Physics 599, Fall 2009

Exotic forms of nuclear matter under extreme conditions in supernovae and compact stars

Jirina Stone

UT/ORNL Theorecal Astrophysics Group Oxford University [email protected] PhD: Charles University of Prague, Czech Republic

Teaching: Technical University of Prague, CZ Oxford University, Oxford, UK

Research work: Experimental nuclear physics Instute for Nuclear Research, Rez near Prague Joint Instute for Nuclear Reasearch, Dubna, Russia Oxford, UK Daresbury, UK Studsvik, Sweden ORNL – Oak Ridge, USA CERN, ISOLDE – Geneva, Switzerland

Theorecal nuclear physics and astrophysics: Oxford, UK UT/ORNL

PhD Students (co) supervisor: 16 + 1 new starng in Spring at UT

Research publicaons: over 150 UT‐ ORNL Theorecal Astrophysics hp://astro.phys.utk.edu

Scienfic focus: Explosive stellar events and the associated nuclear astrophysics

Construcon of theorecal models for supernovae, nova, x‐ray and gamma‐ray bursters.

Macro (hydrodynamics) Micro (equaon of state – interacon between nuclei and parcles in stellar maer)

Models of creaon of chemical elements contribung to the galaxy and forming the basis for new stars Visualizaon of Three‐Dimensional and planets Simulaon of Standing Accreon Shock Instability (SASI) Connecon between these events and their nuclear (Blondin, Mezzacappa, de Marino) products is an important link in the chain in history Astrophysics Journal, Nature connecng us to the beginning of the Universe. Senior group members:

Chrisan Cardall Macroscopic modelling of Core‐Collapse Supernovae (CCS) Michael W. Guidry Nucleosynthesis, High T superconductors, Colliding Galaxies Wm. Raphael Hix Nucleosynthesis in CCS models, weak interacon processes Bronson Messer Computaonal physics, CCS, type IA supernovae, novae Anthony Mezzacappa Program leader, macroscopic mechanism of CCS, General Relavity Jirina Rikovska Stone Microscopic aspects of CCS, Equaon of State, Neutron Stars

Junior members (post‐doc):

Eirik Endeve Magnetohydrodynamic, magnec field effects in CCS Eric Lentz Neutrino physics, Equaon of State Suzanne Parete‐Koon Nucleosynthesis

Students PhD:

Reuben D. Budiardja Macroscopic modelling CCS and gamma‐ray bursts M. Ausn Chertkow Nucleosynthesis in CCS Elisha Feger Numerical methods for nucleosynthesis

Undergraduate: Adrian Sanchez Neutrino physics Cole Lillard Visualizaon, Equaon of State Type II supernovae core collapse: forms a neutron star (if the mass is less then 2‐3 solar masses) or a black hole. Gravitaonal collapse of a massive star:

Progenitor: Nuclear fusion against gravity: Thermal runaway: Increase in T changes the condions in a way that causes a further increase in temperature leading to a destrucve result.

Gravitaonal collapse which starts when the H fuel is exhausted is temporarily halted by the ignion of successive burning processes Involving heavier elements and increasing T and pressure. Each of the burning stages takes shorter me and leads to higher T A.Mezzacappa An.Rev.Nucl.Part.Sci 2005 Sequence of events aer the nickel/iron core is reached (no more fusion possible)

When the mass of the iron core exceeds Chandrasekhar limit:

1. Core starts to collapse under gravity – T and density increases

Photo‐disintegraon Neutronizaon

γ + 56Fe → 13α + 4n Q=-124 MeV p+ + e− → n + ν

Kinec energy of electrons Electron fracon Ye Neutrinos escape Pressure Pressure

Collapse 2. Core collapse proceeds on the me scale of milliseconds

inner core (homologous and subsonic) outer core (free‐fall – supersonic)

3. Collapse slow compared to reacon rates

approximate equilibrium and constant entropy S~1 and the Fe core remains ordered during the collapse

4. As T and density keep rising:

neutrino interacon are stronger and free mean path shorter ‐ origin of neutrino trapping

5. Low entropy – lile nuclear excitaons increased density results in nuclei touching each other macro‐single‐nucleus is formed

Pressure increases dramacally by the repulsive NN interacon at short distances 6. As the transion to nuclear maer (with sff equaon of state) progresses nucleon pressure starts to dominate lepton pressure

7. Rebound: dramac change in pressure makes the core incompressible; the in‐falling layers crash into the core and rebound sending a reflected pressure wave outwards

Pressure wave propagates outwards with the speed of sound – creates a shock wave near the sonic point

BUT – THE SHOCK WAVE STALLES!!! More complex structure?

Supernova (Finite Temperature) Neutron Star Competition between surface tension and Coulomb repulsion of closely spaced heavy nuclei results in a series of shape transitions from the inner crust to the core

Nuclear Pasta! (a) spherical (gnocchi) → (b) rod (spaghetti) → (c) slab (lasagna) → (d) tube (penne) → (e) bubble (swiss cheese?) → uniform matter Accounts for up to 20% mass of collapsing stellar core; up to 50% mass and radius of the Neutron Star inner crust Max Plank Institute for Dynamics and Self – Organisation Soft solids: emulsions, foams, colloids, polymers, gels , liquid crystals, cytoplasma

Flexible internal structure, weak interactions, easily influenced by external conditions

Geometry of fluid interfaces Liquid crystal

Granular matter under stress Ideal gas law:

Variables: pressure, density and temperature

pV = NkT N number of molecules, k Boltzmann constant

from kinetic theory average pressure for an ideal gas

1 N p= mv2 3 V average translational kinetic energy

1 3 mv2 = kT 2 2 NkT p = = ε total energy density of the gas V N at temperature T and density n= V Ludwig Boltzmann p = ε(n,T ) EQUATION OF STATE In nuclear matter

ε = n( +mc2 ) E where E is the binding energy per particle

E / A = (n) or F / A = (n,T ) E F Calculate pressure, entropy, incompressibility etc

2 ∂ (n) ∂ (n,T ) P(n) n E F = s(n) = − |n,Y ∂n p ∂T

∂P(n) ∂ (n) ∂2 (n) K(n) = 9 = 18n E + 9n2 E n n n2 ∂ ∂ ∂ To calculate the expectation value of the total energy of the system we need nuclear and particle physics models:   E ,(T V ) =< φ + φ > T kinetic energy, V total potential energy of a system described by the wave function Φ constructed of single particle states φi

Pauli blocking of intermediate states Density dependence of the effective mass Theories

Relativistic Non-relativistic

Potentials Realistic Phenomenological Reid 93 Quark matter: Skyrme Paris MIT Bag, NJL Gogny Bonn A, B, C CDM SMO CD Bonn NL1, NL-SH, NL3,.. Nijmegen TM1 v14 (+ UVII) GM v18 (+UIX) KVR, KVOR

3 Modern potentials: Vlow k, N LO etc

IT IS AN OPEN AND IMPORTANT QUESTION WHICH OF THESE MODELS ARE CLOSEST TO REALITY. MODELLING OF STELLAR MATTER AND PROCESSES HELPS TO ANSWER THIS QUESTION. Computaonal Method Computaonal Method II

• Computer resources used – Jacquard (NERSC), Lawrence‐Berkely (725 proc) – Jaguar (NCCS), Oak Ridge (11,000 proc) – Milipeia, Universidade de Coimbra (125 proc) – Deepthought, University of Maryland (1000 proc) – Minerva, Universidade de Santa Catarina (75 proc) Neutron density distributions at T=2.5 MeV at particle number Densities ( in fm-3 ): Blue – lowest, orange -- highest.

0.04 0.06 0.08

0.09 0.10 0.11 Neutron density distributions at particle number density 0.10 fm-3 at temperatures given in figures in MeV.

0 2.5

5.0 7.5 NEUTRON T=2.5 MeV N = 350 Neutron

2.5 MeV

nb= 0.039 fm-3

-3 -3 -3 nb= 0.04 fm nb=0.06 fm nb=0.08 fm TRUE MODEL OF THE PASTA PHASE OF NUCLEAR MATTER

We predict continues regions of high and low density

IN CONTRAST WITH

isolated nuclei of exotic shapes in free neutron gas

Consequences for e.g. neutrino transport in supernova models Neutron stars:

Thanks to :

Will Newton Amy Bonsor Dany Page David Blasche John Miller Nils Andresson Jim Lamer Bao‐An‐Li

The COMPSTAR collaboraon

…and many more Neutron Stars are Exoc!

• Of order 1 solar mass • 10km radius • Average density 1014‐15g/cm3 • 1010 humans on Earth @ 50,000g each = 5×1014g • Compress them all into a sugar cube and we reach neutron star density! • g ≈ 1012 ms‐2! • Neutron Stars are test bed for exoc physics under extreme condions • The Physics of Neutron Stars ‐ EM – quantum electrodynamics – magnesm

‐ Gravity in the strong field regime

‐ Condensed maer physics (superconducvity superfluidity, frustrated maer)

‐ Strong nuclear force (hadrons)

‐ Weak interacons (leptons)

‐ Quark maer • Problem: How to observe NSs/ ‐ No energy generaon aer formaon ‐ Small surface > rapid inial cooling and low opcal luminosity

• Crab nebula: remnant of 1054 SN ‐ Radiang in opcal, radio, X‐ray ‐ energy input to nebula ≈ 1038erg/s ‐ The center of the Crab Nebula shows ragged shreds of gas that are expanding away from the explosion site at over three million miles per hour The Crab is arguably the single most interesng The radiaon emission is object, as well as one of the most studied, in all observed in pulses of astronomy. The image is the largest image ever taken with Hubble's WFPC2 workhorse camera. CHANDRA X‐RAY OBSERVATORY

At the center of the Crab Nebula is a city‐ sized, magnezed neutron star that spins 30 mes a second, where ring‐like structures emit x‐rays as high‐energy parcles slam into the nebular material

Being relavely young, the Crab Pulsar was the first known example of a neutron star which was located at the site of an opcally visible object.

The inner part of the ring surrounding the Crab Pulsar spans a light‐year, hiding the neutron star Examples of manifestation of strong interaction – microscopic effects:

The ‘pasta’ phase

Beta-equilibrium nuclear matter

Exotic particles at high density

Quark matter and beyond Testing of models of EOS using neutron stars: Mass-radius relationship, moment of inertia, period of rotation, red-shift, cooling, magnetic fields etc LATTIMER AND PRAKASH, PHYSICS REPORTS, 442, 109 (2007) Non-relativistic Mean Field Theory Various Parameterizations of Skyrme interactions (140 tested)

EoS Mmax R[km] x EoS Mmax R[km] x [ns] [ns] SMO1 1.92 10.0 7.8 SkX 1.39 7.92 13.4 SMO2 1.86 10.2 7.3 SkO 1.97 10.4 10.4 SLy230a 2.08 10.2 7.2 APR 2.2 10.0 7.1

Stone et al., PRC 65, 064312 (2002) and 68, 034324 (2003) Quark-meson coupling model [Stone et al. – Nucl.Phys. A792, 341 (2007)] Heavy Ion Collisions Testing of the density dependence of S

Bao-An Li et al., PRL 78, 1644 (1997):88, 192701, (2002) Danielewicz et al, Science 298, 1592 (2002)

The only terrestrial situation where HD neutron rich matter can be

formed – up to several times nuclear saturation density no (MSU, Darmstadt, RHIC) Observables: π- to π+ ratio neutron-proton collective flow

transverse and elliptical flow of particles from high density regions during collisions Partially constrained EOS for astrophysical studies

Plamen Krastev, Bao-An Li and Aaron Worley, Phys. Lett. B668, 1 (2008).

Danielewicz, Lacey and Lynch, Science 298, 1592 (2002)) Connection with finite nuclei represents a specific nuclear physics interest:

Recent trend and hope is to find new physics at the boundaries of nuclear stability with the ratio of protons and neutrons much different from unity (e.g. N/Z ~ 2-3)

Neutron stars contain highly asymmetric matter N>>Z

A UNIQUE EXTRAPOLATION POINT FOR POTENTIALS FITTED ALONG THE STABILITY LINE ( N ~ Z) The big picture: Conclusions

• High density maer in supernovae and neutron stars theory draws on every area of fundamental physics, oen in their extreme • Observaons of the supernovae phenomenon and neutron stars provide a way to test our physical theories in exoc circumstances not replicable in the laboratory • As we develop more numerous and sophi‐ scated models, we will need more accurate and innovave observaons to test them….