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

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neutrino driven convection in stalled supernova cores
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Neutrino-Driven Convection in Stalled Supernova Cores MICRA, - - PowerPoint PPT Presentation

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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

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SLIDE 1

Neutrino-Driven Convection in Stalled Supernova Cores

David Radice1

Collaborators: E.Abdikamalov, S.Couch, R.Haas, C.Ott, E.Schnetter

1 Walter Burke Fellow, TAPIR, California Institute of Technology

MICRA, Stockholm 2015

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SLIDE 2

The Supernova Problem

Cassiopeia-A

Core-Collapse Supernovae:

  • End of massive stars
  • Birthplace of heavy elements,

neutron stars, black holes …

  • Regulate star formation
  • …

Problem: how do they explode?

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SLIDE 3

Shock Revival by Neutrinos

From Janka 2001

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SLIDE 4

The Roles of Turbulence

Regulates accretion Turbulent pressure Transports heat Increase dwelling time Difficult to simulate!

See talk by Takiwaki

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SLIDE 5

Resolution Dependance

20 40 60 80 100 120 140 0.02 0.04 0.06 120 140 160 180 200

t − tbounce [ms] Rshock,avg [km] σ

s27ULRfheat1.05 s27LRfheat1.05 s27MRfheat1.05 s27IRfheat1.05 s27HRfheat1.05 s27ULRfheat1.05 s27LRfheat1.05 s27MRfheat1.05 s27IRfheat1.05 s27HRfheat1.05

ULR 3.78 km LR 1.89 km MR 1.42 km IR 1.24 km HR 1.06 km

Resolutions

Explosion more difficult at higher resolution!

From Abdikamalov et al. 2015

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SLIDE 6

Turbulent Energy Spectrum

1 10 100 1024 1025 1026

`

E(`) [erg cm−3]

t − tbounce = 90 ms

`−1

s27ULRfheat1.05 s27LRfheat1.05 s27MRfheat1.05 s27IRfheat1.05 s27HRfheat1.05

`−1

s27ULRfheat1.05 s27LRfheat1.05 s27MRfheat1.05 s27IRfheat1.05 s27HRfheat1.05

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SLIDE 7

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

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SLIDE 8

Local Simulations

  • Periodic box
  • Anisotropic
  • Mildly compressible
  • Compare different

methods

PPM+HLLC, N=5123, Vorticity

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SLIDE 9

Energy Cascade (I)

10−2 10−1

E(k) k5/3

100 101 102

k

0.0 0.4 0.8 1.2

Π(k)/✏

PPM+HLLC, N = 5123

  • Energy injection scale
  • Inertial range
  • Bottleneck
  • Dissipation range
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SLIDE 10

Energy Cascade (II)

10−2 10−1

E(k) k5/3

N = 643 N = 1283 N = 2563 N = 5123 100 101 102

k

0.0 0.4 0.8 1.2

Π(k)/✏

PPM+HLLC

  • Global simulations ~ 643

bottleneck dominated!

  • 2x: start to converge
  • 8x: inertial range
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SLIDE 11

Semi-Global Simulations

  • Local simulations: instructive, but very simplified
  • Global simulations: expensive, more difficult to interpret

Semi-global simulations

  • Stationary initial conditions
  • 90º 3D wedge domain
  • Simplified neutrino cooling/

heating

  • Simplified nuclear

dissociation treatment

Semi-global simulations: initial data

50 100 150 200

r [km]

−20 −15 −10 −5

5

s s

−0.3 −0.2 −0.1

0.0 0.1 0.2 0.3

Ω [rad/ms] ΩBV

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SLIDE 12

Ref ∆𝛴=1.8º 2x 4x 12x

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SLIDE 13

Global Dynamics (I)

200 400 600 t [ms] 200 300 400 rshock, avg [km] 1D Ref. 2x 4x 6x 12x

Shock radius

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SLIDE 14

Global Dynamics (II)

0.4 0.8 80 100 120 200 400 600 t [ms] 20 40 60 80 100 Ref. 2x 4x 6x 12x

τadv = Mgain ˙ M [ms] τadv τheat τheat = Ebind ˙ Q [ms]

Typical timescales

  • Low resolution

simulations easier to explode

  • Good convergence of

large scale quantities

  • Caveat: convergence

is going to be worse for nearly-critical models

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SLIDE 15

Turbulent Cascade

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

Turbulent energy spectra

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SLIDE 16

Turbulent Convection

4

4 8 4πF0

H [⇥1050 erg/s]

Ref. 2x 4x 6x 12x

0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2

(r rg)/(rs rg) 8 6 4 2

4πF0

K [⇥1050 erg/s]

Turbulent energy fluxes

80 60 40 20

4πhFHi [⇥1050 erg/s] Ref. 2x 4x 6x 12x

0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2

(r rg)/(rs rg) 10 5

4πhFKi [⇥1050 erg/s]

Total energy fluxes

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SLIDE 17

Turbulent Pressure

Turbulent pressure

0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2

(r rg)/(rs rg)

0.0 0.2 0.4 R r

r /hr2pi

Ref. 2x 4x 6x 12x

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SLIDE 18

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

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SLIDE 19
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SLIDE 20

Initial Data

50 100 150 200

r [km]

106 107 108 109 1010 1011

ρ [g/cm3] ρ

−0.20 −0.15 −0.10 −0.05

0.00 0.05

υ/c υr

50 100 150 200

r [km]

−20 −15 −10 −5

5

s s

−0.3 −0.2 −0.1

0.0 0.1 0.2 0.3

Ω [rad/ms] ΩBV

Stationary initial data