Detecting very long-lived gravitational-wave transients lasting hours to weeks

We explore the possibility of very long-lived gravitational-wave transients (and detector artifacts) lasting hours to weeks. Such very long signals are both interesting in their own right and as a potential source of systematic error in searches for persistent signals, e.g., from a stochastic gravitational-wave background. We review possible mechanisms for emission on these time scales and discuss computational challenges associated with their detection: namely, the substantial volume of data involved in a search for very long transients can require vast computer memory and processing time. These computational difficulties can be addressed through a form of data compression known as coarse graining, in which information about narrow frequency bins is discarded in order to reduce the computational requirements of a search. Using data compression, we demonstrate an efficient radiometer (cross-correlation) algorithm for the detection of very long transients. In the process, we identify features of a very long transient search (related to the rotation of the Earth) that make it more complicated than a search for shorter transient signals. We implement suitable solutions.

Figure 1

The daily modulation of $\mathfrak{p}$. Each panel shows a $(\delta t,\mathrm{\Delta }f)=(158\mathrm{s},1\mathrm{Hz})$ spectrogram consisting of two consecutive days of data. The data consist of Advanced LIGO [36] Monte Carlo noise plus a simulated signal at $f=100\mathrm{Hz}$. The top-left panel (a) shows $\mathrm{Re}(\mathfrak{p})$ while the top-right panel (b) shows $\mathrm{Im}(\mathfrak{p})$. In the top panels, the injected signal, for illustrative purposes, is very loud: $h_0=1\times {10}^{-22}$. (Since the signals are very loud, the color bar is saturated.) At $t=0$, the phase angle is in the lower-right quadrant of the $\mathfrak{p}$ complex plane where $\mathrm{Re}(\mathfrak{p})>0$ and $\mathrm{Im}(\mathfrak{p})<0$. It rotates clockwise so that $\mathrm{Re}(\mathfrak{p})$ crosses zero and becomes negative before $\mathrm{Im}(\mathfrak{p})$ crosses zero and becomes positive. The bottom-left panel (c) shows $\mathrm{Re}[\exp (-i{\mathrm{\Psi }}_i)\mathfrak{p}]$ for a much weaker signal: $h_0=4\times {10}^{-24}$. The phase factor is applied to make the signal entirely real; see Eq. (a1). The bottom-right panel (d) shows the recovered signal (the most significant cluster identified in the bottom-left panel) recovered with $2\times {10}^6$ seedless clustering templates (see Sec. 5 for details). The source is located at $(\mathrm{ra},\mathrm{dec})=(18.5\mathrm{hr},+39°)$ and it is recovered 7° degrees away at $(18.9\mathrm{hr},+35°)$. The recovery algorithm does not assume that the signal is monochromatic.

Figure 2

Recovery of a very long transient signal with seedless clustering. Top-left (a): A $(\delta t,\mathrm{\Delta }f)=(158\mathrm{s},1\mathrm{Hz})$ spectrogram of $\rho (t;f|\widehat{\mathrm{\Omega }})$ [Eq. (a3)] consisting of one day of data. The data consist of Advanced LIGO Monte Carlo noise plus a simulated signal. The signal begins at $f=100\mathrm{Hz}$ and increases with a spin-up given by $\dot{f}=20\mathrm{Hz}{\mathrm{day}}^{-1}$. The amplitude is $h_0=4\times {10}^{-24}$. The signal persists between $t\approx 5–17\mathrm{hr}$. (It grows very faint after $t\approx 12\mathrm{hr}$ due the unfavorable orientation of the Earth during this period.) Top-right (b): The recovered signal recovered with $2\times {10}^6$ cubic Bézier templates; ${\mathrm{SNR}}_{\mathrm{tot}}=11$. Bottom-left (c): A $(\delta t,\mathrm{\Delta }f)=(158\mathrm{s},1\mathrm{Hz})$ spectrogram of $\rho (t;f|\widehat{\mathrm{\Omega }})$ consisting of two weeks of data. The data consist of Advanced LIGO Monte Carlo noise plus a simulated signal. The signal begins at $f=100\mathrm{Hz}$ and increases with a spin-up given by $\dot{f}=10\mathrm{Hz}{\mathrm{day}}^{-1}$. The amplitude is $h_0=4\times {10}^{-24}$. The signal persists between $t\approx 3–10\mathrm{days}$. Bottom-right (d): The recovered signal of the most significant cluster identified in the bottom-left panel recovered with $2\times {10}^6$ cubic Bézier templates; ${\mathrm{SNR}}_{\mathrm{tot}}=67$.