Detectability of Gravitational Waves from High-Redshift Binaries

Recent nondetection of gravitational-wave backgrounds from pulsar timing arrays casts further uncertainty on the evolution of supermassive black hole binaries. We study the capabilities of current gravitational-wave observatories to detect individual binaries and demonstrate that, contrary to conventional wisdom, some are, in principle, detectable throughout the Universe. In particular, a binary with rest-frame mass $\gtrsim {10}^{10}{M}_{\odot }$ can be detected by current timing arrays at arbitrarily high redshifts. The same claim will apply for less massive binaries with more sensitive future arrays. As a consequence, future searches for nanohertz gravitational waves could be expanded to target evolving high-redshift binaries. We calculate the maximum distance at which binaries can be observed with pulsar timing arrays and other detectors, properly accounting for redshift and using realistic binary waveforms.

Figure 1

GW strain versus observed time for binaries with fixed rest-frame chirp mass, emitting at the same observed frequency at time 0. For clarity, we plot inspiral-only waveforms. The higher the redshift, the closer the signal is to merger, causing the binary to be brighter than a similar, less distant one.

Figure 2

$S/N$ versus redshift of inspiralling binaries of certain mass and GW initial observed frequency, and certain detector noise. The dotted line is the $S/N$ threshold and the grey area contains the parameter space where binaries already merged. The solid and dashed lines are, respectively, the $S/N$ with fixed $M_c$ and $M_z$. The triangle and square denote the horizon distance inferred given fixed $M_z$ and $M_c$, respectively. The two circles define a region where the binary $S/N$ is below the threshold.

Figure 3

Redshift versus GW observed frequency of SBHBs, assuming they are monochromatic. The blue-green area shows where SBHBs with $M_c={10}^{9.8}{M}_{\odot }$ (left), $10^{10.0}{M}_{\odot }$ (middle), and $10^{10.2}{M}_{\odot }$ (right) produce a strain larger than the EPTA upper limit [14]. In the shaded area, binaries already finished the inspiral phase, and the red area contains SBHBs with subthreshold strains. The black line shows the horizon distance from [14] assuming $M_z$ (not $M_c$) is ${10}^{9.8}{M}_{\odot }$ (left), $10^{10.0}{M}_{\odot }$ (middle), and $10^{10.2}{M}_{\odot }$ (right).

Figure 4

Redshift versus initial GW observed frequency ($f_{\min }$) at which binaries with $M_c={10}^{9.8}{M}_{\odot }$ (left), $10^{10.0}{M}_{\odot }$ (middle), and $10^{10.2}{M}_{\odot }$ (right) are detectable, assuming ten-year observations. Red and dark grey areas contain undetectable or merged binaries, respectively. The color of blue-green areas gives the $S/N$ of detectable binaries consistent with the EPTA upper limit [14]. Light-shaded areas contain binaries in the merger and ringdown phases.

Figure 5

Horizon distances for aLIGO (left), LISA (middle), and PPTA (right). The assumed observing time is five years for LISA and ten for PPTA. For aLIGO, the observing time is irrelevant given the short duration of binaries in band. Blue-green colors give the maximum $S/N$, whereas red areas contain undetectable binaries. Thin black lines are contours of optimal $f_{\min }$. Blue dots are the binary candidates of [33].