Accelerated binary black holes in globular clusters: forecasts and detectability in the era of space-based gravitational-wave detectors

TL;DR

This paper forecasts the detectability of line-of-sight accelerations in binary black hole mergers within globular clusters using future space-based gravitational wave detectors, linking cluster properties to observable signals.

Contribution

It introduces a comprehensive forecast of detectable accelerations in BBH mergers from globular clusters, considering cluster properties and cosmological distributions.

Findings

Larger metallicities increase detectable accelerations due to more lighter BBHs.

Smaller metallicities lead to fewer detections with more massive BBHs and larger LOSAs.

Cluster properties like virial radius influence the fraction of detectable accelerations.

Abstract

The motion of the center of mass of a coalescing binary black hole (BBH) in a gravitational potential imprints a line-of-sight acceleration (LOSA) onto the emitted gravitational wave (GW) signal. The acceleration could be sufficiently large in dense stellar environments, such as globular clusters (GCs), to be detectable with next-generation space-based detectors. In this work, we use outputs of the \textsc{cluster monte carlo (cmc)} simulations of dense star clusters to forecast the distribution of detectable LOSAs in DECIGO and LISA eras. We study the effect of cluster properties -- metallicity, virial and galactocentric radii -- on the distribution of detectable accelerations, account for cosmologically-motivated distributions of cluster formation times, masses, and metallicities, and also incorporate the delay time between the formation of BBHs and their merger in our analysis. We find that larger metallicities provide a larger fraction of detectable accelerations by virtue of a greater abundance of relatively lighter BBHs, which allow a higher number of GW cycles in the detectable frequency band. Conversely, smaller metallicities result in fewer detections, most of which come from relatively more massive BBHs with fewer cycles but larger LOSAs. We similarly find correlations between the virial radii of the clusters and the fractions of detectable accelerations. Our work, therefore, provides an important science case for space-based GW detectors in the context of probing GC properties via the detection of LOSAs of merging BBHs.