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Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral

Sascha Husa, Mark Hannam, Jose A. Gonzalez, Ulrich Sperhake, Bernd Bruegmann

TL;DR

This work tackles the issue that standard quasi-circular initial data often yield eccentric inspirals in binary black-hole evolutions. It introduces a PN-based method: integrate the post-Newtonian equations of motion over hundreds of orbits from a large separation and read off the momenta at the chosen starting separation to initialize full GR simulations. The approach achieves substantial eccentricity reduction, demonstrated for equal-mass, non-spinning binaries at D=11M (e < 0.002, a factor of at least five improvement). The authors validate the PN-derived momenta with full GR evolutions, showing small relative errors and suggesting the initial data faithfully represent the physical system with minimal impact from junk radiation. The method is extendable to unequal masses and spins, potentially improving waveform accuracy for PN-template matching in gravitational-wave astronomy.

Abstract

Standard choices of quasi-circular orbit parameters for black-hole binary evolutions result in eccentric inspiral. We introduce a conceptually simple method, which is to integrate the post-Newtonian equations of motion through hundreds of orbits, and read off the values of the momenta at the separation at which we wish to start a fully general relativistic numerical evolution. For the particular case of non-spinning equal-mass inspiral with an initial coordinate separation of $D = 11M$ we show that this approach reduces the eccentricity by at least a factor of five to $e < 0.002$ as compared to using standard quasi-circular initial parameters.

Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral

TL;DR

This work tackles the issue that standard quasi-circular initial data often yield eccentric inspirals in binary black-hole evolutions. It introduces a PN-based method: integrate the post-Newtonian equations of motion over hundreds of orbits from a large separation and read off the momenta at the chosen starting separation to initialize full GR simulations. The approach achieves substantial eccentricity reduction, demonstrated for equal-mass, non-spinning binaries at D=11M (e < 0.002, a factor of at least five improvement). The authors validate the PN-derived momenta with full GR evolutions, showing small relative errors and suggesting the initial data faithfully represent the physical system with minimal impact from junk radiation. The method is extendable to unequal masses and spins, potentially improving waveform accuracy for PN-template matching in gravitational-wave astronomy.

Abstract

Standard choices of quasi-circular orbit parameters for black-hole binary evolutions result in eccentric inspiral. We introduce a conceptually simple method, which is to integrate the post-Newtonian equations of motion through hundreds of orbits, and read off the values of the momenta at the separation at which we wish to start a fully general relativistic numerical evolution. For the particular case of non-spinning equal-mass inspiral with an initial coordinate separation of we show that this approach reduces the eccentricity by at least a factor of five to as compared to using standard quasi-circular initial parameters.

Paper Structure

This paper contains 4 sections, 6 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Integration of the PN equations of motion
  3. Numerical results
  4. Conclusions

Figures (3)

  • Figure 1: The radial momentum component is plotted versus separation for PN-inspirals starting from $D=20M$ and $D=40M$. A separation of $D=20M$ is clearly not sufficient to produce non-eccentric inspiral parameters, since small oscillations can still be seen at $D=11M$, while for $D=40M$ the initial eccentricity has essentially decayed away.
  • Figure 2: Coordinate separation of the punctures as a function of time for the quasi-circular (QC11) and PN-inspired low-eccentricity (E11) initial parameters.
  • Figure 3: The functions $e_D(t)$ and $e_{\omega}(t)$ for the QC11 and E11 simulations. The extrema of these functions give an estimate of the eccentricity, as described in the text.