The Effect of a Self-bound Equation of State on the Structure of Rotating Compact Stars

Abstract This paper investigates how a self-bound equation of state (EOS), which describes strange quark stars, affects the rotational properties of compact stars, focusing on deviations from universal relations governing gravitational mass and radius changes due to rotation. The analysis reveals significant deviations in stars with higher surface-to-center total energy-density ratios, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfrac> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>ϵ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>ϵ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfrac> </mml:math> , challenging the established universal relations. For Newtonian stars, hydrostatic equilibrium ensures that the difference between the gravitational potential at the center, Φ c , and at the poles, Φ p , remains constant within sequences of rotating neutron stars characterized by the same central and polar specific enthalpy (Φ c − Φ p = − h c + h p ). Combined with the scaling <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Φ</mml:mi> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , where R e denotes the equatorial radius, this condition naturally leads to a quasi-universal behavior in the rotational change of radius within these sequences. Similarly, in general relativistic stars, the hydrostatic equilibrium maintains that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi mathvariant="normal">Φ</mml:mi> <mml:mi>p</mml:mi> <mml:mi>GR</mml:mi> </mml:msubsup> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mi mathvariant="normal">Φ</mml:mi> <mml:mi>c</mml:mi> <mml:mi>GR</mml:mi> </mml:msubsup> </mml:math> remains unchanged within these sequences, where Φ GR is one of the metric potentials. Inspired by this theoretical framework, a toy model has been developed to capture the dependence of gravitational mass and radius deviations on the surface-to-central total energy density ratio. Subsequently, an improved set of empirical universal relations has been proposed for accurately modeling rapidly rotating compact stars with self-bound EOSs.