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Integrated Impact of Hydrodynamic Processes in Massive Stars Stellar Hydro Days July 26th, 2006 Patrick Young (LANL/Steward) Casey Meakin, David Arnett (Steward) LA-UR-05-3961,4652

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A Sampling of Unresolved Questions Evolution and contribution to environment f(initial mass) f(metallicity) Yields from an initial mass function (IMF) luminosity kinetic energy nucleosynthesis Progenitors of WDs, LBVs, SNeII, SNeIb/c, GRBs, etc. How to identify the progenitor of a particular object Asymmetries in supernova progenitors asymmetries in explosion, mixing of nuclear species

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A Sampling of Unresolved Questions Evolution and contribution to environment f(initial mass) f(metallicity) Yields from an initial mass function (IMF) luminosity kinetic energy nucleosynthesis Progenitors of WDs, LBVs, SNeII, SNeIb/c, GRBs, etc. How to identify the progenitor of a particular object Asymmetries in supernova progenitors asymmetries in explosion, mixing of nuclear species

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A Sampling of Unresolved Questions Evolution and contribution to environment f(initial mass) f(metallicity) Yields from an initial mass function (IMF) luminosity kinetic energy nucleosynthesis Progenitors of WDs, LBVs, SNeII, SNeIb/c, GRBs, etc. How to identify the progenitor of a particular object Asymmetries in supernova progenitors asymmetries in explosion, mixing of nuclear species

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A Sampling of Unresolved Questions Progenitors of WDs, SNeII, SNeIb/c, GRBs, etc. f(initial mass) f(mass loss) f(metallicity) How to identify the progenitor of a particular object Yields from an initial mass function (IMF) luminosity kinetic energy nucleosynthesis Asymmetries in supernova progenitors asymmetries in explosion, mixing of nuclear species

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Structure, Physical Processes, & Evolution Some stellar characteristics which influence evolution and final fate: Mass, core size Density profile, entropy gradients Composition, neutron excess fluid velocities, angular momentum, asymmetries energy transport Determined primarily by: Mass Loss Nuclear & neutrino physics, opacities & EOS Rotation Convection Physics of convective boundaries Hydrodynamics of stable regions

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Structure, Physical Processes, & Evolution Previous slide somewhat misleading We tend to separate out physical processes Physics of stars, especially hydro, strongly coupled For example, convection, waves, rotation, & radiation transport are a single problem Stars are not amenable to direct simulation multi-D gives snapshots analytics treat problems in isolation High energy density experiments don’t do stable hydro Combinations of these can allow us to develop analytic frameworks that account for the coupling seen in more physically complete situations of simulation and experiment

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Stable does not mean static! Standard stellar models treat stars as series of static states Mixing length-like theories: evaluate thermodynamic criteria to determine extent of convection Thermodynamic criteria appropriate for predicting onset of convection in stratified fluid, but not extent of convection once fluid is in motion Stable layer is completely static

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Stable does not mean static! Multidimensional simulations of stellar convection Main sequence 23 M core convection (Meakin/PROMPI)

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The Convective Boundary Three main hydrodynamic regimes in a stratified medium Region 1: fully convective: Brünt-Väisälä frequency N 2 < 0 Unstable - displacements lead to acceleration Driven by entropy generation (nuclear burning) or entropy loss (surface convection) Motion dominated by accelerating plumes Vorticity XHXH Velocity

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The Convective Boundary Boundary characterized by bulk Richardson number Ri = b / ( u/ r) 2 : Ratio of potential energy across a layer to energy in shear ( u = rms turbulent velocity, shear from waves depends on context, r = extent of boundary, b = N 2 dr) Ri ~ 0.25: Boundary region. Impact of plumes deposits energy through Lagrangian displacement of overlying fluid. Internal waves propagate from impacts Conversion of convective motion to wave motion. Shear instabilities, nonlinear waves mix efficiently. Wave amplitudes M 2 + N 2 large buoyancy jump gives large wave amplitudes even at small Mach number VorticityXHXH Velocity

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The Convective Boundary Boundary characterized by bulk Richardson number Ri = b / ( u/ r) 2 : Ratio of potential energy across a layer to energy in shear ( u = rms turbulent velocity, r = extent of boundary, b = N 2 dr) Ri ~ 0.25: Two issues - extent of hydrodynamically unstable region larger that thermodynamically unstable region Entrainment at marginally stable boundary ~ VorticityXHXH Velocity

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The Convective Boundary Radiative regions Internal waves propagate throughout radiative region evaluate stability with gradient Ri, buildup of waves in cavity or coupling with rotation can cause instability Radiative damping of waves generates vorticity (Kelvin’s theorem) Slow compositional mixing Energy transport changes gradients; generates an effective opacity angular momentum transport Baroclinic generation term Vorticity

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Implications for Evolution Predictive Physics can be incorporated into evolution codes Higher radiation pressure -> less restoring force Small effect for small stars More important with increasing stellar mass Larger convective core masses Longer lifetimes Higher luminosity, larger radii Larger C/O cores at collapse (>50% larger for 25 M ) Different composition & entropy gradients, different neutron excess, different yields Mixing of processed material through radiative regions, deeper dredge-up

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Observational Tests Convective core size Indirectly, luminosities, radii of eclipsing binaries Directly from apsidal motion of binaries Standard model cores are systematically undersized Models with hydrodynamics fit well at all masses

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Eclipsing Binaries

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Shell Burning See Casey’s talk Important evolutionary effects: very different extent of late stage shells mixing between shells Urca entrainment of fuel Large perturbations of thermodynamic quantities Spatially correlated perturbations

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Extent of Convection Local mixing length convection ignores effect of KE on marginally stable layers Initial transient input of KE increases extent of mixed region ~30% for mixing length initial models New steady state after O abundance readjusted

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Uncertainties in Nucleosynthesis Structure of progenitor Asymmetries in progenitor Explosion mechanism Method of calculating explosion Method of calculating nucleosynthesis in explosion Asymmetries in explosion

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Structure at Core Collapse Comparison of TYCHO models with and without hydro mixing Models with hydro mixing: Smoother entropy gradients Larger O cores, thus higher Different abundance profiles Multi-D effects Coherent perturbations of ~% on large spatial scales-> rippled interfaces, global asymmetries Merging of shells Wave effects on energy & neutrino transport, opacities

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Structure at Core Collapse Changed density structure changes collapse Large mass accretion rate onto compact remnant for much longer time Delayed explosion relative to standard stellar model Weaker explosion More fallback Relatively low black hole minimum mass Stars above ~ 20M at z either become weak SNe or GRBs (maybe both)

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Effect on Explosion: Changes in 1D Progenitors Yields from 23 M with Grevesse & Sauval 98 solar metallicity Core collapse models from TYCHO with and without hydro mixing 1D collapse from Fryer 1999 Model Explosion Energy Remnant Mass Ni Mass /Fe Standard 1.65 foe 1.57 M 0.42 M 5.74 Hydro weak exp. 0.57 foe 6.01 M <0.1 M large Hydro strong exp. 3.0 foe 1.64 M 0.99 M 6.05

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Effects of Explosion Asymmetries Imposing a small asymmetry during 3D calculation of explosion changes mixing Yields for otherwise consistent models: energy (foe) 44 Ti (M ) 56 Ni 23 M 2.3 1.2x10 -5 2.6x10 -4 23 M Asymm.2.31.8x10 -4 0.019

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Conclusions Stable does not mean static! Hydrodynamics in the convective boundary and radiative regions have substantial effects on evolution radiation pressure, restoring force, effects increasingly important at larger masses Hydro mixing can be approximated in 1D evolutionary models in a predictive way and in agreement with observations Late burning stages cannot be captured in 1D burning shells interact perturbations in T, of perhaps 10% correlated on large angular scales near collapse rippled composition / thermodynamic boundaries different abundance patterns, effects on neutrino physics

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Conclusions Core sizes, explosion energies & remnant masses are substantially different Yields can change by orders of magnitude due to changes in progenitors asymmetries in progenitors (not to mention various aspects of the explosion calculation itself) High resolution 3D simulations and sophisticated analytical work are both necessary - physics must be generalized to apply to a wide range of conditions

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Next Steps Angular momentum transport Geneva group has demonstrated importance of rotation to stellar evolution Analytic - not supplemented with multi-D simulations, treated in isolation Rotation must interact with g-modes & convective boundary instabilities - more efficient transport of angular momentum Talon & Charbonnel show that g-modes can induce ~solid body rotation in sun, where wave flux is small Simulations in progress MHD You can also get solid-body rotation in sun from B fields Requires sophisticated MHD Simulations in stellar context essentially limited to solar convection zone

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Next Steps Nuclear burning - multi-D with larger networks & post-processing Radiation dominated environments - eruptions of Luminous Blue Variables and Supernova Impostors Inefficient convection on the early pre-Main Sequence and late post-Main Sequence Binary Evolution Connecting star formation to stars Sandquist & Taam

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O & C Burning conv ~ nuc ~ thermal No direct observational constraints Initial 23 M models from TYCHO with and without wave physics included 25 element nuclear network for O & C burning 2D & 3D wedges encompassing O or O&C shells prior to Si ignition

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Effects of Burning Calculation Network size (obviously) important. Any calculation requires detailed post- processing Duration of burning important. Network and freezeout calculations must continue for 10’s of seconds Location of -rich freezeout uncertain: even at high Y e (>0.4985) final dominant abundances ( , 56 Ni, neutron rich Fe peak) very sensitive to initial entropy, composition, thermodynamic trajectory

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Effects of the Explosion Calculation Very different neutrino luminosities can produce same final kinetic energy Yields for otherwise consistent models: energy (foe) 44 Ti (M ) 56 Ni 23 M 2.3 1.8x10 -4 0.019 2.43.9x10 -4 0.7

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Effects of the Explosion Energy Explosion energy in a simulation is arbitrary unless constrained by an observed supernova Mechanism dependent: changes neutrino energies, explosion energies, & success of explosion. vs. +convection, different equations of state, jet-driven models, etc. Yields for otherwise consistent models: energy (foe) 44 Ti (M ) 56 Ni 23 M binary1.1 1.2x10 -5 2.6x10 -4 2.05.7x10 -5 0.055

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Simulations vs. Constraints SimulationExplosion Energy (foe) Nitrogen Knots Ejecta MassRemnant Mass 44 Ti Yield 56 Ni Yield 40 M 7.6N6.01.757.5x10 -5 0.33 23 M 0.8N7.55.4<10 -5 23 M 2.3N8.34.61.2x10 -5 2.6x10 -4 23 M asymmetric 2.3N7.45.51.8x10 -4 0.019 23 M asymmetric 2.4N111.93.9x10 -4 0.70 23 M binary1.1Y3.62.61.2x10 -5 2.6x10 -5 23 M bin, asymm 1.1Y3.03.21.6x10 -5 0.02 23 M binary2.0Y3.92.35.7x10 -5 0.055 23 M bin, asymm 2.0Y3.62.68.5x10 -5 0.075 16 M 1.3Y3.21.8<10 -5 16 M asymmetric 1.12Y3.21.8<10 -5 16 M 3.1Y3.81.21.2x10 -5 0.15 16 M asymmetric 3.1Y3.81.21.2x10 -5 0.15 White satisfies constraints, red inconsistent with constraints, yellow marginal

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Observational Constraints High velocity N-rich, H-poor knots Ejecta mass Compact remnant mass 44 Ti and 56 Ni M Ti ~ 1.0 x 10 -4 M from x-rays M Ni ~ 0.05-0.2 M from brightness of supernova Trends identifiable: Ti decreases, Ni increases with explosion energy BUT yields are very model dependent - multi-D effects; cutoff time for calculation of burning & freezeout; network size; neutron excess, entropy, temperature, & density evolution can change yields by orders of magnitude

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Effect on Explosion: 3D Explosion Calculations Initial results from a study of the progenitor of Cassiopeia A Young (325yr), nearby (3.4 kpc) Estimates range from 16 to 60 M single stars and binary scenarios Several independent observational constraints 3D neutrino-driven explosion calculations + a range of advanced progenitor models What parameter space for the progenitor is allowed by each constraint?

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Structural Perturbations Intershell interaction Large wave flux from O shell imposes large displacements on C shell C shell is rippled on large spatial scales KE flux of waves may overcome stability of intershell region?? O and C shells may merge??

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Structural Perturbations Angular variation of X O, nuc Entrained material drawn as streamers into burning region Composition variations of ~10% in 3D nuc varies by factor of a few in local flashes when fresh fuel ingested Rapid burning of ingested material may produce “explosive” rather than “hydrostatic” abundance patterns

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Structural Perturbations Significant wave flux outside convective region T, ~0.1-1% for 3D models Perturbations reflect Lagrangian displacement of material by wave motion Perturbations can be correlated instead of random Low order modes can impose global asymmetries

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Extent of Convection Comparison with TYCHO models with and without hydro mixing Predicted outer edge of mixed region in hydro mixing model more similar Velocity structure more characteristic of waves than plumes in additional extent of mixed region

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White Dwarf Initial-Final Mass Relation Procyon & Sirius Mass & radius of binary members known to <1%, L < 4% Cooling ages (Fontaine et al. models) Sirius B mass of 5.04 ±0.29 M from TYCHO, WD 1.00 M Procyon B mass of 1.91 ±0.23 M from TYCHO, 0.60 M Consistent with Padova group estimate with well calibrated parameterized overshoot Most precise determination yet of initial-final mass relation for massive white dwarfs (Liebert et al. 2005) Sirius Procyon

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Contextual Stellar Evolution Make stellar evolution predictive for all stages, masses, and compositions In order to understand... Nucleosynthetic, KE, luminosity yields Populations (galaxy evolution) Starbursts (first galaxies, interactions) Cluster & debris disk ages Through a strategy of... Using hydro simulations, laboratory astrophysics Avoiding calibration of parameters Stringent tests against observations My god, it's full of stars!

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The Nucleosynthetic Yields of Stellar Populations ● Sources – Supernovae II,Ib/c,Ia; LBVs; Wolf-Rayets; AGB stars; planetary nebulae; novae ● The challenge: accurately connecting microphysics of nucleosynthesis to macrophysics of stellar populations ● Underestimating progenitor mass for a given yield by 10% overestimates the number of stars contributing that yield by ~25% for Salpeter IMF ● Similar problems for kinetic energy yields and photon fluxes

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