Systematic parameter errors in inspiraling neutron star binaries (1310.8288v2)

Abstract: The coalescence of two neutron stars is an important gravitational wave source for LIGO and other detectors. Numerous studies have considered the precision with which binary parameters (masses, spins, Love numbers) can be measured. Here I consider the accuracy with which these parameters can be determined in the presence of systematic errors due to waveform approximations. These approximations include truncation of the post-Newtonian (PN) series and neglect of neutron star (NS) spin, tidal deformation, or orbital eccentricity. All of these effects can yield systematic errors that exceed statistical errors for plausible parameter values. In particular, neglecting spin, eccentricity, or high-order PN terms causes a significant bias in the NS Love number. Tidal effects will not be measurable with PN inspiral waveforms if these systematic errors are not controlled.

Systematic Parameter Errors in Inspiraling Neutron Star Binaries

The paper "Systematic Parameter Errors in Inspiraling Neutron Star Binaries" presents a critical analysis of the systematic errors in parameter estimation of neutron star (NS) binaries during inspiral. This work is particularly relevant for the precision-driven requirements of current and future gravitational-wave detectors such as LIGO and Virgo.

Overview

Neutron star mergers serve as vital sources of gravitational waves and offer unique insights into stellar physics, including dense matter equations of state. Accurate parameter estimation from these events can constrain critical attributes such as NS masses, spins, and tidal deformabilities. The research highlights systematic biases arising from waveform inaccuracies due to truncated post-Newtonian (PN) series and omitted physical effects such as spin and eccentricity. These biases potentially outweigh statistical errors, challenging the fidelity of waveforms used for detections.

Key Findings

The paper identifies several sources of systematic errors:

1. Post-Newtonian Order Truncation: The accuracy of mass parameters directly correlates with the PN order model employed. Notably, 4PN waveforms could be required to minimize mass estimation errors below statistical thresholds. For third-generation detectors like the Einstein Telescope (ET), this requirement may extend to at least 6PN order to ensure precision.
2. Neglect of Spin: Despite typically lower spin magnitudes for neutron stars compared to black holes, spins as small as $\chi \sim 0.003$ can introduce significant systematic biases in parameter estimations. Accurate modeling should thus incorporate spin effects, particularly in precision studies.
3. Eccentricity: Parameters assuming circular orbits are prone to substantial errors if the true binary exhibits an eccentricity greater than $0.002$. Even minimal eccentricities unaccounted for can skew estimations crucial for subsequent theoretical analyses.
4. Tidal Effects: While tidal interaction contributions are minor compared to other waveform inaccuracies in many scenarios, the measurability of tidal deformability parameters $\hat{\lambda}_i$ experiences considerable systematic bias, especially when other waveform elements such as spin and higher-order PN terms are neglected.
5. Parameter Bias Influencing Tidal Deformability: Neglected physical effects, including spin and eccentricity, drastically affect tidal deformability estimation robustness, posing challenges for accurate NS equation of state determinations and potential cosmological insights.

Implications and Future Directions

The paper’s findings accentuate the urgency of developing higher-order PN waveforms to reduce systematic biases, especially for mass parameters. A detailed incorporation of spin and eccentricity in waveform models will enhance the reliability of NS binary parameter extraction. This evolution is essential for efforts in understanding dense matter physics and constraining foundational astrophysical models based on gravitational-wave observations.

Looking forward, it is anticipated that future research will continue refining the models and methods outlined here, incorporating comprehensive waveform corrections and examining additional systematic biases. This effort is imperative, particularly as detectors attain higher sensitivities, making waveform accuracy paramount to underpinning astrophysical and cosmological studies.

The systematic examination conducted in this research provides a robust framework for further inquiry and development in gravitational-wave data analysis, ensuring precision in a field poised for significant expansions in descriptive and predictive power.