Impact of Higher-order Tidal Corrections on the Measurement Accuracy of Neutron Star Tidal Deformability

TL;DR

This paper examines how incorporating higher-order tidal corrections up to 7.5 pN in gravitational wave models affects the measurement accuracy of neutron star tidal deformability, using Fisher Matrix analysis.

Contribution

It introduces a semi-analytic Fisher Matrix approach with Universal Relations to assess higher-order tidal correction impacts on neutron star parameter estimation.

Findings

Tidal correction effects do not converge with increasing pN order.

Measurement error of tidal deformability decreases with higher effective spin.

Stiffer equations of state lead to better measurement accuracy.

Abstract

Gravitational waves emitted by binary neutron stars (BNS) provide information about the internal structure of neutron stars (NSs), helping to verify dense matter equations of state. We investigate how the measurement accuracy of NS's tidal deformability can be improved by incorporating the higher-order post-Newtonian (pN) tidal corrections up to 7.5 pN. We assume an aligned-spin BNS system and adopt TaylorF2, which is the most commonly used pN waveform model. To calculate the measurement error, we use a semi-analytic method, Fisher Matrix, which is much faster than performing parameter estimation simulations. We employ Universal Relation to remove additional parameters that appear in higher-order corrections beyond 6 pN. We find that the effect of tidal corrections shows no behavior of convergence with increasing pN orders. Assuming a fiducial binary NS system whose physical parameters are compatible with GW170817, we find that the measurement error of tidal deformability ($\tilde{\lambda}$) decreases linearly as the effective spin ($\chi_{\rm eff}$) increases and the tidal deformability can be better measured for stiffer equation of states.