Parameter estimation for inspiraling eccentric compact binaries including pericenter precession

Abstract

Inspiraling supermassive black hole binary systems with high orbital eccentricity are important sources for space-based gravitational wave observatories like the Laser Interferometer Space Antenna. Eccentricity adds orbital harmonics to the Fourier transform of the gravitational wave signal, and relativistic pericenter precession leads to a three-way splitting of each harmonic peak. We study the parameter estimation accuracy for such waveforms with different initial eccentricity, using the Fisher matrix method and a Monte Carlo sampling of the initial binary orientation. The eccentricity improves the parameter estimation by breaking degeneracies between different parameters. In particular, we find that the source localization precision improves significantly for higher-mass binaries due to eccentricity. The typical sky position errors are $\ensuremath{\sim}1\text{ }\text{ }\mathrm{deg}$ for a nonspinning, ${10}^{7}{M}_{\ensuremath{\bigodot}}$, equal-mass binary at redshift $z=1$, if the initial eccentricity 1 yr before merger is ${e}_{0}\ensuremath{\sim}0.6$. Pericenter precession does not affect the source localization accuracy significantly, but it does further improve the mass and eccentricity estimation accuracy systematically by a factor of 3--10 for masses between ${10}^{6}{M}_{\ensuremath{\bigodot}}$ and ${10}^{7}{M}_{\ensuremath{\bigodot}}$ for ${e}_{0}\ensuremath{\sim}0.3$.