Non-Gaussianity analysis of a gravitational wave background made by short-duration burst signals

We study an observational method to analyze non-Gaussianity of a gravitational wave (GW) background made by superposition of weak burst signals. The proposed method is based on fourth-order correlations of data from four detectors, and might be useful to discriminate the origin of a GW background. With a formulation newly developed to discuss geometrical aspects of the correlations, it is found that the method provides us with linear combinations of two interesting parameters, $I_2$ and $V_2$ defined by the Stokes parameters of individual GW burst signals. We also evaluate sensitivities of specific detector networks to these parameters.

Figure 1

In the detector network ($D$) frame, the direction of a GW source $\widehat{\mathit{n}}$ is characterized by two angles $D=({\theta }_D,{\varphi }_D)$. In the source ($S$) frame, the direction of the detector network is given by $S=({\theta }_S,{\varphi }_S)$. On the plane normal to the propagation direction $-\widehat{\mathit{n}}$, projections of two $z$ axes (${\theta }_D=0$ and ${\theta }_S=0$) are offset by the polarization angle $\psi$. These five angular parameters fix the relative configuration of two frames other than the distance between them.

Figure 2

Schematic picture for the four effective detectors $A_1$, $E_1$, $A_2$, and $E_2$ made from two triangle units of BBO. In the long-wave approximation, the positional differences between detectors can be neglected and responses to GWs can be identified for the $A_1\mathrm{\text{−}}{A}_2$ pair and $E_1\mathrm{\text{−}}{E}_2$ pair. Two detectors $A_1{E}_1$ have an offset angle 45° (same for $A_2{E}_2$), and their noises are uncorrelated.

Figure 3

Dependence of $⟨K⟩$ and ${\mathrm{SNR}}_K$ on the adjustable parameter $T_{\mathrm{seg}}$. The minimum value $f^{-1}$ of the length $T_{\mathrm{seg}}$ is set by the time resolution at the target frequency $f$ of interest. We can estimate the signal duration $T_d$ by identifying the transition of the slopes for the signal $⟨K⟩$.

Figure 4

Analysis for gravitational wave background from population III SN with BBO. We have the scaling relations ${\mathrm{SNR}}_{C2}\propto r{\mathrm{SNR}}_{bst}^2$ and ${\mathrm{SNR}}_K\propto r{\mathrm{SNR}}_{bst}^4$. The typical model parameters used in the main text are ${\mathrm{SNR}}_{bst}=0.6$ (individual burst strength) and $r=0.01{\sec }^{-1}$ (burst rate). We put the observational time $T_{\mathrm{obs}}=10\mathrm{yr}$, the bandwidth $\Delta f=0.3\mathrm{Hz}$ and $W=5/14$. The dashed line at the upper right is $S_{\mathrm{GW}}=S_N$ for the weak signal condition used in our formulation [see Eq. (65)]. The vertical dashed line ${\mathrm{SNR}}_{bst}=1$ shows the boundary for weak undetectable signals.