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AGB - AGB - Asymptotic Giant BranchAsymptotic Giant Branch

wykład IIIwykład IIIAtmosphers of AGB starsAtmosphers of AGB stars

Ryszard Szczerba

Centrum Astronomiczne im. M. Kopernika, Toruń

szczerba@ncac.torun.pl

(56) 62 19 249 ext. 27

http://www.ncac.torun.pl/~szczerba/

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„„Asymptotic Giant Branch”Asymptotic Giant Branch”

Harm Habing, Hans Olofsson (Eds.)

A&A Library, 2004 Springer-Verlag

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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!!!

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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(Mi; 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;.....

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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.

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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.

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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: C2 and CN molecules dominate. S-stars have ZrO; Zr is s-process element.

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AGB Stars: observational constraints – optical.

High resolution spect. (de Laverny 1997)

Problem to determine continuum!

Line blending!

Situation improves at >2m

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AGB Stars: observational constraints – NIR.

High resolution spect. (Lebzelter 1999)

Problem to determine continuum!

Line blending!

Situation improves at >2m

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AGB Stars: observational

constraints -IR.

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AGB Stars: observational constraints – IR.

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AGB Stars: observational constraints – IR.

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AGB Stars: observational constraints – IR.

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AGB Stars: observational constraints – IR.

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

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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 Teff scale !!! (e.g. Haniff et al. 1995)•Measurements at different=> R* = f()ESO VLT Interferometer => assymetries (3D models)!!!

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AGB Stars: observational constraints – cont.

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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!

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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

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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 ofthen 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. 22

*

4 ~4

F

R

LTeff

•Problems:How to measure (total) F;How to determine angular radius (different at different )?What is the meaning of Teff (assumption of LTE!)?

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2000-3500 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

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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 <1.64m have sufficient energy to ionize the H- ion back to neutral H atom plus a free e- (b-f)

eHheH

eHhH

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AGB Stars: Physics and characteristic conditions – Densities and Scale Heights

4.1;

][104

102

10&)(

104

][;

216

26

5

21785.0

1

Hgas

gas

3830/T5/2gas

gasegas

3830/T5/2e

Hm

m

Tkp

cmpr

ds10Tpd

ppTkHnp

10Tp0.75n(H)

)n(H

cm

cmdsdOptical depth

b-f cross section

From Saha eq.

e-: Mg,Fe < Na,Al,Ca < H2

p(e1) < p(e2) <p(e3)

From the above eqs.:

For d= 1

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4.1;

][104

][104.1)200(1.0216

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Hgas

gas

o

m

Tkp

cmpr

cmRr

•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

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AGB Stars: Physics and characteristic conditions – Densities and Scale Heights

H

rrpp

M

TR

mG

kH

rrTR

M

k

mGpp

constTTr

Mp

k

mG

r

p

m

Tkp

r

MG

r

p

ppppr

MGggp

oogas

H

oH

ogas

gasHgas

Hgas

gas

turbradgas

)(exp;

)(exp

&;

;

)(;;

2*

2*

2

2

2

Hydrostatic equilibrium

Scale Height:

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AGB Stars: Physics and characteristic conditions – Densities and Scale Heights

KTMMRRM

TR

mG

kH oo

H

3000;2;200; *

2*

Atmosphere: r ~ 1.1 10 12 cm

H~ 1.5 x 1011 cm

1

10

5.05.0

2

4/;

)(exp

~;)(

exp

dH

rr

pH

rrpp

oogas

gaso

ogas

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AGB Stars: Physics and characteristic conditions – Densities and Scale Heights

KTC

C

m

Tkc

V

p

Hs 3000;4.1;3/5;

cs~ 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).

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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)?

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AGB Stars: Physics and characteristic conditions – Microscopic State of Matter (velocity)

skmK

T

m

Tk

dTk

m

Tk

mdf

HH /

30008

8

42

exp2

)(

2

12

1

223

2

Elastic collisions: H & He – excitation E>10 eV

Maxwell distribution

The mean speed:

• Problem: H2 in outer layers with low energy levels. However, collisional excitation and de-excitation are ~equally frequent.

T~3000K->kT~0.26eV

2000 H E=0.26+-0.1eV per 1 H E=2.6

T – may be taken as the T of the gas

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AGB Stars: Physics and characteristic conditions – Microscopic State of Matter (excitation)

ijkinii

kinjjji

kin

o

kin

ocji

jicji

radvo

o

ojiji

vji

CTkEg

TkEgC

Tk

E

T

EnQ

dfnC

TBJ

vhm

Jfdv

vh

JR

o

)/(exp

)/(exp

exp

)()(

)(

4

5.0

0

radiative rates [1/cm3s]

Collision rates

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AGB Stars: Physics and characteristic conditions – Microscopic State of Matter (excitation).

Example: formation of H-

5

24

99

392

1041067.14.1

1010

][10;

HadHad

ad

mRnR

scmReHHH

eHhH

photodisociation

associative detachment

a.d. rate:

photoionization rate: Rph~ 2 106 1/s

Non-LTE effects may be important for H-

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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).

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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(Tkin) ?

The deeper in the atmosphere the better the assumption.

Microscopic state of the gas -> a HUGE set of coupled eq. must be solved

Rij terms couple the radiation field to the state equations

„Model atmosphere” -> above eqs.+ rad. transfer + transport of m,p and E

ijijijij

ijijijii CRPPnPnun

dt

dn

;)()(

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AGB Stars: Physics and characteristic conditions – Microscopic State of Matter (excitation).

The statistical equilibrium

ijijijij

chars

char

iii

i

ijij

ijijijij

ijijijii

PnPn

stc

Ht

nn

H

unun

cmHsmusCR

CRPPnPnundt

dn

)(0

][105102

01010

10)(

][10;][10;][1010,

;)()(

1615

5

11

6

1116151

Equations of statistical equilibrium

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AGB Stars: Physics and characteristic conditions – Microscopic State of Matter.

The chemical equilibrium

one of the lectures will be:

Molecule and Dust grain formation

)(exp

),,,,()(

)(/)()()(

TkgU

DUUUTfABK

ABKBnAnABn

i

ii

oABBA

dissociation equilibrium constant

non-LTE effects: rad.disociation more significant than collisions. e.g. In shocks: tdisoc << tasoc

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AGB Stars: Physics and characteristic conditions – Microscopic State of Matter.

Dust formation

one of the lectures will be:

Molecule and Dust grain formation

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AGB Stars: Physics and characteristic conditions – Microscopic State of Matter.

The transfer of radiation

dvrJvvRrnr

rIrrrIrr

vviv

vvvv

)(),(),(),(

),(),(),(),(1

0

'

2

Time-independent case in spherical symmetry

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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

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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!!!