©L. A. Willson 5/2004 Mass Loss at the Tip of the AGB L. A. Willson Iowa State University

©L. A. Willson 5/2004

Mass Loss at the Tip of the AGB

L. A. WillsonIowa State University


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


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


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


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


∆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


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.


Isothermal/

Adiabatic hybridmodel:

Mass loss rate depends on the

cooling rates

(Willson & Hill 1979)


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


Vesc

2 4 6 8 10 12 14 16

R/R*

Shocks form and propagate outward

Bowen model


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


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 …


…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


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


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


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.


-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


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


-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”:


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


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.


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?


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


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

.


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


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


-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?


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


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 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


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


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


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


Their fate is to be white dwarf stars

Nearly all WD have masses < 0.6 solar masses. Observed


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


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


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.


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


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


Is this the usual development?


-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


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


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.

Documents

©L. A. Willson 5/2004 Mass Loss at the Tip of the AGB L. A. Willson Iowa State University