Dense Stellar Matter Strange Quark Matter driven by Kaon Condensation

Hyun Kyu LeeHanyang University

Kyungmin Kim HKL and Mannque Rho arXiv:1102.5167 (2011)

I. IntroductionCompact Stars - neutron stars, quark stars, ….., (black

hole) mass ~ solar mass size ~ 10km neutral object in weak equilibrium - higher density 1057 / (10km)3 ~ 1/ fm3 > n0

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 GravityGravity Pressure

TOV(Tolmann-Oppenheimer-Volkov) Equation

Equation of state for hadronic mater: Fermi pressure of hadrons + Strong in-

teraction

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 , n0 = 0.16 fm-3

• Compact star, n > n0 with central den-sity ncenter > 3 n0

• 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, 1081-1083(2010)

• Neutron stars are composed of the densest form of matter known to exist in our Universe, the composition and properties of which are still theoreti-cally uncertain. Measurements 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 composition1, 2. The observed range of neutron star masses, however, has hitherto been too narrow to rule out many pre-dictions of ‘exotic’ non-nucleonic components3, 4, 5, 6. The Shapiro delay is a general-relativistic increase in light travel time through the curved space-time near a massive body7. For highly inclined (nearly edge-on) binary mil-lisecond radio pulsar systems, this effect allows us to infer the masses of both the neutron star and its binary companion to high precision8, 9. Here we present radio timing observations of the binary millisecond pulsar J1614-223010, 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 currently proposed2, 3, 4, 5 hyperon or boson condensate equations of state (M⊙, solar mass). Quark matter can support a star this massive only if the quarks are strongly interacting and are therefore not ‘free’ quarks12.

PSR J1614-2230(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 parti-cle

(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 po-tentials of proton and neutron becomes comparable to kaon mass in medium or nucleon-hyperon mass difference in medium, the corresponding strange parti-cles 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 condensationNPKe(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 chemi-cal 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 mat-ter 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 MatterHadronic Matter

Kaon condensationat 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

KMNM

• Numerical results

- Nucleon interaction

- Kaon -nucleon interaction

- SQM

Discussion• Higher density, n > n0 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 J1614-2230(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