GW150914: Implications for the stochastic gravitational wave background from binary black holes

Abstract

The LIGO detection of the gravitational wave transient GW150914, from the inspiral and merger of two black holes with masses $\gtrsim 30\, \text{M}_\odot$, suggests a population of binary black holes with relatively high mass. This observation implies that the stochastic gravitational-wave background from binary black holes, created from the incoherent superposition of all the merging binaries in the Universe, could be higher than previously expected. Using the properties of GW150914, we estimate the energy density of such a background from binary black holes. In the most sensitive part of the Advanced LIGO/Virgo band for stochastic backgrounds (near 25 Hz), we predict $Ω_\text{GW}(f=25 Hz) = 1.1_{-0.9}^{+2.7} \times 10^{-9}$ with 90\% confidence. This prediction is robustly demonstrated for a variety of formation scenarios with different parameters. The differences between models are small compared to the statistical uncertainty arising from the currently poorly constrained local coalescence rate. We conclude that this background is potentially measurable by the Advanced LIGO/Virgo detectors operating at their projected final sensitivity.

Figures (2)

• Figure 1: Expected sensitivity of the network of advanced LIGO and Virgo detectors to the Fiducial field model. Left panel: Energy density spectra are shown in blue (solid for the total background; dashed for the residual background, excluding resolved sources, assuming final advanced LIGO and Virgo cqg.27.084006.10cqg.32.074001.15 sensitivity). The pink shaded region "Poisson" shows the 90% CL statistical uncertainty, propagated from the local rate measurement, on the total background. The black power-law integrated curves show the $1\sigma$ sensitivity of the network expected for the two first observing runs O1 and O2, and for 2 years at the design sensitivity in O5. (O3 and O4 are not significantly different than O5; see Table \ref{['tab:phases']}.) If the astrophysical background spectrum intersects a black line, it has expected $\text{SNR} \geq 1$. In both panels we assume a coincident duty cycle of 33% for O1 (actual) and 50% for all other runs (predicted). Right panel: Predicted SNR as a function of total observing time. The blue lines and pink shaded region have the same interpretation as in the left panel. Each observing run is indicated by an improvement in the LIGO-Virgo network sensitivity Aasi:2013wya, which results in a discontinuity in the slope. The thresholds for $\text{SNR}=1$, $3$ (false-alarm probability $<3\times 10^{-3}$) and $5$ (false-alarm probability $< 6 \times 10^{-7}$) are indicated by horizontal lines.
• Figure 2: Energy density spectra for the different models summarized in the text. The pink shaded region "Poisson" shows the 90% CL statistical uncertainty propagated from the local rate measurement, on the Fiducial model. The black dashed curve shows the design sensitivity of the network of Advanced LIGO cqg.27.084006.10cqg.32.074001.15 and Virgo cqg.32.024001.15jpcs.610.012014.15; see Tab. \ref{['tab:phases']}. If the astrophysical background spectrum intersects with the dashed black line, it has expected $\text{SNR} \geq 1$.