Prelimiary results for the structure of neutron stars QCD phase transition and structure of compact stars G X Peng Graduate University of Chinese Academy of Sciences Institite of High Energy Physics, CAS The National Natural Science Foundation of China Introduction EOS of quark matter EOS of nuclear matter Prelimiary results for the structure of neutron stars gxpeng@gucas.ac.cn, 86-10-88233565

Introduction nm qm Vqm/Vtot 道可道，非常道，名可名，非常名。无名，天地之始；有名，万物之母。故常无，欲以观其妙；常有，欲以观其徼。此两者，同出而异名，同谓之玄；玄之又玄，众妙之门。

Gibbs Conditions 吉布斯条件 道可道，非常道，名可名，非常名。无名，天地之始；有名，万物之母。故常无，欲以观其妙；常有，欲以观其徼。此两者，同出而异名，同谓之玄；玄之又玄，众妙之门。

Conservation laws 守恒律 1. Baryon number 2. Electric charge 道可道，非常道，名可名，非常名。无名，天地之始；有名，万物之母。故常无，欲以观其妙；常有，欲以观其徼。此两者，同出而异名，同谓之玄；玄之又玄，众妙之门。

EOS of quark matter Nonperturbative effects Bag model: the simplest? NJL model: no confinement? Confinement-by-quark-mass model [G.X.Peng,A.Li, U.Lombardo, PRC77(2008)065807] Self-consistent running coupling model (SCRC)

RG dependence of QCD running coupling & quark masses

Matching-invariant beta and gamma functions

RG dependence of QCD running coupling G.X.Peng, PLB 634:413

Fastest convergent expression for the running coupling G.X.Peng, PLB 634:413

QCD scale Lambda

QCD mass scales

Comparison of the coupling & quark masses

Fastest convergent expression for the running coupling G.X.Peng, PLB 634 (2006) 413

Thermodynamically consistent quark model

Thermodynamically consistent quark model

One-flavor case

Energy per quark as a function of density G.X.Peng, EPL 72 (2005) 69

Density dependence of bag constant EPL 72 (2005) 69

Velocity of sound in quark matter EPL 72 (2005) 69

Mass-radius relation of quark stars G.X.Peng, EPL 72:69

EOS of nuclear matter 核物质态方程 Hagedorn factor Bruekner-Hatree-Fock Relativistic Mean Field ……

Hagedorn Factor

Brueckner-Hatree-Fock with three-body forces W.Zuo et.al. EPJA14(‘02)469, L.G.Cao et.al. PRC (06)

Phase structure

Summary Present model indicates that mixed phases of nuclear and quark matter appears, in the neutron star conditions, at a density a little bit above the nuclear saturation, and transit to pure quark phase at about six times the saturation. Therefore, a quark phase seems favorite in neutron stars. It hinders the appearance of kaon condensation.

Two-types of compact stars

The end 谢谢 道可道，非常道，名可名，非常名。无名，天地之始；有名，万物之母。故常无，欲以观其妙；常有，欲以观其徼。此两者，同出而异名，同谓之玄；玄之又玄，众妙之门。

Beijing electron-positron colider 中国科学院高能物理研究所 Beijing electron-positron colider P.O.Box 918-4, Beijing 100039, gxpeng@ihep.ac.cn, 010-88233565

中国科学院高能物理研究所 羊八井国际宇宙线观察站

THE END