Core States of Neutron Stars from Anatomizing Their Scaled Structure Equations
Bao-Jun Cai, Bao-An Li, Zhen Zhang
Abstract
Abstract Given an Equation of State (EOS) for neutron star (NS) matter, there is a unique mass–radius sequence characterized by a maximum mass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>NS</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> at radius R max . We first show analytically that the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>NS</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> and R max scale linearly with two different combinations of the NS central pressure P c and energy density ε c , by dissecting perturbatively the dimensionless Tolman–Oppenheimer–Volkoff (TOV) equations governing NS internal variables. The scaling relations are then verified via 87 widely used and rather diverse phenomenological as well as 17 microscopic NS EOSs with/without considering hadron–quark phase transitions and hyperons, by solving numerically the original TOV equations. The EOS of the densest NS matter allowed before it collapses into a black hole is then obtained. Using the universal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>NS</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> and R max scalings and Neutron Star Interior Composition Explorer and XMM-Newton mass–radius observational data for PSR J0740+6620, a very narrow constraining band on the NS central EOS is extracted directly from the data for the first time, without using any specific input EOS model.