Compact binary systems and gravitational waveforms

Weak gravitational fields and slow motion sources are described by the post-Newtonian (PN) approximation in a perturbative treatment where the dynamics of the binary and the emitted gravitational radiation is given to high accuracy. The PN approximation is proved to be accurately applied below the critical value ∼0.1 of the PN parameter. Both the radial motion and the parameterization of the orbit are known to high PN orders. As a first approximation, only the masses of the orbiting bodies are used to characterize the binary. The effects of other physical parameters (e.g. spins or the eccentricity of the orbit) and higher order general relativistic corrections have to be included for a more accurate description.

Comparison of post-Newtonian and phenomenological templates for eccentric inspirals

Binaries that evolved through typical main sequence evolution are expected to shed their formation eccentricities over time due to gravitational radiation reaction. For this reason, isolated binary sources are commonly assumed to move on quasi-circular orbits by the time they spiral into the sensitive frequency band of terrestrial GW observatories. Some relatively young sources, nevertheless, which had too short time to completely circularize their orbits retain some residual eccentricity. Therefore, binary inspirals with non-negligible orbital eccentricities are plausible sources. Some results support the qualitative conclusion that neglecting residual orbital eccentricities (even small ones) in binary searches may seriously deteriorate matched-filter detection performance. A number of possible astrophysical scenarios and mechanisms allows the formation of observationally relevant eccentric binaries e.g. by dynamical captures in dense stellar environments, present in both galactic central regions and globular clusters, or by tidal capture of compact object by NSs. Roughly 0.1 – 10 eccentric inspiral events per year up to redshift z ~ 0.2 are anticipated to be discovered by advanced LIGO-type observatories. To investigate present waveform models for these type of sources we compare different PN and phenomenological templates.

Higher-order corrections and Hamiltonian formulation with CBwaves

In order to investigate the gravitational radiation emitted by generic binary systems with possibly spinning components on highly eccentric orbits, our group has developed the numerical package CBwaves. It is an open-source software for the generation of gravitational waveforms produced by generic spinning binary configurations moving on eccentric closed or open orbits, which uses a 4th-order Runge–Kutta solver to integrate the center of mass PN equations of motion. Originally, this program package was able to compute the orbital evolution, gravitational waveform, eccentricity, and spin effects of binary sources up to the 3PN accuracy. Recently, it was upgraded with the inclusion of 4PN terms. To further improve CBwaves we add the following features:

  • ADM Hamiltonian formalism of the post-Newtonian extension, which will allow us to analyse scenarios such as zoom-whirl orbits, and also Kerr black holes.
  • Effective-one-body Taylor formalism to simulate the merger of binary neutron stars.
  • The effect of NS deformation will be considered as a parameter in CBwaves waveform generation.

Extension of CBwaves describe full inspiral-merger-ringdown (IMR) waveforms

The routines currently used for gravitational-wave data analysis use restricted stationary-phase approximations to the Fourier transform of 3.5PN-accurate circular inspiral-only waveforms (such as spin-aligned TaylorF2 or SpinTaylorT4). In order to extend the scope of application beyond the zero-eccentricity limit, CBwaves was developed. Nevertheless, composite waveforms that fully cover all the IMR stages can be constructed by matching the inspiral and NR waveforms of merger stages in either the time or frequency domain and then fitting this ’hybrid’ waveform to the ring-down part. The transition from the inspiral phase to the plunge can be defined by the minimum energy circular orbit (MECO). The gap between the initial part of the waveform and its final ring-down part, described by damped exponentials, is bridged by a phenomenological phase.

Early warning for the detection of GW events

The improvement in sensitivity of the advanced detectors allows GW signals from binary sources to stay in the sensitive band for a longer time period, giving the possibility of their detection before the final coalescence of the system. In order to make predictions on binary sources which can be detected by the Advanced GW detectors prior to coalescence we analyse the accumulated signal-to-noise ratio. The low-frequency part of the sensitivity band of the GW detectors is dominated by seismic noise. As a natural continuation of our earlier studies, and, in addition to the goals of the proposed project we analyse the low-frequency-sensitivity constraints to early-warning predictions.