Upper limits on a stochastic gravitational-wave background using LIGO and Virgo interferometers at 600–1000 Hz

A stochastic background of gravitational waves is expected to arise from a superposition of many incoherent sources of gravitational waves, of either cosmological or astrophysical origin. This background is a target for the current generation of ground-based detectors. In this article we present the first joint search for a stochastic background using data from the LIGO and Virgo interferometers. In a frequency band of 600–1000 Hz, we obtained a 95% upper limit on the amplitude of ${\Omega }_{\mathrm{GW}}(f)={\Omega }_3(f/900\mathrm{Hz}{)}^3$, of ${\Omega }_3<0.32$, assuming a value of the Hubble parameter of $h_{100}=0.71$. These new limits are a factor of seven better than the previous best in this frequency band.

Figure 1

Plot of the overlap reduction function (ORF) for the pairs of sites used in this analysis. The dashed curve is the ORF for the two LIGO sites (HL), the solid curve is for the Hanford-Virgo sites (HV), and the dashed-dotted curve is for Livingston-Virgo (LV). We see that the LIGO orientations have been optimized for low-frequency searches, around 10–100 Hz. However, this ORF falls off rapidly with frequency, such that at frequencies over $\sim 500\mathrm{Hz}$, the amplitude of the ORF of the HL pair is smaller than that of the Virgo pairs. The LV and HV overlap reduction functions oscillate more with frequency, but fall off more slowly, due to the larger light-travel time between the USA and Europe.

Figure 2

Posterior PDFs on ${\Omega }_3$. The dashed line shows the posterior PDF obtained using just the LIGO detectors, the solid line shows the PDF obtained using LIGO and Virgo detectors. The filled areas show the 95% probability intervals.

Figure 3

Sensitivity integrands for the LIGO-only result (dashed) and for the full LIGO-Virgo result (solid). We can see that the sensitivity is increased across the band by the addition of the Virgo interferometer to the search. The vertical lines correspond to frequency bins removed from the search.

Figure 4

95% probability intervals on ${\Omega }_{\alpha }$, calculated using different values of $\alpha$. These upper limits were all calculated using the same data, with a band width of 600–1000 Hz and a reference frequency of 900 Hz. The dashed line shows the upper limit calculated using the LIGO interferometers only, while the solid line shows the upper limits calculated using all of the available data. The lower limits were all zero.

Figure 5

Plot of the recovered values of ${\Omega }_3$ for five software injections. The error bars show the 95% probability intervals. The quietest injection had a lower limit equal to zero. Note that all analyses excluded H2. Each injection used the same data, with the simulated signal scaled to different amplitudes.

Figure 6

Comparison of the strain sensitivity of two searches for an isotropic stochastic background of gravitational waves. The two solid grey lines show strain sensitivity of the Hanford 4 km interferometer (dark grey) and the Virgo interferometer (light grey), these spectra were obtained by averaging over the data analyzed in this paper. The dot-dashed line shows the main result of this paper, the search for a SGWB with ${\Omega }_{\mathrm{GW}}(f)\propto f^3$, which is white in strain amplitude, and corresponds to an upper limit of ${\Omega }_3<0.32$. The dashed line shows the result of the same search, but for constant ${\Omega }_{\mathrm{GW}}(f)$, and corresponds to an upper limit of ${\Omega }_0<0.16$. The solid black line shows the strain sensitivity of the LIGO-ALLEGRO search, which corresponds to an upper limit of ${\Omega }_0<1.02$ and was calculated over a frequency range of $850\mathrm{Hz}\le f\le 950\mathrm{Hz}$ [18]. The two dotted lines show the extrapolation of the spectra obtained by the analysis of LIGO data in the frequency band $40\mathrm{Hz}\le f\le 500\mathrm{Hz}$. The lower dotted line corresponds to a 95% upper limit of ${\Omega }_0<6.9\times {10}^{-6}$, while the upper dotted line corresponds to an upper limit of ${\Omega }_3<0.0052$ at a reference frequency of 900 Hz.