Delavega 171 611 Presentation

8/17/2019 Delavega 171 611 Presentation

1/16

Computational Difficulties in

Modeling AGB Evolution

5 May 2016

Alex de la Vega

http://find/


2/16

The AGB Evolutionary Track

Stars with mass 0.8 M ≤ M∗ ≤ 8 M evolve through AGB

H fuses into He within core; fusion stopsGravitational contraction leads to H-burning shell, leads to RGBIf M ∗ ≥ 4 M convective envelope may penetrate H-shell, bottom of envelopeburns, ’Hot Bottom Burning’Core burns He, goes to horizontal branch, back to RGB asymptotically when HedepletedCO core, H- and He-shells, thermal instabilities lead to periodic ’thermal pulses’Inner material mixes with outer layers (dredge-up), s -process nuclei, mass loss rates

∼ 10−8 − 10−4 M yr−1

Stellar winds lead to planetary nebulae, white dwarfs

http://find/http://goback/


3/16

The AGB Evolutionary Track (cont.)

http://find/


4/16

Model Uncertainties

Sensitive dependence on convective and mixing processesand mass loss

Good qualitative matches with data, but there exist plentyof quantitative uncertainties

Believed that stellar convection is still not entirelyunderstood

Dredge-ups may not even occur depending on howconvection is modeled

http://goforward/http://find/http://goback/


5/16

Modeling Convection

Simulations use adaptive grid, hydrodynamic, or hydrostatic codes

Mixing Length Theory of Böhm-Vitense very common for 1D codes – L = αH P –turbulence is incompressible1 < α < 2 normally – free parameter!Schwartzschild criterion used to establish size of convective regionsFull Spectrum of Turbulence (Canuto & Mazzitelli(1991)) – elements spectrum of diff.sizes, turbulence compressibleSynthetic models combine previous models and/or obs. – cheaper, used for pop.synth.

Pasetto et al. (2014) - FST but non-local, time depend., Bernoulli

321D of Arnett et al. (2015) – numerical sol. of Navier-Stokes – can model top &

bottom boundary layers of stellar convection zones – can’t w/ MLT



6/16

Convection in AGB Stars

Schwartzschild criterion – assumes a = 0, but v = 0 necessarily

Extend convective regions with overshoot – leads to increased mixing, e.g.third dredge-up (TDU)

Herwig et al. (1997) – TDU only w/ overshoot for M ∗ ≥ 3 M

Ventura & D’Antona (2005) – vast differences between FST and MLT – see

below

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7/16

Mixing Processes – The Third Dredge-Up

Occurs during thermal pulse phase – carries nucleosynthesis products from H and He

burning to surfaceThermal pulse – dredge-up – interpulse cycle, depends on initial mass, composition,mass lossTDU efficiency – λ =

∆M DU ∆M H

Mowlavi (1999) – no TDU w/o overshoot – using ∇rad = ∇ad gives discontinuity in X(H)Adding overshoot region avoids discontinuity; results in efficient TDUHerwig (2005) – premix several grid shells before determining boundary – repeat untilconvergence

Frost & Lattanzio (1996) – iteratively mix X i near boundary, keep X i fixed until models

converge, then mix X i

http://find/


8/16

Mixing Processes – Hot Bottom Burning

HBB arises in intermediate mass stars (M ∗ ≥ 4 M) when convectiveenvelope dips into H-burning shell

shell acquires more fuel, bottom of envelope has large rise in temperature,

increases luminosityHBB can turn dredged-up C into N and increases Li production

Under MLT, HBB more efficient with larger α – but FST more efficient than MLT

To get HBB:

FST: M ∗ ≥ 4 M

MLT: M ∗ ≥ 6 M

Towards end of AGB mass loss reduces – HBB efficiency decreases



9/16

Mass Loss Modeling

AGB stars suffer mass loss ∼ 10−8 − 10−4 M yr−1

Determines number of thermal pulses, dredge-up may not happen

First and most common – Reimers (1975) empirical formula:

Ṁ = −4 × 10−13η L

gR

13 η 3 – free parameter!

Catelan (2009):

None of the current mass loss formulae fit derived rates (for Origlia et al. (2002))

No clear dependence of mass loss on L, g or R No clear correlation between mass loss and metallicity

Mass loss appears to be episodic, not continuous

http://find/


10/16


11/16

Nucleosynthesis Modeling

Mostly due to the interaction between H- and He-burning shells

Modeling nucleosynthesis largely depends on how one treats convection,mixing processes and mass loss

Often handled through postprocessing – thermodynamic info fromnumerical stellar models as input for chemical calculations

Feedback between assumed mixing processes and stellar structure does

not occur – but yields good qual. & quant. results!



12/16

Nucleosynthesis Modeling – s -process

Slow neutron capture process (or s -process) – responsible for half of allelements heavier than Fe

Nuclei products begin with Fe group and ascend closely valley of stability

main source for s -process neutrons is 13C(α,n)16O reaction

During TDUs H-rich convective envelope dips into 12C-rich intershell, givingrise to 13C

Overshoot is important – can affect s -process production

Herwig et al. (1997), Herwig (2000) gives time-dependent, convectiveovershoot code with exponential diffusion:

dX i

dt =

∂ X i

∂ t

nuc

+ ∂

∂ M r

4πr 2ρ

2D ∂ X i

∂ M r

,

D depends on choice of convection

For above, w/ overshoot we get TDU; without overshoot, no TDU (thoughthis depends on mass)

Lugaro et al. (2003) – uncertainty in s -process predictions may be from 13C,

not presence/absence of overshoot

http://find/


13/16

Progress in the Thermal Pulse Phase

Schwartzschild & Härm (1965) – discover thermal pulses – thermalinstabilities in helium-burning shells in non-degenerate stars

Eggleton (1971, 1972) – developed codes that could solve implicitly and

simultaneously equations for stellar structure and abundance profiles from

mixing and reactions

MLT with diffusion to describe convection in AGB stars

Very recent work – Marigo et al. (2013) – COLIBRI code

self-consistently computes convective envelope structures, HBBnucleosynthesis, abundances after each thermal pulseon-the-fly calculations of the equation of state for 800 atoms, ions, molecules

very computationally fast, able to generate entire TP-AGB grids in a few hours

Rosenfield et al. (2016) – mass loss relation for low-mass, low-metallicity

stars consistent with HST observations



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Super-AGB

Usually between ∼ 8 M just below which leads to CO white dwarfs, to∼ 11 M leads to ONeMg cores

Still suffer from uncertainties in modeling convection – convectiveprocesses determine temperature at base and extent of stellar envelope,thereby affecting mass loss

Jin et al. (2015) – find X (H ) discontinuity from MLT w/ overshoot for

Super-AGB

http://find/


15/16

The Low Metallicity Regime

CNO material for H-burning absent – pp-chain must produce nuclearenergy, at least initially

for Z


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Image References

Herwig, F. 2005, Annu. Rev. Astron. Astrophys. 43, 435 - 79

Karakas, A. I., Lattanzio, J. C., & Pols, O. R. 2002, Publ. Astron. Soc. Aust., 19, 515https://en.wikipedia.org/wiki/Mixing length model

Ventura, P., & D’Antona, F. 2005, A&A, 431, 279

Mowlavi, N. 1999, A&A, 344, 617

Origlia, L., Ferraro, F. R., Fusi Pecci, F., & Rood, R. T. 2002, ApJ, 571, 458

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Delavega 171 611 Presentation