Exact versus Taylor-expanded energy density in the study of the neutron star crust-core transition

TL;DR

This paper compares exact and Taylor-expanded energy density approaches to better understand the neutron star crust-core transition, emphasizing the significance of higher-order terms and their impact on astrophysical predictions.

Contribution

It provides analytic expressions for higher-order derivatives in the Taylor series and assesses their effects on neutron star transition properties.

Findings

Higher-order terms significantly influence transition density predictions.

Analytic formulas for derivatives improve the accuracy of energy density expansions.

Different equations of state affect the predicted crustal moment of inertia and pulsar radius.

Abstract

The importance of the fourth and higher order terms in the Taylor series expansion of the energy of the isospin asymmetric nuclear matter in the study of the neutron star crust-core phase transition is investigated using the finite range simple effective interaction. Analytic expressions for the evaluation of the second and fourth order derivative terms in the Taylor series expansion for any general finite range interaction of Yukawa, exponential or Gaussian form have been obtained. The effect of the nuclear matter incompressibility, symmetry energy and slope parameters on the predictions for the crust-core transition density is examined. The crustal moment of inertia is calculated and the prediction for the radius of the Vela pulsar is analyzed using different equations of state.