# Measurement of Tidal Deformability in the Gravitational Wave Parameter Estimation for Nonspinning Binary Neutron Star Mergers

## TL;DR

This paper introduces a new gravitational waveform model incorporating tidal deformability at 5 PN order and uses the Fisher matrix method to efficiently estimate measurement errors, improving accuracy in neutron star internal structure studies.

## Contribution

The study develops a 5 PN order waveform model including tidal effects and demonstrates faster, more precise error estimation for tidal deformability using the Fisher matrix approach.

## Key findings

- Measurement error for tidal deformability reduced by 25% with 6 PN correction.
- Fisher matrix method provides faster error estimates than MCMC.
- Inclusion of higher PN order improves measurement accuracy.

## Abstract

One of the main targets for ground-based gravitational wave (GW) detectors such as Advanced LIGO (Laser Interferometer Gravitational wave Observatory) and Virgo is coalescences of neutron star (NS) binaries. Even though a NS's macroscopic properties such as mass and radius have been obtained from electro-magnetic wave observations, its internal structure has been studied mainly by using theoretical approaches. However, with the advent of Advanced LIGO and Virgo, the tidal deformability of a NS, which depends on the internal structure of the NS, has been recently obtained from GW observations. Therefore, reducing the measurement error of tidal deformability as small as possible in the GW parameter estimation is important. In this study, we introduce a post-Newtonian (PN) gravitational waveform model in which the tidal deformability contribution appears from 5 PN order, and we use the Fisher matrix (FM) method to calculate parameter measurement errors. Because the FM is computed semi-analytically using the wave function, the measurement errors can be obtained much faster than those of practical parameter estimations based on Markov Chain Monte Carlo method. We investigate the measurement errors for mass and tidal deformability by applying the FM to the nonspinning TaylorF2 waveform model. We show that if the tidal deformability corrections are considered up to the 6 PN order, the measurement error for the dimensionless tidal deformability can be reduced to about $75 \%$ compared to that obtained by considering only the 5 PN order correction.