Direct mapping of tidal deformability to the isoscalar and isovector nuclear matter parameters

Sk Md Adil Imam, Arunava Mukherjee, B. K. Agrawal, and Gourab Banerjee

Phys. Rev. C 109, 025804 – Published 16 February 2024

Abstract

Background: The equations of state (EoSs) which determine the properties of neutron stars (NSs) are often characterized by the isoscalar and isovector nuclear matter parameters (NMPs). Recent attempts to relate the radius and tidal deformability of a NS to the individual NMPs have been inconclusive. These properties display strong correlations with the pressure of NS matter which depends on several NMPs. It may be necessary to map the NS properties to the NMPs.

Purpose: To identify the important NMPs required to describe the tidal deformability of neutron star for astrophysically relevant range of their gravitational masses (1.2–1.8 $M_{⊙}$ ) as encountered in the binary neutron star merger events.

Method: We construct a large set of EoSs using four isoscalar and five isovector NMPs. These EoSs are employed to perform a systematic analysis to isolate the NMPs that predominantly determine the tidal deformability parameter obtained by solving the Tolman-Oppenheimer-Volkoff (TOV) equations. The tidal deformability for the EoSs consistent with the chiral effective field theory ( $χ EFT$ ) at the lower density and satisfying maximum gravitational mass of stable NS $\geq$ 2 $M_{⊙}$ are directly mapped to these NMPs.

Results: We provide empirical relations between tidal deformability parameter and a minimal set of essential NMPs through lower order polynomial functions. The tidal deformability of the NS with mass 1.2–1.8 $M_{⊙}$ can be determined within 10–30 % directly in terms of linear function of four nuclear matter parameters, namely, the incompressibility coefficient $K_{0}$ and skewness $Q_{0}$ of symmetric nuclear matter, and the slope $L_{0}$ and curvature parameter $K_{sym 0}$ of symmetry energy. The inclusion of the remaining NMPs improves the predictability of tidal deformability to 5–10 %.

Conclusion: Empirical relations are developed for quick estimation of reliable values of tidal deformability, in terms of the NMPs, across a wide range of NS mass for a given EoS model. Our method can also be extended to other NS observables.