Upper Limits on the Stochastic Gravitational-Wave Background from Advanced LIGO’s First Observing Run

A wide variety of astrophysical and cosmological sources are expected to contribute to a stochastic gravitational-wave background. Following the observations of GW150914 and GW151226, the rate and mass of coalescing binary black holes appear to be greater than many previous expectations. As a result, the stochastic background from unresolved compact binary coalescences is expected to be particularly loud. We perform a search for the isotropic stochastic gravitational-wave background using data from Advanced Laser Interferometer Gravitational Wave Observatory’s (aLIGO) first observing run. The data display no evidence of a stochastic gravitational-wave signal. We constrain the dimensionless energy density of gravitational waves to be ${\mathrm{\Omega }}_0<1.7\times {10}^{-7}$ with 95% confidence, assuming a flat energy density spectrum in the most sensitive part of the LIGO band (20–86 Hz). This is a factor of $\sim 33$ times more sensitive than previous measurements. We also constrain arbitrary power-law spectra. Finally, we investigate the implications of this search for the background of binary black holes using an astrophysical model for the background.

Figure 1

We show the estimator for ${\mathrm{\Omega }}_0$ in each frequency bin, along with $\pm 2\sigma$ error bars, in the frequency band that contains 99% of the sensitivity for $\alpha =0$. The loss of sensitivity at around 65 Hz is due to a zero in the overlap reduction function. There are several lines associated with known instrumental artifacts which do not lead to excess cross-correlation. The data are consistent with Gaussian noise, as described in the Results section.

Figure 2

Following [56], we present 95% confidence contours in the ${\mathrm{\Omega }}_{\alpha }-\alpha$ plane. The region above these curves is excluded at 95% confidence. We show the constraints coming from the final science run of Initial LIGO-Virgo [36] and from O1 data. Finally, we display the projected (not observed) design sensitivity to ${\mathrm{\Omega }}_{\alpha }$ and $\alpha$ for Advanced LIGO and Virgo [58].

Figure 3

Presented, here, are constraints on the background in PI form [59], as well as some representative models, across many decades in frequency. We compare the limits from ground-based interferometers from the final science run of Initial LIGO-Virgo, the colocated detectors at Hanford (H1–H2), Advanced LIGO (aLIGO) O1, and the projected design sensitivity of the advanced detector network assuming two years of coincident data, with constraints from other measurements: CMB measurements at low multipole moments [60], indirect limits from the cosmic microwave background (CMB) and big bang nucleosynthesis [61, 62], pulsar timing [62], and from the ringing of Earth’s normal modes [63]. We also show projected limits from a space-based detector such as LISA [59, 64, 65], following the assumptions of [59]. We extend the BNS and BBH distributions using an $f^{2/3}$ power-law down to low frequencies, with a low-frequency cutoff imposed where the inspiral time scale is of the order of the Hubble scale. In Fig. 5, we show the region in the black box in more detail.

Figure 4

Displayed, here, are the 95% confidence contours on the local rate and average chirp mass parameters, using the model described in the astrophysical implications section. In addition to the constraint from aLIGO O1 data, we show the constraint from the final science run of Initial LIGO-Virgo, and the projected design sensitivity of Advanced LIGO-Virgo. We also show the median rate with 90% uncertainty inferred from O1 data for the power-law and flat-log mass distributions [47], along with the band containing 68% of the chirp mass for each distribution. The gray band separates BNS from BBH backgrounds. The dip at $30M_{\odot }$ is due to the metallicity cutoff, as described in the astrophysical implications section.

Figure 5

We present a range of potential spectra for a BBH background, using the flat-log, power-law, and three-delta mass distribution models described in [47, 78], with the local rate inferred from the O1 detections [47]. For the flat-log and power-law distributions, we show the 90% Poisson uncertainty band due to the uncertainty in the local rate measurement. In addition, we show the measured O1 PI curve and the projected PI curve for Advanced LIGO-Virgo operating at design sensitivity.