The equation of state (EOS) for cold dense matter inside neutron stars is investigated by using holographic QCD models that consist of the Einstein-Maxwell-dilaton system and the improved Karch-Katz-Son-Stephanov action for the flavor part. This method of describing holographic nuclear matter in the $\mathrm{Einstein}\text{\ensuremath{-}}\mathrm{Maxwell}\text{\ensuremath{-}}\mathrm{dilaton}+\mathrm{Karch}\text{\ensuremath{-}}\mathrm{Katz}\text{\ensuremath{-}}\mathrm{Son}\text{\ensuremath{-}}\mathrm{Stephanov}$ framework is different from that by using the Dirac-Born-Infeld action and the Chern-Simons terms. Combining with the Hebeler-Lattimer-Pethick-Schwenk intermediate EOS, the hybrid EOS inside the neutron stars is constructed. The obtained hybrid EOS is located in the range that is defined by the low-density chiral effective theory, the high-density perturbative QCD, and the polytropic interpolations between them, and is constrained by the astrophysical observations. The square of the sound velocity reaches a maximum value larger than 0.8 in the region of 2--5 times the saturation baryon number density and approaches the conformal limit at the high baryon density range. The mass-radius relation and the tidal deformability of the neutron stars are in agreement with astrophysical measurements. The possible maximum mass for the neutron star is about $2.5\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and the radius is about 12 km then. It is noticed that the holographic quark matter branch in the mass-radius relation is always unstable and the holographic nuclear matter can produce a stable branch. These results indicate that even in the core of the NS, the matter is still in the confinement phase and the quark matter is not favored.
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