Accelerated detection of the binary neutron star gravitational-wave background

Most gravitational-wave signals from binary neutron star coalescences are too weak to be individually resolved with current detectors. We demonstrate how to extract a population of subthreshold binary neutron star signals using Bayesian parameter estimation. Assuming a merger rate of one signal every 2 hours, we find that this gravitational-wave background can be detected after approximately 3 months of observation with Advanced LIGO and Virgo at design sensitivity, versus several years using the standard cross-correlation algorithm. We show that the algorithm can distinguish different neutron star equations of state using roughly 7 months of Advanced LIGO and Virgo design-sensitivity data. This is in contrast to the standard cross-correlation method, which cannot.

Figure 1

A spectrogram of 200 s of simulated data showing 13 binary neutron stars and one binary black hole merger (the black hole merger is the third signal from left to right). Our strategy for detecting the binary neutron star background is based around searching for signals above a low-frequency cutoff $f_{\mathrm{low}}=100\mathrm{Hz}$ (red dotted line), where binary neutron star signals can be cleanly separated into data segments on the order of 16 s in duration, even though the signals overlap at lower frequencies.

Figure 2

Time to detection of a binary neutron star background. Top panel: Posterior distributions for the binary neutron star duty cycle $\xi$ recover the true value. We simulate aLIGO and Virgo data with a realistic binary neutron star duty cycle of $\xi =0.002$, which corresponds to observing all subthreshold events in the Universe out to a maximum luminosity distance of 1 Gpc. The three posterior distributions show the duty cycle at three different observation times, showing that this eventually becomes unbiased for long observation times. Bottom panel: Evolution of the log Bayes factor showing we can detect the binary neutron star gravitational-wave background after ${97}_{-17}^{+32}$ days (one-sigma confidence), assuming a merger rate of one signal every 2 hours.

Figure 3

Evolution of the average log BF as a function of time comparing two different equations of state, SLY and H4, for 30 different realizations of the background. The black dotted line is the detection threshold $\log (\mathrm{BF})=8$, which is reached after ${221}_{-51}^{+140}$ days of observation. This threshold is reached using exclusively sub-threshold signals.