x-ray image of crab nebula pulsar credit: nasa/cxc/asu/j. hester et al.) liliana caballero with pf....
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X-Ray image of Crab Nebula Pulsar Credit: NASA/CXC/ASU/J. Hester et al.)
Liliana CaballeroWith Pf. Horowitz
Molecular Dynamics Molecular Dynamics Simulations of Non-uniform Simulations of Non-uniform Dense Matter and Neutrino Dense Matter and Neutrino Interactions in SupernovaeInteractions in Supernovae
Indiana University
NNPSS June/13/2005
OutlineOutline
Introduction: Supernova and Neutron Introduction: Supernova and Neutron StarsStars
Ion ResponseIon ResponseNeutrino-Nucleus scattering Neutrino-Nucleus scattering ModelModelSimulation ResultsSimulation Results
Future WorkFuture Work
Supernova NeutrinosSupernova Neutrinos
Collapse of a Massive StarCollapse of a Massive Star
Gravitational Force vs. Nuclear FusionGravitational Force vs. Nuclear Fusion Iron Core -> energy barrier->collapseIron Core -> energy barrier->collapseMost of the energy is lost by neutrino emission: p+e -> n+Most of the energy is lost by neutrino emission: p+e -> n+ννeeDensity increment->Strong Force & Fermi Degeneracy->Outward Density increment->Strong Force & Fermi Degeneracy->Outward
PressurePressureNeutron StarNeutron Star
SN1987A
Image taken from Dany Pierre Page, Neutron Star (Theory) Group at UNAM
Mass= 1.4 Sun MassRadius=10 km
~10~101212 g/cm g/cm33
Medium= Plasma Electrons and NucleiMedium= Plasma Electrons and NucleiNeutrino Trapping in SupernovaNeutrino Trapping in Supernova
Neutrino-Nucleus elastic scatteringNeutrino-Nucleus elastic scattering Ion, Electron Screening have important effectIon, Electron Screening have important effect
Ion ResponseIon Response
Ion ResponseIon Response
Linear Response -> Neutrino-Nucleus Elastic Linear Response -> Neutrino-Nucleus Elastic Cross Section: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)
FreedEd
dqS
dEd
d
),(
Correlation Function g(r)Correlation Function g(r)
Probability of finding another ion a distance r Probability of finding another ion a distance r from a given ion.from a given ion.
r
Static Structure FactorStatic Structure Factor
)exp(1)(1)( 3 rqirgrdqS
2
0000 )(ˆ)(ˆ)(ˆ1
)( qqqN
qS
N
iirqiq
1
)exp()(Charge Density
Ground State 0
ModelModel
Classical Approximation Classical Approximation Ions interact via screened Coulomb potentialIons interact via screened Coulomb potential
e
ij
ijij
r
r
eZrV
exp4
)(22
e electron screening
rij distance between Ions
c
e
ekFe
4
,2
ijB r
Monte Carlo SimulationMonte Carlo SimulationT= 1 MevT= 1 MevN ionsN ions 5656FeFe
ρρ =1x10 =1x1012 12 g/cmg/cm33
Periodic Boundary ConditionsPeriodic Boundary Conditions
rrii at equilibrium, i=1,N at equilibrium, i=1,N
jijiij xxLxxMinx ,
1
2
1
2
L
Correlation FunctionCorrelation FunctionN=1000 λe=10 fm L=382 fm
r (fm)
0 100 200 300 400
g (r
)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Static Structure FactorStatic Structure FactorN=1000 λe=10 fm L=382 fm
q (fm-1)
0.0 0.2 0.4 0.6 0.8 1.0
S(q
)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Dynamic ResponseDynamic Response
Dynamic Structure FactorDynamic Structure Factor
)0,(),()0,(),(1
),( qtqqtqN
tqS
dttqStiqS
),()exp(2
1),(
1
0
1111
),(),(1
)0,(),(t
dttqttqt
qtq
N
ii trqitq
1
))(exp(),(
Molecular Dynamics AlgorithmMolecular Dynamics Algorithm
Verlet AlgorithmVerlet Algorithm
tttattvttv
ttrVm
tta
ttatvttv
ttattvtrttr
)(2
1)2/()(
)(1
)(
)(2
1)()2/(
)(2
1)()()( 2
Molecular Dynamic SimulationMolecular Dynamic Simulation
T= 1 MeVT= 1 MeVN ionsN ions 5656FeFe
ρρ =1x10 =1x1012 12 g/ccg/ccPeriodic Boundary ConditionPeriodic Boundary Condition
rrii(t), i=1,N(t), i=1,N
Dynamic Structure FactorDynamic Structure FactorN=500 λe=10 fm L=304 fm
(fm-1)
0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012
S(q
, )
0
200
400
600
800
1000
q=2/L
q=221/2/L
q=231/2/L
q=241/2/L
q (fm-1)q (fm-1) *10*10-4 -4 (fm-1)(fm-1) ΩΩpp*10*10-4-4(fm-1)(fm-1)
qq00=2=2ππ/L/L 3.33.3 4.24.2
qq00* 2* 21/21/2 4.54.5 5.75.7
qq00 *3 *31/21/2 5.15.1 6.96.9
qq00 *4 *41/21/2 66 7.87.8
22
222 4
e
ip q
q
MZc
PeaksPeaks
Future WorkFuture Work
Ion-Ion Screening model break down at Ion-Ion Screening model break down at large densitylarge density
N=100000 nucleons MDGRAPE N=100000 nucleons MDGRAPE Dynamical Response PastaDynamical Response Pasta
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