1. X-Ray image of Crab Nebula Pulsar Credit: NASA/CXC/ASU/J. Hester et al.) Liliana Caballero With Pf. Horowitz Molecular Dynamics Simulations of Non-uniform Dense Matter and Neutrino Interactions in Supernovae Indiana University NNPSS June/13/2005

2. Outline Introduction: Supernova and Neutron Stars Introduction: Supernova and Neutron Stars Ion Response Ion Response Neutrino-Nucleus scattering Neutrino-Nucleus scattering Model Model Simulation Results Simulation Results Future Work Future Work

3. Supernova Neutrinos Collapse of a Massive Star Gravitational Force vs. Nuclear Fusion Iron Core -> energy barrier->collapse Iron Core -> energy barrier->collapse Most of the energy is lost by neutrino emission: p+e -> n+ν e Most of the energy is lost by neutrino emission: p+e -> n+ν e Density increment->Strong Force & Fermi Degeneracy->Outward Pressure Density increment->Strong Force & Fermi Degeneracy->Outward Pressure Neutron Star Neutron Star SN1987A

4. Image taken from Dany Pierre Page, Neutron Star (Theory) Group at UNAM Mass= 1.4 Sun Mass Radius=10 km

5.  ~10 12 g/cm 3 Medium= Plasma Electrons and Nuclei Medium= Plasma Electrons and Nuclei Neutrino Trapping in Supernova Neutrino Trapping in Supernova Neutrino-Nucleus elastic scattering Neutrino-Nucleus elastic scattering Ion, Electron Screening have important effect Ion, Electron Screening have important effect Ion Response

6. Linear Response -> Neutrino-Nucleus Elastic Cross Section: Linear Response -> Neutrino-Nucleus Elastic Cross Section: Correlation Function g(r) Correlation Function g(r) Static Structure Factor S(q) Static Structure Factor S(q) Dynamic Structure Factor S(q,w) Dynamic Structure Factor S(q,w)

7. Correlation Function g(r) Probability of finding another ion a distance r from a given ion. r

8. Static Structure Factor Charge Density Ground State

9. Model Classical Approximation Classical Approximation Ions interact via screened Coulomb potential Ions interact via screened Coulomb potential e electron screening r ij distance between Ions

10. Monte Carlo Simulation T= 1 Mev T= 1 Mev N ions N ions 56 Fe 56 Fe ρ =1x10 12 g/cm 3 ρ =1x10 12 g/cm 3 Periodic Boundary Conditions Periodic Boundary Conditions r i at equilibrium, i=1,N r i at equilibrium, i=1,N 1 2 1 2 L

11. Correlation Function N=1000 λe=10 fm L=382 fm

12. Static Structure Factor N=1000 λe=10 fm L=382 fm

13. Dynamic Response Dynamic Structure Factor

14. Molecular Dynamics Algorithm Verlet Algorithm Verlet Algorithm

15. Molecular Dynamic Simulation T= 1 MeV T= 1 MeV N ions N ions 56 Fe 56 Fe ρ =1x10 12 g/cc ρ =1x10 12 g/cc Periodic Boundary Condition Periodic Boundary Condition r i (t), i=1,N r i (t), i=1,N

16. Dynamic Structure Factor N=500 λe=10 fm L=304 fm

17. q (fm-1)  *10 -4 (fm-1) Ω p *10 -4 (fm-1) q 0 =2π/L 3.34.2 q 0 * 2 1/2 4.55.7 q 0 *3 1/2 5.16.9 q 0 *4 1/2 67.8Peaks

18. Future Work Ion-Ion Screening model break down at large density Ion-Ion Screening model break down at large density N=100000 nucleons MDGRAPE N=100000 nucleons MDGRAPE Dynamical Response Pasta Dynamical Response Pasta