A stochastic search for intermittent gravitational-wave backgrounds

A likely source of a gravitational-wave background (GWB) in the frequency band of the Advanced LIGO, Virgo, and KAGRA detectors is the superposition of signals from the population of unresolvable stellar-mass binary-black-hole (BBH) mergers throughout the Universe. Since the duration of a BBH merger in band ($\sim 1\mathrm{s}$) is much shorter than the expected separation between neighboring mergers ($\sim {10}^3\mathrm{s}$), the observed signal will be “popcornlike” or intermittent with duty cycles of order ${10}^{-3}$. However, the standard cross-correlation search for stochastic GWBs currently performed by the LIGO-Virgo-KAGRA Collaboration is based on a continuous-Gaussian signal model, which does not take into account the intermittent nature of the background. The latter is better described by a Gaussian mixture model, which includes a duty cycle parameter that quantifies the degree of intermittence. Building on an earlier paper by Drasco and Flanagan [Detection methods for non-gaussian gravitational wave stochastic backgrounds, Phys. Rev. D 67, 082003 (2003).], we propose a stochastic-signal-based search for intermittent GWBs. For such signals, this search performs better than the standard continuous cross-correlation search. We present results of our stochastic-signal-based approach for intermittent GWBs applied to simulated data for some simple models, and we compare its performance to the other search methods, in terms of both detection and signal characterization. Additional testing on more realistic simulated datasets, e.g., consisting of astrophysically motivated BBH merger signals injected into colored detector noise containing noise transients, will be needed before this method can be applied with confidence on real gravitational-wave data.

Figure 1

ln Bayes factors of the $\mathrm{signal}+\mathrm{noise}$ model to the noise-only model as a function of the duty cycle $\xi$ for the intermittent search (blue) and the continuous search (orange) where the signal consists of single sample bursts drawn from a Gaussian distribution of variance ${\sigma }_b^2$.

Figure 2

Left: Example of simulated data with amplitudes drawn from a uniform-in-volume distribution along with a subplot zooming in on a single burst. The parameters used for this injection are given in the “Extension of previous work” section of Table 1. Right: Distribution of the burst variances drawn from a uniform-in-volume distribution, with theoretical minimum and maximum burst variances evaluated at $r_{\max }$ and $r_{\min }$, respectively, and average burst variance $⟨{\sigma }_b^2⟩$ computed according to (29).

Figure 3

Corner plot for the full version of the SSI analysis, combining the posteriors of 100 realizations of the data. The black lines show the injected values of the parameters used for the simulated data, and the three shaded regions for the two-dimensional joint posteriors correspond to $1\sigma$, $2\sigma$, and $3\sigma$ uncertainty levels. All parameters are recovered within a $1\sigma$ credible interval.

Figure 4

Left: Example of one stochastic burst in the time-domain. Right: Averaged power spectral density of a population of stochastic burst signals as a function of frequency for the noise and signal separately, along with their theoretical predictions according to the injected values.

Figure 5

For intermittent, stochastic bursts with an $f^{-7/3}$ power spectrum, we demonstrate recovery of our search (left) and compare it to that of a deterministic-signal-based search (right). Our search recovers the injected signal parameters within a $1\sigma$ credible interval, while DSI recovers the uniform prior on $r_{\max }$ and the lower boundary of the prior imposed on the duty cycle ($\xi ={10}^{-4}$). Thus, the DSI analysis finds no signal in the data.

Figure 6

Left: Example BBH chirp signal in the time domain as given by (41). Right: Averaged power spectral density of an ensemble of BBH chirp signals as a function of frequency for the noise and signal separately, together with their theoretical predictions according to the injected values.

Figure 7

Plots of the ln Bayes factor averaged over 100 data realizations for SSC and SSI (left) and DSI (right) for deterministic chirp signals occurring with various values of the duty cycle $\xi$. Both intermittent searches are well-suited for detecting signals with a low duty cycle.

Figure 8

Left: Posterior corner plot combined over 100 data realizations analyzed with SSI reduced (blue) and DSI reduced (green). Both searches recover the injected signal parameters ($\xi =2.98\times {10}^{-3}$ and $⟨{\mathrm{\Omega }}_b⟩=0.803$) within a $1\sigma$ confidence interval. The recovered values and error bars are those recovered by the SSI reduced search. Right: The 1D posterior plot of ${\mathrm{\Omega }}_{\mathrm{gw}}$ samples from SSI reduced (blue), SSC reduced (orange), and DSI reduced (green) constructed by combining posterior samples for $\xi$ and $⟨{\mathrm{\Omega }}_b⟩$ using (13). Note, the inference done with the DSI likelihood gives posterior samples for the parameters $\xi$ and $r_{\max }$, and the values of $r_{\max }$ are then converted to samples in $⟨{\mathrm{\Omega }}_b⟩$ by (38), since the other variables in (38) are fixed and known.

Figure 9

Left: Comparison of recovered values to the injected value of ${\mathrm{\Omega }}_{\mathrm{gw}}$ for SSI reduced (blue), SSC reduced (orange), and DSI reduced (green) for different values of the duty cycle. All injected parameters are equivalent to the parameters used in the left panel of Fig. 7, and the recovered values are those after combining 100 realizations of data. The shaded regions represent the $1\sigma$ credible interval of the combined 100 realizations of data. Right: ln Bayes factor vs $N_{\mathrm{seg}}$ for data with $⟨{\rho }_{\mathrm{seg},\mathrm{stoch}}⟩=2$ and $\xi =2.98\times {10}^{-3}$. We define a detection threshold of $\ln \mathcal{B}=12.5$. SSI crosses this threshold after $\sim 12,000$ segments of data, while SSC crosses this threshold after $\sim 650,000$ segments of data, corresponding to a factor of improvement in detecting the signal of roughly 54 for SSI relative to SSC.