Measurement Accuracy of Inspiraling Eccentric Neutron Star and Black Hole Binaries Using Gravitational Waves

Abstract

In a recent paper, we determined the measurement accuracy of physical parameters for eccentric, precessing, non-spinning, inspiraling, stellar-mass black hole - black hole (BH-BH) binaries for the upcoming second-generation LIGO/VIRGO/KAGRA detector network at design sensitivity using the Fisher matrix method. Here we extend that study to a wide range of binary masses including neutron star - neutron star (NS-NS), NS-BH, and BH-BH binaries with BH masses up to $110M_{\odot }$. The measurement error of eccentricity $e_{10\mathrm{Hz}}$ at a gravitational-wave (GW) frequency of $10\mathrm{Hz}$ is in the range $(10^{-4}-10^{-3})\times (D_L/100\mathrm{Mpc})$ for NS-NS, NS-BH, and BH-BH binaries at a luminosity distance of $D_L$ if $e_{10\mathrm{Hz}}\gtrsim 0.1$. For events with masses and distances similar to the detected 10 GW transients, we show that nonzero orbital eccentricities may be detected if $0.081\lesssim e_{10\mathrm{Hz}}$. Consequently, the LIGO/VIRGO/KAGRA detector network at design sensitivity will have the capability to distinguish between eccentric waveforms and circular waveforms. In comparison to circular inspirals, we find that the chirp mass measurement precision can improve by up to a factor of $\sim 20$ and $\sim 50-100$ for NS-NS and NS-BH binaries with BH companion masses $\lesssim 40M_{\odot }$, respectively. The identification of eccentric sources may give information on their astrophysical origin; it would indicate merging binaries in triple or higher multiplicity systems or dynamically formed binaries in dense stellar systems such as globular clusters or galactic nuclei.

22 pages, 1 table, 12 figures, version accepted for publication in ApJ