A Model for GW Emission from CCSN Explosions

byJeremiah W. Murphy

NSF AAP Fellow(University of Washington)

Collaborators:Christian Ott (Caltech), Adam Burrows (Princeton U.)

What is the mechanism of explosion?

Multi-Messenger Astrophysics: Exhibit A

Learn from GW?

IndirectDirect

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?

Mechanism is inherentlymulti-dimensional

Mechanism is inherentlymulti-dimensional

GW Emission

Explosion Dynamics

Theory: to appreciate what we can learn from GWs

Fundamental Question of Core-Collapse Theory

?

Steady-StateAccretion

Explosion

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?

M.

Le

Critical Curve

Steady-state accretion(Solution)

Explosions!(No Solution)

Burrows & Goshy ‘93Steady-state solution (ODE)

Is a critical luminosity relevant in hydrodynamic simulations?

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

Murphy & Burrows ‘08

Murphy & Burrows ‘08

Nordhaus et al. ‘10

Why is critical luminosity of 2D simulations ~70% of 1D?

Turbulence

Solutions for successful explosions• Develop Turbulence model for CCSN• Use 3D simulations to calibrate • Derive critical curve with turbulence• Use turbulence model in 1D rad-hydro simulationsoQuick self consistent explosionsoSystematic investigations of explosions, NS masses, etc.

A Theoretical Framework

Murphy, Ott, and Burrows, ‘09

Initial LIGO

Enhanced LIGO

Advanced LIGO

Source Region for GWs?

Characteristic GW frequencies and amplitudes?

N2 < 0Convectively unstable

N2 > 0

N2 > 0Stably stratified(gravity waves)

b(r) = ∫ N2dr = buoyant accel.

N2 < 0Convectively unstable

N2 > 0

N2 > 0Stably stratified(gravity waves)

Dp Over shoot

The Model: Buoyant Impulse

vp

Dp ~ vp / N

fp ~ N/(2)

h+ fp vp

Similar analysis for 3D convection in stellar interiors(Meakin & Arnett 2007, Arnett & Meakin 2009)

The Model: Buoyant Impulse

Rb =b Dp

vp2

b(r) = ∫ N2dr

Dp ~ vp / N

fp ~ N/(2)

h+ fp vp

Similar analysis for 3D convection in stellar interiors(Meakin & Arnett 2007, Arnett & Meakin 2009)

Rb =b Dp

vp2

b(r) = ∫ N2dr

The Model: Buoyant Impulse

fp ~ N/(2)

Progenitor Mass and Luminosity Dependence

h+ fp vp

N2 = GMr

r3 Γ1

dlnPdlnr dlnr

dlnρ( )1 -

N2 = GMr

r3 Γ1

dlnPdlnr dlnr

dlnρ( )1 -

Dense matter EOS Local Thermodynamics andNeutrino transport

Summary

GW Emission•Explosion Mechanism•Protoneutron Star Structure•Dense Matter EOS•Explosion Dynamics