Neutrino-Driven Convection and Neutrino-Driven Explosions

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1 Neutrino-Driven Convection and Neutrino-Driven Explosions by Jeremiah W. Murphy (Princeton U.) Collaborators: Adam Burrows (Princeton U.), Josh Dolence (Princeton U.) & Casey Meakin (U. Arizona)

2 1D simulations (Rad-hydro) Wilson 85 Bethe & Wilson 85 Liebendoerfer et al. 01 Rampp & Janka 02 Buras et al. 03 Thompson et al. 03 Liebendoer et al. 05 Kitaura et al. 06 Burrows et al. 07 Neutrino mechanism suggested No Explosions (Except lowest masses) Spherical symmetry! No GW emission?

3 Fundamental Question of Core-Collapse Theory Steady-State Accretion Explosion?

4 Relax 1D assumption?

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8 Neutrino Mechanism: Neutrino-heated convection Standing Accretion Shock Instability (SASI) Explosions? Maybe Acoustic Mechanism: Explosions but caveats. Magnetic Jets: Only for very rapid rotations Collapsar?

9 Fundamental Question of Core-Collapse Theory Steady-State Accretion Explosion?

10 Why is it easier to explode in 2D compared to 1D?

11 Two Paths to the Solution Detailed 3D radiation-hydrodynamic simulations ( Accurate energies, NS masses, nucleo., etc.) Parameterizations that capture essential physics (Tease out fundamental mechanisms)

12 Burrows & Goshy 93 Steady-state solution (ODE) Explosions! (No Solution) L νe Critical Curve Steady-state accretion (Solution) Ṁ

13 Explosion is a global, boundaryvalue problem 13

14 Explosion is a global, boundaryvalue problem In other words: What neutrino forcing is required to change the global structure between the NS and shock such that explosions occur? 14

15 Explosion is a global, boundaryvalue problem This also means that one can t easily and cleanly pick out one simple diagnostic Hence... Mazurek s Law 15

16 Is a critical luminosity relevant in hydrodynamic simulations? 1D 2D Convection and SASI?

17 How do the critical luminosities differ between 1D and 2D?

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20 Nordhaus et al

21 SASI activity as key to successfu 3.0 Lνe [1052 erg/s] D D D D D D Ṁ[M /s] Hanke et al

22 CCSNE NEUTRINO MECH L e (10 52 erg s 1 ) LS220 LS180 STOS 1D 2D Ṁ (M s 1 ) Couch

23 Why is critical luminosity of multi-d simulations ~70% of 1D?

24 Comparison of Timescales (Thompson et al. 00, Janka 01, Thompson et al. 03, Murphy et al. 08, Pejcha 11, Fernandez 12) τ adv = Δr gain vr Q. τ q = E Q. M gain τ adv > 1 τ ~ q

25 ΔS Q T 1D one time mulit-d distribution of times More heating?.

26 2D & 3D critical luminosity lower than 1D Turbulence plays an important role!

27 A Theoretical Framework for Successful Explosions L ν + Turbulence Model Murphy & Meakin 2011 Ṁ

28 A Theoretical Framework for Successful Explosions L ν + Turbulence Model Ṁ Calibrate with 3D Simulations Murphy et al. 2012, in prep

29 A Theoretical Framework for Successful Explosions L ν + Turbulence Model Ṁ

30 A Theoretical Framework for Successful Explosions L ν + Turbulence Model Ṁ 1D Rad-hydro simulations Realistic and quantitative explosions Systematic exploration

31 N 2 < 0, s < 0 Convectively unstable N 2 > 0 N 2 > 0 Stably stratified (gravity waves)

32 N 2 < 0 Convectively unstable N 2 > 0 D p Over shoot N 2 > 0 Stably stratified (gravity waves) b(r) = N 2 dr = buoyant accel.

33 N 2 < 0 Convectively unstable F = F rad + F conv F conv = C p ρ(v T ) N 2 > 0 D p Over shoot N 2 > 0 Stably stratified (gravity waves) b(r) = N 2 dr = buoyant accel. F = F rad

34 F = F rad + F conv F conv = C p ρ(v T )

35 Need a More General Turbulence Model (Reynolds Decomposition)

36 Back to the Beginning 36

37 Reynolds Decomposition Hydro Equations Mean-Field Equations New steady-state solutions & Critical Curve 37

38 Reynolds-Averaged Equations Murphy & Meakin

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42 Reynolds-Averaged Equations Murphy & Meakin

43 Turbulent Moment Equations Equations for 2nd order moments and more... 43

44 Turbulent Moment Equations Equations for 2nd order moments Depends upon higher order moments 44

45 Turbulent Moment Equations Equations for 2nd order moments A Closure Problem! 45

46 Closure Strategies Local Algebraic Local Single-Point Global 46

47 Closure Strategies Local Algebraic Local Single-Point Global 47

48 Closure Strategies Local Algebraic Local Single-Point Global MLT is a classic example 48

49 Closure Strategies Local Algebraic Local Single-Point Global Local models for these 49

50 Closure Strategies Local Algebraic Local Single-Point Global 50

51 Global Closure Examples Earth s Atmospheric Convective Layer Tennekes

52 Global Closure Examples Stellar Convection Meakin & Arnett

53 Global Closure For CCSNe Use And simulations to inform assumptions about profiles 53

54 Comparison of Timescales Q. M gain Heuristic & Emperical See... Thompson et al. 00 Janka 01 Thompson et al. 03 Murphy et al. 08 Buras 06 Pejcha 11 Fernandez 12

55 Comparison of Timescales Q. M gain

56 Comparison of Timescales

57 Comparison of Timescales

58 Comparison of Timescales

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60 What about the SASI? 60

61 What dominates the post shock flow? Convection, SASI... both? 61

62 Compare nonlinear theories for convection and SASI with post shock flow SASI nonlinear theory? 62

63 Compare nonlinear theories for convection and SASI with post shock flow Convection nonlinear theory 100+ years In CCSN...Murphy & Meakin

64 Compare nonlinear theories for convection and SASI with post shock flow Convection nonlinear theory 100+ years In CCSN...Murphy & Meakin 2012 We can test this theory with 3D simulations 64

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72 Nonlinear Convection is Consistent with Post Shock Flow 1. Consistent buoyancy flux profile 2. Consistent Reynolds stresses 3. Buoyant driving balances dissipation 4. Analytic scaling between buoyant flux and neutrino driving 5. Expansion of shock due to turbulent ram pressure

73 Nonlinear Convection is Consistent with Post Shock Flow But what about the SASI?

74 A theory for neutrino-driven explosions A turbulence model for CCSNe Post shock flow is consistent with nonlinear convection theory