Searching for stochastic gravitational waves using data from the two colocated LIGO Hanford detectors

Searches for a stochastic gravitational-wave background (SGWB) using terrestrial detectors typically involve cross-correlating data from pairs of detectors. The sensitivity of such cross-correlation analyses depends, among other things, on the separation between the two detectors: the smaller the separation, the better the sensitivity. Hence, a colocated detector pair is more sensitive to a gravitational-wave background than a noncolocated detector pair. However, colocated detectors are also expected to suffer from correlated noise from instrumental and environmental effects that could contaminate the measurement of the background. Hence, methods to identify and mitigate the effects of correlated noise are necessary to achieve the potential increase in sensitivity of colocated detectors. Here we report on the first SGWB analysis using the two LIGO Hanford detectors and address the complications arising from correlated environmental noise. We apply correlated noise identification and mitigation techniques to data taken by the two LIGO Hanford detectors, H1 and H2, during LIGO’s fifth science run. At low frequencies, 40–460 Hz, we are unable to sufficiently mitigate the correlated noise to a level where we may confidently measure or bound the stochastic gravitational-wave signal. However, at high frequencies, 460–1000 Hz, these techniques are sufficient to set a 95% confidence level upper limit on the gravitational-wave energy density of $\mathrm{\Omega }(f)<7.7\times 10^{-4}(f/900\mathrm{Hz}{)}^3$, which improves on the previous upper limit by a factor of $\sim 180$. In doing so, we demonstrate techniques that will be useful for future searches using advanced detectors, where correlated noise (e.g., from global magnetic fields) may affect even widely separated detectors.

Figure 1

Coherence ${\widehat{\mathrm{\Gamma }}}_{12}$ between H1 and H2 computed in the frequency band 80–160 Hz using all of the S5 data, for three different frequency resolutions: 1 mHz, 10 mHz, and 100 mHz (from top panel to bottom). The insets show that the histograms of the coherence at the analyzed frequencies follow the expected exponential distribution for Gaussian noise, as well as the presence of a long tail of high coherence values at notched frequencies. A stochastic broadband GW signal of $\mathrm{SNR}=5$ would appear at a level of $\lesssim 10\times \text{below}$ the dashed $1/N$ line.

Figure 2

Same as Fig. 1 but at higher frequencies, 460–1000 Hz. Note the coherence peaks at the harmonics of the 60 Hz power lines (notched in the analysis). The elevated coherence near 750 Hz at 100 mHz resolution is due to acoustic noise coupling to the GW channels. The long tail in the 100 mHz plot is due to excess noise around 750 Hz, which was removed from the final analysis using PEM notchings (see Sec. 5). A stochastic broadband GW signal of $\mathrm{SNR}=5$ would appear at a level of $\lesssim 10\times$ below the dashed $1/N$ line.

Figure 3

Comparison of the (absolute value of the) SNRs calculated by the PEM-coherence and time-shift techniques. The vertical dotted lines indicate the frequency bands used for the low- (80–160 Hz; black dotted lines) and high-frequency (460–1000 Hz; magenta dotted lines) analyses. Note that ${\mathrm{SNR}}_{{\mathrm{\Omega }}_{\alpha },\text{TS}}(f)$ is a true signal-to-noise ratio, so values $\lesssim 2$ are dominated by random statistical fluctuations. ${\mathrm{SNR}}_{{\mathrm{\Omega }}_{\alpha },\mathrm{PEM}}(f)$, on the other hand, is an estimate of the PEM contribution to the signal-to-noise ratio, so values even much lower than 2 are meaningful measurements (i.e., they are not statistical fluctuations). The two methods agree very well in identifying contaminated frequency bins or bands. Note that both methods indicate that the 80–160 Hz and 460–1000 Hz bands have relatively low levels of contamination.

Figure 4

Spectrograms displaying the absolute value of ${\mathrm{SNR}}_{\mathrm{\Omega },\mathrm{PEM}}(f)$ for 80–160 Hz (left panel) and 460–1000 Hz (right panel) as a function of the week in S5. The horizontal dark (blue) bands correspond to initial frequency notches as described in Step 2 (Sec. 5) and vertical dark (blue) lines correspond to unavailability of data due to detector downtime. The large SNR structures seen in the plots were removed from the low- and high-frequency analyses.

Figure 5

Plots of ${\widehat{\mathrm{\Omega }}}_3(f)$ and ${\widehat{\mathrm{\Omega }}}_{3,\mathrm{PEM}}(f)$ (left panels), and the inverse Fourier transform of ${\widehat{\mathrm{\Omega }}}_3(f)$ (right panels), for the (noisiest) 628–733 Hz subband after various stages of noise removal were applied to the data. The four rows correspond to the four different stages of cleaning defined in Table 1. (The top right plot has $y$-axis limits $13\times \text{greater}$ than the other three.)

Figure 6

Plots of ${\widehat{\mathrm{\Omega }}}_3(f)$ and ${\widehat{\mathrm{\Omega }}}_{3,\mathrm{PEM}}(f)$ (left panel), and the inverse Fourier transform of complex ${\widehat{\mathrm{\Omega }}}_3(f)$ (right panel) for the full band (460–1000 Hz) after the final stage of noise removal cuts.

Figure 7

Running point estimates ${\widehat{\mathrm{\Omega }}}_3$ and ${\widehat{\mathrm{\Omega }}}_0$ for the high-frequency (460–1000 Hz) and low-frequency (80–160 Hz) analyses, respectively (left and right panels). The final stage of noise removal cuts has been applied for both analyses.

Figure 8

Plots of ${\widehat{\mathrm{\Omega }}}_0(f)$ and ${\widehat{\mathrm{\Omega }}}_{0,\mathrm{PEM}}(f)$ (left panels), and the inverse Fourier transform of ${\widehat{\mathrm{\Omega }}}_0(f)$ (right panels) for the 80–160 Hz band after various stages of noise removal were applied to the data. The four rows correspond to the four different stages of cleaning defined in Table 1.

Figure 9

(Left panel) Recovered spectrum for a software injection with an amplitude ${\mathrm{\Omega }}_3=5.6\times 10^{-3}$ ($\mathrm{SNR}\sim 17$). (Right panel) The inverse Fourier transform of the recovered ${\widehat{\mathrm{\Omega }}}_3(f)$ and a $\pm 10\mathrm{ms}$ zoom in around zero lag.

Figure 10

Upper limits from the current H1-H2 analysis, previous SGWB analyses and the projected advanced LIGO limit, along with various SGWB models. The BBN limit is an integral limit on ${\mathrm{\Omega }}_{\text{gw}}$ i.e., $\int {\mathrm{\Omega }}_{\text{gw}}(f)d(lnf)$ in the $10^{-10}–10^{10}\mathrm{Hz}$ band derived from the big bang nucleosynthesis and observations of the abundance of light nuclei [28, 49]. The measurements of CMB and matter power spectra provide a similar integral bound in the frequency range of $10^{-15}–10^{10}\mathrm{Hz}$ [50]. The pulsar limit is a bound on the ${\mathrm{\Omega }}_{\text{gw}}(f)$ at $f=2.8\mathrm{nHz}$ and is based on the fluctuations in the pulse arrival times from millisecond pulsars [51]. In the above figure, the slow-roll inflationary model [52] assumes a tensor-to-scalar ratio of $r=0.2$, the best fit value from the BICEP2 analysis [13]. In the axion based inflationary model, for certain ranges of parameters the backreaction during the final stages of inflation is expected to produce strong GWs at high frequencies [53]. The stiff equation of state (EOS) limit corresponds to scenarios in the early Universe (prior to BBN) in which GWs are produced by an unknown “stiff” energy [54]. For the above figure we used the equation of state parameter $w=0.6$ in the stiff EOS model. The cosmic string model corresponds to GWs produced by cosmic strings in the early Universe [55]. The Earth’s normal mode limits are based on the observed fluctuations in the amplitudes of Earth’s normal modes using an array of seismometers [56]. The astrophysical SGWBs (BBH and BNS) are due to the superposition of coalescence GW signals from a large number of binary black holes (BBH) and binary neutron stars (BNS) [57].