Dense Stellar Matter Strange Quark Matter driven by Kaon Condensation Hyun Kyu Lee Hanyang University Kyungmin Kim HKL and Mannque Rho arXiv: (2011)arXiv:

I. Introduction Compact Stars - neutron stars, quark stars, ….., (black hole) mass ~ solar mass size ~ 10km neutral object in weak equilibrium - higher density / (10km) 3 ~ 1/ fm 3 > n 0

A. Constituents of compact star Hadrons responsible for mass of star neutrons, protons, hyperons pions, kaons, ……. Quarks(deconfined phase) Leptons electrons, muons, neutrinos(e-, mu-) Exotics ?

B. Stars and Gravity Gravity Pressure TOV(Tolmann-Oppenheimer-Volkov) Equation

Equation of state for hadronic mater: Fermi pressure of hadrons + Strong interaction Strong interaction appears in different forms in nuclei, neutron star and quark star Much more complicated than cosmological EoS C. EoS of compact stars: pressure and energy

Heavier nuclei Nuclear matter Symmetry energy: measure of n-p asymmetry in nuclear matter

Up to nuclear density, n 0 = 0.16 fm -3 Compact star, n > n 0 with central density n center > 3 n 0 Simple extrapolation of what are known at low density nuclear matter(?) Nucleon Interaction : S(n) and V(n)

D. Mass of neutron stars

A two-solar mass neutron star measured using Shapiro delay, Nature 467, (2010) Neutron stars are composed of the densest form of matter known to exist in our Univ erse, the composition and properties of which are still theoretically uncertain. Measur ements of the masses or radii of these objects can strongly constrain the neutron star matter equation of state and rule out theoretical models of their composition 1, 2. The o bserved range of neutron star masses, however, has hitherto been too narrow to rule out many predictions of ‘exotic’ non-nucleonic components 3, 4, 5, 6. The Shapiro delay i s a general-relativistic increase in light travel time through the curved space-time nea r a massive body 7. For highly inclined (nearly edge-on) binary millisecond radio pulsa r systems, this effect allows us to infer the masses of both the neutron star and its bin ary companion to high precision 8, 9. Here we present radio timing observations of the binary millisecond pulsar J , 11 that show a strong Shapiro delay signature. We calculate the pulsar mass to be (1.97 ± 0.04)M ⊙, which rules out almost all curre ntly proposed 2, 3, 4, 5 hyperon or boson condensate equations of state (M ⊙, solar mas s). Quark matter can support a star this massive only if the quarks are strongly intera cting and are therefore not ‘free’ quarks PSR J (1.97 ± 0.04)M ⊙

Higher nucleon number density inside n =0  n_0  6n_0  1. nucleon-nucleon interaction with density 2. Emerging of new hadrons with density kaons, hyperons(strange hadrons), quarks,.. Dense Hadronic Matter at the Core Change of EOS with density Lattice QCD, Effective theory for hadrons, Many body inetractions, … E. EoS at high density : open problem

QCD phase diagram

What is the role of symmetry energy(n-p asymmetry ) in compact star? Symmetry energy provides a channel for new degrees of freedom in n-p system via weak interaction: electron, muon, strange particles(kaon, hyperon),.. II. Symmetry energy in compact star Composition of compact star

Npe(mu)-weak equilibrium: : When neutrino escaped and equilibrium is frozen with zero neutrino chemical potential : (1) Hadron interaction: (2) Charge neutrality condition: (3) Eq(1,2,3) solved for neutron, proton and electron(muon) densities equation of state

Balance between symmetry energy and weak interaction Proton abundance

Compact stars with Npe(mu) (example)

Change of effective theory with density (1) n_0< n < n_t (2) n_t < n < n_c (3) n_c < n Degree of freedom(new): strange particle (1) nucleon (2) nucleon and kaon (3) quark (u,d,s) Continuous change (1)  (2)  (3) III. Strategy(simple-minded)

When the difference between chemical potentials of proton and neutron becomes comparable to kaon mass in medium or nucleon-hyperon mass difference in medium, the corresponding strange particles begin populating and the EOS get changed significantly. Kaon condensation Kaplan and Nelson, Bethe and Brown, Brown, Rho and Kubodera, … A. Nuclear matter with kaon condensation NPKe(mu) system

Equation of state Hadron interaction nucleon-nucleon interaction kaon-nucleon interaction

S-wave condensed kaon

Effective kaon mass(chemical potential) Kaon energy density Kaon pressure negative pressure for off-shell condensation: soft EOS smaller mass

For a hadron system, where kaon chemical potential becomes smaller than electron mass, there is no leptons to balance the positive charge of protons but kaons. This is equivalent to strange quark matter with high enough density. It defines the transition surface between hadronic phase with kaon condensation and strange quark matter B. Strange quark matter driven by kaon condensation

Quark Matter Hadronic Matter Kaon condensation at zero chemical potential SQM

Quantum Chromodynamics(QCD)

Boundary condition at NM-SQM inter-phase With kaon condensation at critical density Strange Quark Matter(SQM)

SQM ( massless limit) perturbative correction bag constant: confinement

IV. Triple-layered neutron star SQM KM NM

Numerical results - Nucleon interaction - Kaon -nucleon interaction - SQM

Discussion Higher density, n > n 0 at the core of compact star  new physics Emergence of strangeness at the core  kaon condensation, hyperon, quarks Mass, radius and compositions,.... Cooling, GW, GRB, ….. Triple-layered star with SQM driven by kaon condensation :,, PSR J (1.97 ± 0.04)M ⊙

Vacuum property under extreme condition: high T and density Probed by experiments : High T frontier: RHIC and LHC High density frontier: LHC, FAIR, RIB’s Quest for origin of hadron mass Remarks