Neutrino-Driven Convection in Stalled Supernova Cores MICRA, - PowerPoint PPT Presentation

Neutrino-Driven Convection in Stalled Supernova Cores MICRA, Stockholm 2015 David Radice 1 1 Walter Burke Fellow, TAPIR, California Institute of Technology Collaborators: E.Abdikamalov, S.Couch, R.Haas, C.Ott, E.Schnetter

The Supernova Problem Core-Collapse Supernovae: • End of massive stars • Birthplace of heavy elements, neutron stars, black holes … • Regulate star formation • … Cassiopeia-A Problem: how do they explode?

Shock Revival by Neutrinos From Janka 2001

The Roles of Turbulence Regulates accretion Turbulent pressure Transports heat Increase dwelling time Difficult to simulate! See talk by Takiwaki

Resolution Dependance 200 s 27ULR f heat 1.05 s 27ULR f heat 1.05 s 27LR f heat 1.05 s 27LR f heat 1.05 R shock,avg [km] 180 s 27MR f heat 1.05 s 27MR f heat 1.05 s 27IR f heat 1.05 s 27IR f heat 1.05 160 s 27HR f heat 1.05 s 27HR f heat 1.05 ULR 3.78 km 140 LR 1.89 km 120 MR 1.42 km 0.06 IR 1.24 km 0.04 σ HR 1.06 km 0.02 0 20 40 60 80 100 120 140 Resolutions t − t bounce [ms] From Abdikamalov et al. 2015 Explosion more difficult at higher resolution!

Turbulent Energy Spectrum 10 26 E ( ` ) [erg cm − 3 ] 10 25 ` − 1 ` − 1 s 27ULR f heat 1.05 s 27ULR f heat 1.05 s 27LR f heat 1.05 s 27LR f heat 1.05 s 27MR f heat 1.05 s 27MR f heat 1.05 10 24 s 27IR f heat 1.05 s 27IR f heat 1.05 t − t bounce = 90 ms s 27HR f heat 1.05 s 27HR f heat 1.05 1 10 100 `

Open Questions • When is the resolution good enough? • How does neutrino-driven convection work? • What is the main role of turbulence? Our approach: local and semi-global simulations

Local Simulations • Periodic box • Anisotropic • Mildly compressible • Compare different methods PPM+HLLC, N=512 3 , Vorticity

Energy Cascade (I) 10 − 1 • Energy injection scale E ( k ) k 5 / 3 10 − 2 • Inertial range 1 . 2 • Bottleneck 0 . 8 Π ( k ) / ✏ • Dissipation range 0 . 4 0 . 0 10 0 10 1 10 2 k PPM+HLLC, N = 512 3

Energy Cascade (II) 10 − 1 E ( k ) k 5 / 3 • Global simulations ~ 64 3 N = 64 3 10 − 2 bottleneck dominated! N = 128 3 N = 256 3 N = 512 3 1 . 2 • 2x: start to converge 0 . 8 Π ( k ) / ✏ • 8x: inertial range 0 . 4 0 . 0 10 0 10 1 10 2 k PPM+HLLC

Semi-Global Simulations Local simulations: instructive, but very simplified • Global simulations: expensive, more difficult to interpret • 5 0.3 Semi-global simulations s 0.2 0 Stationary initial conditions • 0.1 Ω [ rad/ms ] 90º 3D wedge domain • − 5 0.0 s Simplified neutrino cooling/ • − 10 − 0.1 heating − 15 − 0.2 Ω BV Simplified nuclear • − 20 − 0.3 dissociation treatment 50 100 150 200 r [ km ] Semi-global simulations: initial data

2x Ref 4x ∆ 𝛴 =1.8º 12x

Global Dynamics (I) 400 Ref. 4x 12x 2x 6x r shock, avg [ km ] 300 200 1D 0 200 400 600 t [ ms ] Shock radius

Global Dynamics (II) 0.8 τ adv τ heat Low resolution • 0.4 simulations easier to explode 120 τ adv = M gain Good convergence of 100 • [ms] ˙ M large scale quantities 80 100 Caveat: convergence • 80 is going to be worse τ heat = E bind 60 [ms] for nearly-critical ˙ Q 40 models Ref. 4x 12x 20 2x 6x 0 0 200 400 600 t [ ms ] Typical timescales

Turbulent Cascade 10 − 9 Ref. 4x 12x 2x 6x 20x E ( k ) ( 1 cm × k ) 5/3 10 − 10 10 − 11 10 − 12 10 − 7 10 − 6 10 − 5 k [ 1/cm ] Turbulent energy spectra

Turbulent Convection 0 4 π h F H i [ ⇥ 10 50 erg/ s ] 8 Ref. 6x H [ ⇥ 10 50 erg/ s ] 2x 12x � 20 4 4x � 40 Ref. 6x 0 � 60 2x 12x 4 π F 0 4x � 80 � 4 0 4 π h F K i [ ⇥ 10 50 erg/ s ] K [ ⇥ 10 50 erg/ s ] 0 � 2 � 4 � 5 4 π F 0 � 6 � 10 � 8 � 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 � 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 ( r � r g ) / ( r s � r g ) ( r � r g ) / ( r s � r g ) Total energy fluxes Turbulent energy fluxes

Turbulent Pressure 0.4 r / h r 2 p i 0.2 R r 0.0 Ref. 4x 12x 2x 6x � 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 ( r � r g ) / ( r s � r g ) Turbulent pressure

Conclusions • Convergence: large scales converge even at moderate resolution ( ∆ 𝜘 ≲ 2º) • Turbulence is only resolved at very high resolutions ( ∆ 𝜘 ≲ 0.1º) • Kolmogorov spectrum • Turbulence pressure dominates over energy transfer

Initial Data 10 11 0.05 5 0.3 s υ r 0.2 10 10 0.00 0 0.1 Ω [ rad/ms ] ρ [ g/cm 3 ] 10 9 − 0.05 − 5 υ / c ρ 0.0 s 10 8 − 0.10 − 10 − 0.1 10 7 − 0.15 − 15 − 0.2 Ω BV 10 6 − 0.20 − 20 − 0.3 50 100 150 200 50 100 150 200 r [ km ] r [ km ] Stationary initial data