Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors (0907.0700v1)

Abstract: The two-body dynamics in general relativity has been solved perturbatively using the post-Newtonian (PN) approximation. The evolution of the orbital phase and the emitted gravitational radiation are now known to a rather high order up to O(v^8), v being the characteristic velocity of the binary. The orbital evolution, however, cannot be specified uniquely due to the inherent freedom in the choice of parameter used in the PN expansion as well as the method pursued in solving the relevant differential equations. The goal of this paper is to determine the (dis)agreement between different PN waveform families in the context of initial and advanced gravitational-wave detectors. The waveforms employed in our analysis are those that are currently used by Initial LIGO/Virgo, that is the time-domain PN models TaylorT1, TaylorT2, TaylorT3, TaylorT4 and TaylorEt, the effective one-body (EOB) model, and the Fourier-domain representation TaylorF2. We examine the overlaps of these models with one another and with the prototype effective one-body model (calibrated to numerical relativity simulations, as currently used by initial LIGO) for a number of different binaries at 2PN, 3PN and 3.5PN orders to quantify their differences and to help us decide whether there exist preferred families that are the most appropriate as search templates. We conclude that as long as the total mass remains less than a certain upper limit M_crit, all template families at 3.5PN order (except TaylorT3 and TaylorEt) are equally good for the purpose of detection. The value of M_crit is found to be ~ 12M_Sun for Initial, Enhanced and Advanced LIGO. From a purely computational point of view we recommend that 3.5PN TaylorF2 be used below Mcrit and EOB calibrated to numerical relativity simulations be used for total binary mass M > Mcrit.

• The paper examines overlaps and phasing at 2PN, 3PN, and 3.5PN orders to identify optimal templates for detecting compact binary inspirals.
• The study recommends the 3.5PN TaylorF2 model for lower mass systems and the calibrated EOB model for higher masses to enhance computational efficiency.
• The research highlights analytical models' limitations in late inspiral, merger, and ringdown phases, emphasizing the necessity of numerical relativity simulations.

Post-Newtonian Comparisons for Binary Inspirals in Gravitational Wave Detection

The paper "Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors" investigates the compatibility and differences between multiple post-Newtonian (PN) waveform templates used for detecting gravitational waves from binary systems, such as those involving neutron stars and black holes. Understanding these differences is crucial for improving gravitational wave detectors like LIGO and Virgo, especially as they progress into more sensitive operational phases.

Summary of Post-Newtonian Waveforms

The authors analyze several time-domain models (TaylorT1, TaylorT2, TaylorT3, TaylorT4) and a frequency-domain model (TaylorF2), as well as the Effective-One-Body (EOB) model and its calibrations to numerical relativity simulations. These templates are essential tools for matched filtering techniques used in detecting gravitational wave signals from binary inspirals.

The paper explores the evolution of the orbital phase up to order $\mathcal{O}(v^8)$ for post-Newtonian expansions, where $v$ is the characteristic velocity. Despite advancements in PN calculations, the waveform evolution is not straightforwardly defined due to the inherent freedom in choosing certain parameters within the PN expansion and differences in methods for solving the differential equations governing the system dynamics.

Key Findings

1. Overlap and Phasing: The paper examines overlaps (i.e., effectualness) between different PN waveform families at 2PN, 3PN, and 3.5PN orders to identify the most suitable ones for gravitational wave detection. These overlaps are critical in determining which waveforms can effectively serve as templates for capturing gravitational wave signals. Their research finds that, for total masses below $M_{\rm crit} \approx 12\,M_\odot$, most template families at 3.5PN order, except for TaylorT3 and TaylorEt, are adequate for detection purposes.
2. Computational Recommendations: Given the findings, the 3.5PN TaylorF2 model is recommended for compact binary systems below this threshold due to its computational efficiency. For higher mass systems where merging and ringdown phases become significant, the EOB model calibrated to numerical relativity simulations is favored.
3. Theoretical Implications: The paper points out that while the analytical models give a robust understanding of the inspiral, they fall short in describing the late inspiral, merger, and ringdown phases. This highlights the importance of numerical relativity simulations to complement PN approximations in these regimes.

Practical and Theoretical Implications

Practical Implications

• Detector Sensitivity: Enhanced sensitivity in gravitational wave detectors, including those planned in the near future, necessitates more accurate waveform models for effective detection. This paper informs the choice of such models based on mass and expected merger outcomes.
• Waveform Search Strategy: The recommendation to use the TaylorF2 model below certain mass limits suggests predefined strategies for waveform searches during data acquisition, optimizing computational resources and performance of the detectors.

Theoretical Speculations

• Advancements in Modeling: Future developments in the PN approximation, potentially through higher order calculations or improved numerical simulations, could further refine the choices of detection templates.
• Incorporating Full Waveform: As the models evolve, integrating additional waveform features, including amplitude corrections and multipolar expansions, could enhance the fidelity of gravitational waveforms and make detections more robust against noise.

In conclusion, this paper presents a thorough analysis of PN waveform families, guiding the development of gravitational wave data analysis techniques. By identifying suitable waveform templates for varying mass ranges, the authors contribute significantly to optimizing gravitational wave detection methodologies, crucial for astrophysical discoveries in the field of compact binary mergers.