Characterization of low-significance gravitational-wave compact binary sources

Advanced LIGO and Virgo have so far detected gravitational waves from 10 binary black hole mergers (BBH) and 1 binary neutron star merger (BNS). In the future, we expect the detection of many more marginal sources, since compact binary coalescences detectable by advanced ground-based instruments are roughly distributed uniformly in comoving volume. In this paper we simulate weak signals from compact binary coalescences of various morphologies and optimal network signal-to-noise ratios (henceforth SNRs), and analyze if and to which extent their parameters can be measured by advanced LIGO and Virgo in their third observing run. We show that subthreshold binary neutron stars, with SNRs below 12 (10) yield uncertainties in their sky position larger than 400 (700) ${\mathrm{deg}}^2$ (90% credible interval). The luminosity distance, which could be used to measure the Hubble constant with standard sirens, has relative uncertainties larger than 40% for BNSs and neutron star black hole mergers. For sources with SNRs below 8, it is not uncommon that the extrinsic parameters, sky position and distance, cannot be measured. Next, we look at the intrinsic parameters, masses and spins. We show that the detector-frame chirp mass can sometimes be measured with uncertainties below 1% even for sources at SNRs of 6, although multimodality is not uncommon and can significantly broaden the posteriors. The effective inspiral spin is best measured for neutron star black hole mergers, for which the uncertainties can be as low as $\sim 0.08$ ($\sim 0.2$) at SNR 12 (8). The uncertainty is higher for systems with comparable component masses or lack of spin precession.

Figure 1

PSD of the recolored data for advanced LIGO (green for Livingston, blue for Hanford) and advanced Virgo (purple). The black lines are PSD for each instrument at the projected O3 sensitivities [4].

Figure 2

90% credible interval of the marginalized posteriors of the sky location vs network SNR.

Figure 3

Relative 90% credible interval of the marginalized posteriors of the luminosity distance $d_L$ vs network SNR.

Figure 4

Relative 90% credible interval of the marginalized posteriors of the detector-frame chirp mass $\mathcal{M}$ vs network SNR. The dashed lines represent the relative 90% width of the prior.

Figure 5

Representative posterior distribution for $\mathcal{M}$. All systems are BBHs with true inclination angle of 80°. The range is the same in all panels in the x axis.

Figure 6

Proportions for unimodal, unimodal (wide) and multimodal posterior distributions for detector-frame chirp mass $\mathcal{M}$ (%) vs network SNR.

Figure 7

Relative 90% credible interval of the marginalized posteriors of the source-frame chirp mass ${\mathcal{M}}^{\text{source}}$ vs network SNR.

Figure 8

90% credible interval of the marginalized posteriors of the mass ratio q vs network SNR. The dashed line represents the 90% CI for q prior.

Figure 9

90% credible interval of the marginalized posteriors of the effective spin ${\chi }_{\mathrm{eff}}$ vs network SNR. The dashed line represents the 90% CI for ${\chi }_{\mathrm{eff}}$ prior.

Figure 10

K-L divergence for ${\chi }_{\mathrm{eff}}$ vs network SNR.

Figure 11

Log likelihood for injection minus the maximum recovered log likelihood vs network SNR.

Figure 12

Relative 90% credible interval of the marginalized posteriors of the arrival GPS time vs network SNR.