

8 AGB Stars: observational constraints – optical. High resolution spect. (de Laverny 1997) Problem to determine continuum! Line blending! Situation improves at >2  m

9 AGB Stars: observational constraints – NIR. High resolution spect. (Lebzelter 1999) Problem to determine continuum! Line blending! Situation improves at >2  m

10 AGB Stars: observational constraints -IR.

11 AGB Stars: observational constraints – IR.

12 AGB Stars: observational constraints – IR.

13 AGB Stars: observational constraints – IR.

14 AGB Stars: observational constraints – IR.

15 AGB Stars: observational constraints – cont. Photometry (e.g. De Laverny et al. 1997)

16 AGB Stars: observational constraints – cont. Interferometry: AGB stars are so large that using phase or speckle interferometry, or lunar occultation – stellar radius can be determined. A realiable T eff scale !!! (e.g. Haniff et al. 1995) Measurements at different => R * = f( ) ESO VLT Interferometer => assymetries (3D models)!!!

17 AGB Stars: observational constraints – cont.

18 AGB Stars: observational constraints – cont. Velocities (microturbulence); Velocities in the upper atmospheres (SiO masers); Masers (magnetic fields – effect Zeemana); chromospheres (UV). Not predicted by models!

19 AGB Stars: Physics and characteristic conditions – Introduction Interaction between radiation and matter (dominates!).  Transfer of energy and momentum;  Diagnostic tool to study stars. Time-dependent dynamical processes  convection – energy transport, cells => deviations from sph. symmetry  pulsations – shock waves – matter levitation => formation of molecules and dust grains => mass loss

20 AGB Stars: Physics and characteristic conditions – Temperature Temperature determination is not trivial in AGB stars (the flux distribution is not like a Planck function!).  If   [cm -1 ] - absorption coefficient - is not function of  then observer see the same part of the star in all, with a well defined radius. In AGB stars   strongly depends on molecular absorption and at longer wavelengths dust starts to contribute. Problems:  How to measure (total) F;  How to determine angular radius (different at different )?  What is the meaning of T eff (assumption of LTE!)?

K AGB Stars: Physics and characteristic conditions – Temperature Temperature is well defined since elastic collisions in the gas are so frequent that velocities follow the Maxwell distribution. Thus kinetic temperature may be estimated for each region. The derived effective temperatures of AGB stars are between

22 AGB Stars: Physics and characteristic conditions – Densities and Scale Heights The main source of opacity in solar-type and cooler stars is H - The H atom is capable of holding a second electron in a bound state (binding energy 0.754eV). All photons with <1.64  m have sufficient energy to ionize the H- ion back to neutral H atom plus a free e- (b-f)

23 AGB Stars: Physics and characteristic conditions – Densities and Scale Heights Optical depth b-f cross section From Saha eq. e - : Mg,Fe < Na,Al,Ca < H 2 p(e 1 ) < p(e 2 ) <p(e 3 ) From the above eqs.: For d  = 1

24 Quirrenbach et al. (1993) measured radii in TiO band at 712 nm and in band at 754 nm (with smaller absorption) AGB Stars: Physics and characteristic conditions – Densities and Scale Heights T=3000 K =>  ~10 -9 g cm -3

25 AGB Stars: Physics and characteristic conditions – Densities and Scale Heights Hydrostatic equilibrium Scale Height:

26 AGB Stars: Physics and characteristic conditions – Densities and Scale Heights Atmosphere:  r ~ cm H  ~ 1.5 x cm

27 AGB Stars: Physics and characteristic conditions – Densities and Scale Heights c s  ~ 5.4 km/s Sound speed Microturbulent and macroturbulent velocities in non- Miras tend to be subsonic! In Miras, where pulsations (and shock fronts) are present, splitting of IR CO lines shows velocities of 34 km/s (Scholz & Wood 2000).

28 AGB Stars: Physics and characteristic conditions – Microscopic state of matter To what extent T and  (like in LTE) determine the rate of collisonal processes? To what extent noclocal effects (radiation) play a role? How state of gas depends on the history of gas (time- dependence)?

29 AGB Stars: Physics and characteristic conditions – Microscopic State of Matter (velocity) Elastic collisions: H & He – excitation E>10 eV Maxwell distribution The mean speed: Problem: H 2 in outer layers with low energy levels. However, collisional excitation and de-excitation are ~equally frequent. T~3000K->kT~0.26eV 2000 H  E= eV per 1 H  E=2.6 T – may be taken as the T of the gas

30 AGB Stars: Physics and characteristic conditions – Microscopic State of Matter (excitation) radiative rates [1/cm 3 s] Collision rates

31 AGB Stars: Physics and characteristic conditions – Microscopic State of Matter (excitation). Example: formation of H - photodisociation associative detachment a.d. rate: photoionization rate: R ph  ~ /s Non-LTE effects may be important for H -

32 AGB Stars: Physics and characteristic conditions – Microscopic State of Matter (excitation). Example: CO ro-vib bands. CO has strong vibration-rotation lines in IR:  The fundamental (  =1) at 4.6  m;  The 1st overtone (  =2) at 2.3  m;  The 2nd overtone (  =3) at 1.6  m; These are important for diagnostic for atmospheric structure, velocity field, and chemical abundance (including isotopes). Rotational transitions (  E very small) – collisionally dominated (~Boltzman distribution) Vibrational transitions:  at inner atmosphere LTE holds (collisions dominate);  in outer regions non-LTE distribution of energy levels (radiation dominates).

33 AGB Stars: Physics and characteristic conditions – Microscopic State of Matter (excitation). The statistical equilibrium Radiative processes are important in populating most atomic states (non-LTE). Wheter radiation field is isotropic and ~B (T kin ) ?  The deeper in the atmosphere the better the assumption. Microscopic state of the gas -> a HUGE set of coupled eq. must be solved R ij terms couple the radiation field to the state equations „Model atmosphere” -> above eqs.+ rad. transfer + transport of m,p and E

34 AGB Stars: Physics and characteristic conditions – Microscopic State of Matter (excitation). The statistical equilibrium Equations of statistical equilibrium

35 AGB Stars: Physics and characteristic conditions – Microscopic State of Matter. The chemical equilibrium one of the lectures will be: Molecule and Dust grain formation dissociation equilibrium constant non-LTE effects: rad.disociation more significant than collisions. e.g. In shocks: t disoc << t asoc

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37 AGB Stars: Physics and characteristic conditions – Microscopic State of Matter. Dust formation one of the lectures will be: Molecule and Dust grain formation

38 AGB Stars: Physics and characteristic conditions – Microscopic State of Matter. The transfer of radiation Time-independent case in spherical symmetry

39 AGB Stars: Physics and characteristic conditions – Microscopic State of Matter. Line absorption Molecules are more important than atoms in AGB stars Absorption depends on: - abundance of molecules -absorption coefficient(T) -wavelength

40 AGB Stars: Physics and characteristic conditions – Microscopic State of Matter. Line absorption Molecules are more important than atoms in AGB stars Absorption depends on: - abundance of molecules -absorption coefficient(T) -wavelength Polyatomic molecules have hundreds of milions VR lines!!!