Post-1-Newtonian Tidal Effects in the Gravitational Waveform from Binary Inspirals
The paper of gravitational waveforms from binary neutron star inspirals presents a unique opportunity to extract detailed information about the internal physics of neutron stars. This is primarily achieved by analyzing tidal couplings within the inspiralling system. However, such an analysis requires highly precise models for the gravitational waveform due to the subtle nature of tidal interactions in these stellar encounters. This paper provides a rigorous calculation of the gravitational wave signal from a binary system involving quadrupolar tidal interactions, incorporating all post-1-Newtonian (1PN) effects in both the conservative dynamics and wave generation.
Key Findings and Contributions
The paper's primary focus is on binary systems composed of neutron stars with adiabatically induced quadrupoles moving in circular orbits. The paper operates to linear order in the stars' quadrupole moments. A significant result highlighted in the paper is that 1PN corrections augment the tidal signal by approximately 20% at gravitational wave frequencies of 400 Hz.
Theoretical Framework and Methodology
The theoretical foundation is rooted in the concepts of inspiralling and coalescing binary neutron stars, which are essential sources for ground-based gravitational wave detectors. These detectors aim to obtain reliable information on the equation of state (EoS) of neutron star matter, a crucial physics problem that remains highly uncertain. The EoS significantly affects the gravitational wave signal during late inspiral and merger stages when the gravitational wave frequencies exceed 500 Hz. This demands the use of fully relativistic numerical simulations due to the strong gravitational forces and complex hydrodynamics involved.
In the low-frequency regime (below 500 Hz), the gravitational wave signal possesses a smaller but distinct EoS signature attributable to tidal coupling effects. In this context, the authors employ a post-Newtonian-based approach for waveform modeling, enabling accurate approximation within this frequency range.
The tidal contribution to gravitational wave signals is parameterized by a single tidal deformability parameter, λ, that characterizes the star's response to the tidal field and is sensitive to the EoS. This parameter has been formulated in a fully relativistic setting and computed for various EoS models.
Implications and Future Directions
This research has several implications for both theoretical and practical advancements in gravitational wave physics. The 1PN corrections facilitate more precise modeling of tidal effects, necessary for constraining candidate equations of state or accurately measuring tidal deformability using gravitational wave observations. This is particularly relevant for low-frequency gravitational waves within the most sensitive bands of detectors like Advanced LIGO.
The numerical results suggest that including 1PN effects can enhance observability and provide richer analytical models, potentially bridging the gap between the analytical and numerical simulations in hybrid gravitational waveform models. These corrections can be seamlessly integrated into effective-one-body (EOB) formalism and could assist in refining gravitational wave templates for improved data analysis.
In conclusion, while this paper primarily addresses circular orbits and quadrupolar tidal interactions, the presented methods and results offer a detailed framework for expanding the analysis to more general scenarios, including non-circular orbits and higher multipolar tidal interactions, thereby paving the way for more comprehensive modeling efforts in this domain.