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©L. A. Willson 5/2004
Mass Loss at the Tip of the AGB
L. A. WillsonIowa State University
©L. A. Willson 5/2004
I will try to persuade you that
• 1. None of the mass loss formulae now in print provide what is needed for stellar evolution and PN formation
• 2. However, we know quite well which stars are dying from terminal mass loss
• 3. There is a problem with standard core mass - luminosity relations
©L. A. Willson 5/2004
The physics of mass loss
Quenched chemistry vs. equilibrium: What is the equilibrium state of cake in a hot oven?
Radiative transfer in dynamical atmospheres with periodic shocks -- Non-LTE, non-RE
Molecules and grains in quenched flow
Non-equilibrium H2/H (Bowen)Metastable eutectic condensates? (Nuth)
Gas-grain interactions
©L. A. Willson 5/2004
Some things we do know
• Periodicity condition applied to Miras– Constraints on M and R of AGB tip stars, i.e.
constraints on the evolutionary tracks
• Importance of departure from LTE and RE in the dynamics (adiabatic shocks)– Mass loss is enhanced by departures from RE– Makes it difficult to use dynamic models for radiative
transfer– Makes it difficult to study the mass loss process
observationally
©L. A. Willson 5/2004
Periodicity condition
If the material does not have enough time to fall back to its initial position, then the atmosphere expands.
Expansion => a stable periodic structure with larger scale height and/or a wind
Po must be ≤ P
NOT ∆v = gP because ∆r/r is not <<1
H&W, W&H 1979
©L. A. Willson 5/2004
∆v/vescape depends on Q = P√(/Sun)
2vo/vescape
Q = 0.01 0.1 1
2
1.5
1
0.5
∆v=gP
Note: Overtone models have both smaller Q and smaller vescape for a given P
F-mode Mira models
©L. A. Willson 5/2004
Isothermal or adiabatic shocks?
LTE cooling times are fast; Non-LTE cooling (or heating) times increase with decreasing density
At some critical density, cooling times become ~ P
For densities << critical, the shocks will be effectively adiabatic.
Deep in the atmosphere, cooling times are << P and the shocks are effectively isothermal.
©L. A. Willson 5/2004
Isothermal/
Adiabatic hybridmodel:
Mass loss rate depends on the
cooling rates
(Willson & Hill 1979)
©L. A. Willson 5/2004
Shock compression -> heating -> radiative losses; expansion between shocks -> cooling and slower radiative gains.
T<TRE
Bowen model
The level of T here depends on details of the model including non-LTE cooling and mass outflow
2 4 6 8 10 12 14 16 R*
10
8
6
4
2
T/1000K
©L. A. Willson 5/2004
Vesc
2 4 6 8 10 12 14 16
R/R*
Shocks form and propagate outward
Bowen model
©L. A. Willson 5/2004
Two kinds of models• Models developed to study physical and
chemical processes in detail– Höfner, others:
• Dynamics with radiative transfer to fit spectra.
– Sedlmayr, others: • Dust nucleation & growth in carbon stars
• Models developed to study the pattern of mass loss at the tip of the AGB– Bowen models approximate nonLTE, transfer and
dust processes for O-rich stars
©L. A. Willson 5/2004
NOTE
One cannot run LTE radiative transfer on a Bowen model (or any other model with approximate nLTE) because the cooling assumes nLTE; LTE transfer gets more energy out than was put in and detailed nLTE doesn’t generally match schematic cooling rates everywhere.
Bowen’s models were not designed for radiative transfer computations, but rather …
©L. A. Willson 5/2004
…to study the evolutionary pattern
• Models designed to reveal the evolution of stars through the Mira region at the tip of the AGB
• Mass loss rates are very sensitive to L, M, R, Teff …
• R(L, M) sensitive to mixing length (and hard to measure)
=> Hard to predict what a particular star will do, but there is a
very robust pattern for the evolution at the tip of the AGB
©L. A. Willson 5/2004
Some reasons for believing these models get the pattern right
• They fit and explain the Mira P-L relation
• They fit and explain empirical correlations of mass loss rates with stellar parameters
©L. A. Willson 5/2004
Matching models to populations
• Evolutionary tracks => R(L, M, Z, ) and L(t)
• Mass loss models => M(R, L, M, Z)
• Together, these produce predictions of M(t) and thus of the maximum LAGB
©L. A. Willson 5/2004
100000100001000
10
-10
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
Mdot vs. L — Solar metallicity
L/Lsun
Mdot (Msun/yr)
M = 0.7 1.0 1.4 2.0 2.8 4.0
The dependence of mass loss rates on stellar parameters along the AGB is VERY steep (fit by LxM-y with 10<x, y<20.
Models by Bowen (1995 grid) using Iben R(L, M, Z):
Note: Because R vs. L, M is given by the evolutionary track, L serves as proxy for L, R, and Teff, and the steep dependence on L in the figure could be all R, all L, all Teff or (most likely) a combination of these.
©L. A. Willson 5/2004
-10 -8 -6-4
log=
0.7
1
1.4
2
2.8
4
core mass
Chandrasekhar limit
0.6
0.4
0.2
0.0
-0.2
logM
3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8
logL
Stars evolving up the AGB lose little mass until they are close to “the cliff” where tmassloss ~ tnuclear:
Bowen and Willson 1991
This is a “lemming diagram”
Mass Loss Rates Too Low To Measure
Short lifetime, obscured star
First surveys will find mostly stars near the cliff
©L. A. Willson 5/2004
7.06.86.66.46.26.05.85.6
-8
-7
-6
-5
-4
logLR/M
log(Mdot)
cliff stars with
M/Sun indicated
Reimers' formula
slope -10
slope -0.1
0.7
1.0
1.4
2.0
2.8
4.0
Empirical relations result from selection effects with very steep dependence of mass loss rates on stellar parameters.
Reimers’ relation is a kind of main-sequence for mass loss: It tells us which stars are losing mass, not how one star will lose mass.
x10
x0.1
©L. A. Willson 5/2004
-10 -8 -6-4
log=
0.7
1
1.4
2
2.8
4
core mass
Chandrasekhar limit
0.6
0.4
0.2
0.0
-0.2
logM
3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 logL
Bowen and Willson 1991
Miras have high mass loss rates, extended atmospheres, and large visual amplitudes: Miras markers for the “cliff”:
©L. A. Willson 5/2004
Observations of Miras and OH-IR stars confirm that Miras mark the location of the cliff:
(K-L is a mass loss Rate indicator.)
• = Miras
©L. A. Willson 5/2004
0.7 1
1.42
2.8
4
2 2.2 2.4 2.6 2.8
logP
5
4
5
4
3
logL
logL
The cliff fits the observed Mira P-L relation from the LMC very well.
Hipparcos distances to Miras show a lot of scatter.
No parameters were adjusted to obtain this fit.
©L. A. Willson 5/2004
How sensitive are these results to uncertain parameters -
mixing length (=> R vs. L, M)cooling rates (affecting mass loss rate vs.
R, L, M)dust formation physics (affecting mass loss
rate vs. R, L, M)etc?
©L. A. Willson 5/2004
100000100001000
10
-10
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
Mdot vs. L — Solar metallicity
L/Lsun
Mdot (Msun/yr)
M = 0.7 1.0 1.4 2.0 2.8 4.0
Increase mass loss rates by a factor of 10 - what happens to the predictions?
The critical mass loss rate = M (L/L) does not depend on the mass loss models, but Lcliff does.
.
Result: Cliff values of L (and associated R) for a given M are not very sensitive to the mass loss law
©L. A. Willson 5/2004
Effect on L vs. P of ∆logM = 1 is no more than ∆logL ~ 0.1
0.7 1
1.42
2.8
4
2 2.2 2.4 2.6 2.8
logP
5
4
5
4
3
logL
logL
.
©L. A. Willson 5/2004
What about other mass loss laws?
From Willson 2000 ARAA (Vol 38)
Bowen (Theory), Reimers, Baud & Habing, and Vassiliadis & Wood (two independent observed relations) all identify the same Lcliff(M):
Reimers formula kills stars at higher L because it is not steep enough - hence the introduction of and BH’s introduction of 1/Menvelope
©L. A. Willson 5/2004
New, improved mass loss law?Wachter et al 2002
Wachter et al 2002
Using Iben tracks and assuming zero (or small) RGB mass loss, this law kills stars at too high L
Perhaps the problem is with the Iben tracks. What would be needed to get stars to die at the right L, M with the Wachter et al mass loss law?
103 L/Sun 105
-4
-8
©L. A. Willson 5/2004
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.5 1 1.5 2 2.5 3 3.5 4 4.5
WachterMdotvL
0.1 delta1 delta10 delta
Mass
=> Wachter et al.’s mass loss law cannot be forced into agreement with observed deathline for normal evolutionary tracks
Their M ~ T6.81 To get the right death-line we need to shift the evolutionary tracks by ∆LogT = -0.2 to -0.9 -- more of a shift for higher masses
∆logT = 0.3 takes 3500K to 1750K - much lower than indicated by any observations
Can we use their mass loss law with different evolutionary tracks?
©L. A. Willson 5/2004
0.1
1
10
1000 104
105
HR diagram data Bowen Wachter
mass
L
Models by Wachter et al. Relative to the cliff:
Their models are all low mass & high L, and may describe post-Mira, post-cliff carbon stars accurately,
but they do not kill stars at the right L(Minitial) and should not be used for stellar evolution calculations
cliff3
2
1
©L. A. Willson 5/2004
Helium Shell Flashes - another complication!
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
1.647 10
8
1.648 10
8
1.649 10
8
1.65 10
8
1.651 10
8
1.652 10
8
logL
t
An L-Mcore relation fits this part
During a flash, ∆logL ≤ 0.4 (apart from very short-lived minimum)
©L. A. Willson 5/2004
L and R variation => M modulation*
60
80
100
120
140
160
180
200
1.6 10
5
1.8 10
5
2 10
5
2.2 10
5
2.4 10
5
2.6 10
5
2.8 10
5
3 10
5
3.2 10
5
Radius/RSun
F
Quiescent H-burning
The height of Rmax (or Lmax) is not well determined - different models predict different contrast, from ≤1 to ≥2 x quiescent H burning L. Where most of the mass comes off is very sensitive to this contrast, and thus whether most CSPN are H or He burning.
Post-flash He burning
©L. A. Willson 5/2004
0.7 1
1.42
2.8
4
2 2.2 2.4 2.6 2.8
logP
5
4
5
4
3
logL
logL
During a shell flash, a Mira moves along the P-L relation for P < 300d but should leave it for P > 300d
©L. A. Willson 5/2004
Initial-final mass relation
From Weidemann V., 2000, A&A, 363, 647
Evolution with mass loss and standard core mass - luminosity relations don’t fit.
Mass loss pre-AGB tip or ??
There is a deeper problem
Agnes Bischof Kim, MS Thesis 2003
©L. A. Willson 5/2004
P => L => Mcore for Miras
dndlogP
200 400 600 days
0.56 0.60 0.64 0.72 0.85
Nearly all Miras have L such that we’d expect Mcore > 0.6 solar masses.0.7 1 21.4 2.8
Obs. theory
©L. A. Willson 5/2004
Their fate is to be white dwarf stars
Nearly all WD have masses < 0.6 solar masses. Observed
©L. A. Willson 5/2004
With or without overshoot
Shell flash peak (not H-burning luminosity)
From Herwig, 2000
Although this is 3 solar masses and shows a limiting core mass >0.6this is what has to happen for M ≥ 1 to keep the Mira core masses low
to match white dwarf masses
©L. A. Willson 5/2004
Another problem: ∆MRGB
• Mass loss on the RGB may be– By reaching the Death Zone (cliff region)– As a result of an ejection during the core flash
The character of the Death Zone is that it is hard to go there and come out alive -
Most stars lose everything, or nothing
Losing a lot -> Blue HB and no Miras
Therefore, those that ascend the AGB probably have ∆MRGB mainly from the core flash event
©L. A. Willson 5/2004
masses of Miras on the cliff
200 400 600 days
0.7 1.0 1.4 2 2.8
This is consistent with little or no mass loss before the Mira stage.
©L. A. Willson 5/2004
Can we predict Lfinal vs. Z, t?
These models have dlogLf/dlogZ ~ -0.1 to -0.2; even if details are wrong, this should be a good estimate, as the dominant effect (the only effect outside the green patch) is the shift in evolutionary tracks dlogT/dlogZ at constant M.
Again, it’s Lfinal not Mcore this analysis tells us
©L. A. Willson 5/2004
Robust ResultsMass loss rates increase precipitously stars die very soon after reaching dlogM/dlogL = -1observations of mass loss rates and/or location of the Mira variables tells you which stars are now dying.
Mass loss rates are sensitive to a combination of R, L, and M such that low metallicity stars, smaller at a given L, M, reach higher L before dying.
The generation of dust and oxygen- or carbon-rich molecules further enhances mass loss rates for high Z stars.
Core masses do not grow as large as standard Mc-L relations predict they should
©L. A. Willson 5/2004
Is this the usual development?
©L. A. Willson 5/2004
-10 -8 -6-4
log=
0.7
1
1.4
2
2.8
4
core mass
Chandrasekhar limit
0.6
0.4
0.2
0.0
-0.2
logM
3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 logL
Miras
Where bipolarity arises for most PNe
OH-IR stars
Symmetrical stars -> bipolar PNe
To spin up the envelope with a companion, need m/Menvelope > ~ 0.1
Other reservoirs of angular momentum also => low envelope mass is necessary to get bipolar symmetry
All stars pass through the low-envelope-mass zone
©L. A. Willson 5/2004
Conclusions: What we don’t know
• We can’t yet derive a remnant mass from an initial mass
• We can’t yet predict the mass loss rate for a given star accurately
• We don’t know whether AGB stars lose mass mostly near the He shell flash peak or mostly during quiescent H shell burning
• The models that fit the aggregate properties of the populations can’t be used for radiative transfer
• Models used for radiative transfer and/or studies of dust nucleation do not yet include all the physics needed to map the mass loss accurately
©L. A. Willson 5/2004
Conclusions: What we do know• We do know reasonably well where these stars die
- that is, the location of the “cliff”or death-lineboth from empirical studies and from theory
• We also know that lower Z stars will reach the same mass loss rate at a higher L for a given M,
mostly because they are smaller but also because they make fewer molecules and grains
• We also know that the standard core mass - luminosity relations overestimate Mcore for the bulk of the Miras.