Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?

TL;DR

The paper develops a Fisher-misher approach to quantify how accurately LIGO/VIRGO can extract binary parameters from inspiral gravitational waves, highlighting that the chirp mass is measured with exceptional precision while individual masses and distance are more vulnerable to PN corrections and spin effects.Using Newtonian and post-Newtonian waveform models, it demonstrates that a three-detector network markedly improves sky localization and distance estimates, though spin–mass correlations can degrade mass determinations unless certain combinations of parameters are exploited.It introduces the Marković approximation and a Bayesian extension to address non-linear and non-Gaussian effects in distance estimation, and provides Monte-Carlo results showing realistic distance accuracies (roughly 15% for about 8% of events and 30% for about 60%), underscoring the value of expanding the detector network to improve polarization sensitivity.

Abstract

The most promising source of gravitational waves for the planned detectors LIGO and VIRGO are merging compact binaries, i.e., neutron star/neutron star (NS/NS), neutron star/black hole (NS/BH), and black hole/black-hole (BH/BH) binaries. We investigate how accurately the distance to the source and the masses and spins of the two bodies will be measured from the gravitational wave signals by the three detector LIGO/VIRGO network using ``advanced detectors'' (those present a few years after initial operation). The combination ${\cal M} \equiv (M_1 M_2)^{3/5}(M_1 +M_2)^{-1/5}$ of the masses of the two bodies is measurable with an accuracy $\approx 0.1\%-1\%$. The reduced mass is measurable to $\sim 10\%-15\%$ for NS/NS and NS/BH binaries, and $\sim 50\%$ for BH/BH binaries (assuming $10M_\odot$ BH's). Measurements of the masses and spins are strongly correlated; there is a combination of $μ$ and the spin angular momenta that is measured to within $\sim 1\%$. We also estimate that distance measurement accuracies will be $\le 15\%$ for $\sim 8\%$ of the detected signals, and $\le 30\%$ for $\sim 60\%$ of the signals, for the LIGO/VIRGO 3-detector network.

Figures (22)

• Figure : The rms errors for signal parameters and the correlation coefficient $c_{{\cal M} \mu}$, calculated assuming spins are negligible. The results are for a single "advanced" detector, the shape of whose noise curve is given by Eq. (\ref{['snf']}). $M_1$ and $M_2$ are in units of solar masses, while $\Delta t_c$ is in units of msec. The rms errors are normalized to a signal-to-noise ratio of $S/N = 10$; the errors scale as $(S/N)^{-1}$, while $c_{{\cal M} \mu}$ is independent of $S/N$.
• Figure : The rms errors for signal parameters and the correlation coefficient $c_{{\cal M} \mu}$, calculated assuming spins are negligible. The results are for a single "advanced" detector, the shape of whose noise curve is given by Eq. (\ref{['snf']}). $M_1$ and $M_2$ are in units of solar masses, while $\Delta t_c$ is in units of msec. The rms errors are normalized to a signal-to-noise ratio of $S/N = 10$; the errors scale as $(S/N)^{-1}$, while $c_{{\cal M} \mu}$ is independent of $S/N$.
• Figure : The rms errors for signal parameters and the correlation coefficient $c_{{\cal M} \mu}$, calculated assuming spins are negligible. The results are for a single "advanced" detector, the shape of whose noise curve is given by Eq. (\ref{['snf']}). $M_1$ and $M_2$ are in units of solar masses, while $\Delta t_c$ is in units of msec. The rms errors are normalized to a signal-to-noise ratio of $S/N = 10$; the errors scale as $(S/N)^{-1}$, while $c_{{\cal M} \mu}$ is independent of $S/N$.
• Figure : The rms errors for signal parameters and the correlation coefficient $c_{{\cal M} \mu}$, calculated assuming spins are negligible. The results are for a single "advanced" detector, the shape of whose noise curve is given by Eq. (\ref{['snf']}). $M_1$ and $M_2$ are in units of solar masses, while $\Delta t_c$ is in units of msec. The rms errors are normalized to a signal-to-noise ratio of $S/N = 10$; the errors scale as $(S/N)^{-1}$, while $c_{{\cal M} \mu}$ is independent of $S/N$.
• Figure : The rms errors for signal parameters and the correlation coefficient $c_{{\cal M} \mu}$, calculated assuming spins are negligible. The results are for a single "advanced" detector, the shape of whose noise curve is given by Eq. (\ref{['snf']}). $M_1$ and $M_2$ are in units of solar masses, while $\Delta t_c$ is in units of msec. The rms errors are normalized to a signal-to-noise ratio of $S/N = 10$; the errors scale as $(S/N)^{-1}$, while $c_{{\cal M} \mu}$ is independent of $S/N$.