The mixed phase quark core in massive hybrid stars

Abstract We investigate the properties of hybrid star and the mixed phase core to explore the radius ratio of the mixed phase in hybrid star. In the context of observed massive neutron stars (NSs), we examine the internal structure, phase transitions, and the impacts of the equation of state (EOS) in maximum hybrid star. We investigate the stiffness changes in the EOS during the hadron-quark phase transition within the hybrid stars. The relativistic mean-field (RMF) model is used to describe hadronic matter, while to the represent quark matter, the Nambu–Jona–Lasinio (NJL) model is applied. We explore the strength of vector coupling in quark matter, which delays the onset density of the mixed phase and reduces the size of the mixed-phase core in a hybrid star, but does not exhibit a clear correlation with the central density. In a hybrid star with a maximum mass of approximately 2 solar masses ( $$M_\odot $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:math> ), a mixed-phase core of $$\sim $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∼</mml:mo> </mml:math> 5 km may exist, comprising about $$40\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>40</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> of the total radius. However, our results do not support the existence of a sizable quark core containing the mixed phase ( $$R_\mathrm{{MP}}&gt;1/2~R_\mathrm{{total}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>MP</mml:mi> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:mspace/> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>total</mml:mi> </mml:msub> </mml:mrow> </mml:math> ) for the maximum-mass hybrid star or for a 2 $$M_\odot $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:math> massive star.