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Feasibility of Core-Collapse Supernova Experiments at the National Ignition Facility. Timothy Handy. Euler Equations. H yperbolic system of conservation laws Requires an additional closure relation. de Laval Nozzle – A Basic Example. Assumptions: Ideal Gas
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Feasibility of Core-Collapse Supernova Experiments at the National Ignition Facility Timothy Handy
Euler Equations • Hyperbolic system of conservation laws • Requires an additional closure relation
de Laval Nozzle – A Basic Example • Assumptions: • Ideal Gas • Isentropic (Reversible & Adiabatic) • One-dimensional flow • Compressible • Examples: • Rocket Engines • Astrophysical Jets
Stratified Mediums (Atmospheres) • 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
Euler with Sources Gravity Gravity + Heating
What counters gravity? • 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!
Core-Collapse Supernovae Iron core grows Mass is added from silicon burning TOO BIG! Bigger Big Okay Gravity > Degeneracy Pressure Electrons and Protons combine to form Neutrons and Neutrinos + + = + - Sudden loss of pressure at the core
Bounce • 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
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)
Ohnishi Design • 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 continue to move through the shock
Ohnishi Design • Loss of gravity and heating/cooling • Can a laboratory shock be similar to a real shock?
Scaling Law (Euler number) and HEDP • Characterization of the flow via Euler number [Ryutov et al. (XXX)] • HEDP diagram
State of Affairs at this Time • The outer stellar envelope is infalling • Material passes through the shock • Advected downstream subsonicallyand settles down near the surface of the reflector (proto-neutron star) The above are essential nozzle components Highlight difference with SN 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 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 subsonicallyand 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)
