Multi-D Modelling of the End Stagesof Massive Star Evolution

Bernhard MüllerMonash University

Meakin & Arnett (2007)

Multi-D Effects in theEnd Stages of Stellar
Evolution - Questions●●●●

Impact on bulk pre-collapse
structure (compactness...)
Implications for explosion
mechanism & asymmetries
Mixing and angularmomentum transport (longterm effects)
Wave-driven mass loss anderuptive events(cp. Monday & Tuesday talks)
Grefenstette et al. (2017)

Late Convective Burning Stages –1D vs. 3Dburning

EntropyO massfraction

neutrino coolingOburns

here

Mass coordinate

Radialvelocity

Convective energy flux ∝superadiabatic gradient:Plumes of various scales●
Advective transport instead ofdiffusive mixing●
Shear instabilities at boundaries●“Natural” association of preexplosion mass loss with
Ne/O/Si burning timescales?
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Overshoot parameterised (extend convectiveboundaries, exponential diffusion law as inFreytag 1996,...) if treated at all

Early Attempts & Challenges
Cost of reaction networks (especially for
Si burning)
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Initial transients & thermal relaxation ofmodels (→ long simulation time scales)
Explicit codes challenged by low Mach
number flow & thermal balance ofburning and neutrino cooling
Axisymmetry introduces artefacts, need
3D
For SN progenitors: core evolution
influences shells (contraction, adiabaticBazan & Arnett(1998)

3D SN Progenitor Models

Si mass fraction in O
shell, 18 M⊙xdMüller et al. (2016)

Couch et al. (2015)

Immediate pre-collapse phase iseasier (higher Mach number,short timescales)●
3D simulations with ~10 or more
turnovers feasible (Monash/MPA,MSU, Tokyo/Fukuoka groups)●Yadav et al. (2020)

Beneficial Effect of Convective Seed
Perturbations on “Explodability”
Shock, gain &neutron star radii

1D progenitor

3D O shell

3D O shell withartif. reducedburning

Mass accretion rateMüller et al. (2017)

Forced shock deformation facilitates
asymmetric explosions – less neutrino
luminosity needed for runaway: L crit 24×Ma prog
~L critℓLong-Time Evolution of theExplosion

Red: Si-rich ashes
Cyan: Outer O shell boundary
Grey: Si core

Neutrino-heated bubbles in ensuing supernova (red/yellow)

Geometry of convective flow in progenitor remains imprinted on shock during firstseconds(but inner ejecta not perfectly aligned)

3D Models vs. Mixing-Length Theory:

Adjustment forseveral turnover times

Steady state

Deviation from adiabatic gradient differs locally, but vconv agrees
well with mixing-length theory (MLT)●
Stationary MLT break down a few ms before collapse whenconvective flow can't react to increased burning rates any more●Time-dependent MLT (e.g. KEPLER code) captures this freezeout pretty well●

Beyond Mixing Length Theory:
Entrainment●●Shell burning simulations(Meakin & Arnett 2007, Müller
et al. 2016, Jones et al. 2017,Cristini et al. 2018) well in linewith entrainment law:3vconv
Ṁ ≈0.1×4 π r 2 ρg Λ δ ρ /ρ
Λ : pressure scale heightδ ρ / ρ : density contrast at interface

Müller et al. (2016)

Entrainment rate – Simulation vs.

Beyond Mixing Length Theory:
Entrainment●

Estimate for total shell growth byentrainment (Müller 2016):

Müller et al. (2016)δ ρ −1 Δ Q
Δ M ≈0.1×M shell ρ2e( )intin terms of effective Q-value ΔQ
for burning stage●●Expect O(10%) effects on shellmasses

Entrainment rate – Simulation vs.
empirical entrainment law

Wave Excitation in Multi-D Simulations

Convection with Magnetic Fields

Little effect on convective dynamics, but●Magnetic stress at shell boundaries
may reduce entrainment “spikes”●Fields can be relatively large (1091010G in O shell – not core!)3D Hydro andStellar Rotation
Yoshida et al.
(2021)

McNeill & Mueller (2021): Equatorial
superrotation

Constant j vs. constant Ω vs.
superrotation (dΩ/dr>0):
Beware of timescales!

Fields (2022)

Coupling of Shells by Magnetic Fields
Rotational velocity (km/s)

Field strength (G)O/Ne/Mg
C/Ne

MHD shell burning simulation (Varma et al. in prep.)
Inner shell initially rotating ~4 times faster than C/Ne shell●
Braked efficiently by strong fields (~1011G)●
Strong fields shut off convection in inner shell●
Lots of subtleties (resolution, magnetic Prandtl number...)●Coupling of Shells by Magnetic Fields

Angular velocity

Field strength (G)MHD shell burning simulation (Varma et al. in prep.)
Inner shell initially rotating ~4 times faster than C/Ne shell●
Braked efficiently by strong fields (~1011G)●Strong fields shut off convection in inner shell●Lots of subtleties (resolution, magnetic Prandtl number...)●Collins, Müller & Heger (2018)

Towards Eruptive Events: Shell Mergers?

14.4M815.4M817.4M817.57M8

Sizeable fraction of progenitors between16M8 and 26M8 undergo shellmergers (O/Ne/C) within a few turnover times before collapse●
In 40% of these, the merger is still in progress in the 1D models●Prevalence of late mergers related to increased O burning rate without
sufficiently fast response of neutrino cooling●Studied in 3D simulations (Mocak et al. 2018, Yadav et al. 2020)●

●Explore parameter space further

Oscillatory Burning Instabilities?

Simulations divided about(quasi-)periodic instability ofconvective burning●
Interplay with entrainment provides
clear physical mechanism inHerwig et al. (2014, GOSHinstability)●
Physical conditions for instability &impact on mass loss need to bebetter understood●

Herwig et al. (2014): GOSH instability
Note that this was discovered for H ingestion, but
feedback between entrainment and burning isconceivable for later stages as well

Next Challenges

Si flashes around 10M⊙ (single stars): Dynamical phases of pairMulti-D treatment of convective
instability pulses within reach ofbounded flame essential, but toughmulti-D?
problem

Surprises during Ne burning?
(Cp. Fuller 2017: wave heating during core Ne burning)Convective burning in multi-D

Radiation hydro for stellar envelopes

xd

Müller et al. (2016)

How to put everything together
to obtain pre-SN mass loss
on the right timescale andIn the right amounts?

Jiang et al. (2017)
Heger et al. (1997)

Fuller (2017)
Wave excitation, propagation & heating

Red supergiant pulsations

Summary & Outlook
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Advent of reasonably well resolved 3D simulations of late shell burning
stages over ~10 turnover times or more
Big impact of multi-D structure on supernova explosion mechanism &explosion geometry
1D MLT is a good approximation for stellar interiors – modest effect of
turbulent entrainment on shell structure expected
Wave excitation in simulations consistent with analytic theory (i.e. noextra help for wave-driven mass loss)
3D simulations starting to explore angular momentum transport →potentially big changes compared to 1.5D, but beware prematureconclusions
No convincing scenario for pre-explosion outbursts from 3D hydro ofstellar interiors yet:●

Shell mergers: Violent, but probably too late before collapse●

Oscillatory burning instabilities: still too elusive●

Degenerate burning in low-mass stars and PPISN to be explored inmulti-D