Feasibility of Core-Collapse Supernova Experiments at

the National Ignition FacilityTimothy Handy

Hyperbolic system of conservation laws Requires an additional closure relation

Conserved Quantity

Multidimensional Time Dependent

One-dimensional, Steady, Arbitrary Cross-

section Area

Mass

Momentum

Energy

Euler Equations

Assumptions:◦ Ideal Gas◦ Isentropic (Reversible &

Adiabatic)◦ One-dimensional flow◦ Compressible

Examples:◦ Rocket Engines◦ Astrophysical Jets

de Laval Nozzle – A Basic Example

Layers of material◦ Density gradient◦ Generated due to gravity

Steady State vs. Static Equilibrium◦ Steady State – balanced state with change

(dynamic processes)◦ Static Equilibrium – balanced state without

change Atmospheres are generally steady with

dynamics◦ Pressure changes move flow◦ Heating and cooling processes trigger convection

Stratified Mediums (Atmospheres)

Euler with SourcesGravity Gravity

+ Heating

What’s stopping us from falling?

This pressure term comes from the interaction between atoms (well, fermions…)◦ Two atoms can’t share the same space

What happens if the pressure disappears?◦ Our businessman is in trouble!

What counters gravity?

Core-Collapse SupernovaeIron core grows

Mass is added from silicon burning

Gravity > Degeneracy

PressureElectrons and Protons combine

to form Neutrons and Neutrinos

Sudden loss of pressure at the core

Okay BigBigge

rTOO BIG!

+ -+ = +

Falling fluid parcels doesn’t know new equilibrium◦ Possible overshoot of equilibrium◦ Motion becomes supersonic at some point -> sonic point

inside the flow◦ Compressed, high density plasma changes its properties

(phase transition) and becomes nuclear matter◦ NM is much harder to compress and starts effectively

acting as a solid boundary◦ This boundary acts as a reflector for the incoming flow◦ Reflected flow perturbations propagate upstream and

evolve into a shock String of springs

Bounce

Bounce Animation

The outer stellar envelope is infalling Material passes through the shock Advected downstream subsonically and

settles down near the surface of the reflector (proto-neutron star)

State of Affairs at this Time

Ohnishi et al. (XXX) proposed an experimental design to study the shock

Drive material toward a central reflector using lasers

The material would then strike the reflector and produce a shock

Material would continueto move through the shock

Ohnishi Design

Loss of gravity and heating/cooling◦ Can a laboratory

shock be similar to a real shock?

Ohnishi Design

Characterization of the flow via Euler number [Ryutov et al. (XXX)]

HEDP diagram

Scaling Law (Euler number) and HEDP

The outer stellar envelope is infalling Material passes through the shock Advected downstream subsonically and settles down near the

surface of the reflector (proto-neutron star)

The above are essential nozzle componentsHighlight difference with SN

SettlingCooling by NeutrinosGravity

ConvectionHeating by Neutrinos

The problem can now be reformulated as the composite of two problemsShock Stability ProblemSettling Flow Problem

Here our focus is on the first problem and initially without Heating

State of Affairs at this Time

The outer stellar envelope is infalling Material passes through the shock Advected downstream subsonically and settles down near the surface of

the reflector (proto-neutron star)

The above are essential nozzle components Supernova’s additional processes

◦ Settling Cooling by Neutrinos Gravity

◦ Convection Heating by Neutrinos

The problem can now be reformulated as the composite of two problems◦ Shock Stability Problem◦ Settling Flow Problem

Our focus is on the shock stability problem (initially without heating)

State of Affairs at this Time

Analytic

Critical Mach number (Ppre>0)

Maximum Aspect Ratio

Euler Number vs. Mpre

Initial BC constraints

Semi-Analytic

Latin Hypercube Sampling

Semi-analytic Setup

Semi-analytic Results

Semi-analytic Results

One-D

Setup

Coupling of Shock to Pert

Stable Advective Times

Two-D

Setup

Qualitative Results

Flux Decomposition

Conclusions – Parameter Ranges

Conclusions – SASI Recreation

Future Work