Probing nontensorial gravitational waves with a next-generation ground-based detector network

In general relativity, there are only two polarizations for gravitational waves. However, up to six polarizations are possible in a generic metric theory of gravity. Therefore, measuring the polarization content of gravitational waves provides an efficient way to test theories of gravity. We analyze the sensitivity of a next-generation ground-based detector network to nontensorial polarizations. We present our method to localize gravitational wave signals in the time-frequency domain and construct the model-independent null stream for events with known sky locations. We obtain results based on simulations of binary neutron star mergers in a six-detector network. For a single event at a luminosity distance $D_L=100\mathrm{Mpc}$, at $5\sigma$ confidence, the smallest amplitude for detection of scalar and vector modes relative to tensor modes are respectively $A_s=0.045$ and $A_v=0.014$. For multiple events in an averaged observing run of ten years, the detection limits at $5\sigma$ confidence are $A_s=0.05$ and $A_v=0.02$. If we are fortunate, a few strong events might significantly improve the limits.

Figure 1

An example of localizing GW signal. The network SNR is ${\rho }_{\mathrm{net}}=141.2$ in this case. The left panel shows the result of the normalized WDM transform, while the right panel shows the pixels that are selected for the polarization test.

Figure 2

Normalized sky maps of optimal network sensitivity at 100 Hz. The blue $△$ is the location of the pair of ET-like detectors, and the red $+$ signs stand for three CE-like detectors. The plots in each polarization category are normalized by the maximum value of the optimal network sensitivity before projection, which means that the maximum values of the left panels are one. The normalization factors are given in Eqs. (24)–(26).

Figure 3

The left panels show the relative amplitude sensitivity sky maps for scalar modes and vector modes, where the relative amplitude sensitivity is defined as the minimum $A_s$ or $A_v$ in sky position $\widehat{\mathrm{\Omega }}$ for $p$-value to reach the $5\sigma$ threshold. The resolution of the event’s sky location is 120 pixels in longitude and 60 pixels in latitude, and each pixel has a same solid angle. The histograms on the right are the distribution of the minimum relative amplitudes. The minimum relative amplitude sensitivities for scalar modes and vector modes are given in Eqs. (27)–(28) and the mean values are given in Eqs. (29)–(30).

Figure 4

Combined $p$-value against the number of BNS events with ${\rho }_{\mathrm{net}}>350$. Each line denotes a different relative amplitude for scalar modes (left) or vector modes (right). The horizontal dashed line corresponds to the $5\sigma$ level.