# Impact of unmodeled eccentricity on the tidal deformability measurement and implications for gravitational wave physics inference

**Authors:** Poulami Dutta Roy, Pankaj Saini  
**arXiv:** [2403.02404](https://arxiv.org/abs/2403.02404)  
**Date:** 2024-03-04  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2403.02404v1/

## Key points

- Third-generation detectors Cosmic Explorer (CE) and Einstein Telescope (ET) will revolutionize understanding of neutron stars (NS) through binary neutron star (BNS) observations
- Precise measurements of tidal deformability enabled, shedding light on NS interiors' equation of state (EoS)
- Study by Blanchet et al. (2023) found systematic errors due to unmodeled eccentricity impacting NS EoS inference at specific levels
- Biases in tidal deformability parameters can distort source frame NS mass estimates and redshift inferences using Love siren method
- Systematic errors can lead to non-zero values for tidal deformability in binary black hole systems, falsely suggesting deviations from Kerr black hole properties
- Incorporating eccentricity into waveform models increases statistical errors in tidal deformability measurements by a factor less than two

## Summary

In the era of gravitational wave astronomy, the upcoming third-generation detectors - Cosmic Explorer (CE) and Einstein Telescope (ET) - are poised to revolutionize our understanding of neutron stars (NS) through binary neutron star (BNS) observations. These advanced detectors will enable precise measurements of tidal deformability, shedding light on the equation of state (EoS) governing NS interiors. A recent study by Blanchet et al. (2023) investigated systematic errors due to unmodeled eccentricity in tidal deformability measurements and found that at an eccentricity level of around $10^{-3}$ ($3\times 10^{-4}$) at a reference frequency of 10Hz for CE (ET), these errors can surpass statistical uncertainties and significantly impact NS EoS inference. Furthermore, these biases in tidal deformability parameters can propagate to distortions in source frame NS mass estimates, consequently biasing redshift inferences using the Love siren method. Specifically, for CE, redshift estimations are notably affected at an eccentricity level of approximately $10^{-3$ at 10Hz reference frequency. Moreover, the implications of biased tidal deformability extend beyond NS studies to testing the nature of black holes. The presence of systematic errors can lead to non-zero values for tidal deformability in binary black hole systems, falsely suggesting deviations from Kerr black hole properties. Additionally, incorporating eccentricity into waveform models was shown to increase statistical errors in tidal deformability measurements by a factor less than two. This underscores the importance of utilizing accurate eccentric waveform models for robust gravitational wave parameter inference. Overall, this comprehensive analysis highlights the critical role that accounting for eccentricity plays in refining our understanding of NS properties and gravitational wave physics inference as we enter an exciting new phase in astrophysical research.