Prospects for gravitational-wave polarization tests from compact binary mergers with future ground-based detectors

There exist six possible polarization modes of gravitational waves in a general metric theory of gravity, while two tensor polarization modes are allowed in general relativity. The properties and number of polarization modes depend on gravity theories. For transient signals, the number of the detectors needs to be basically equal to the number of the gravitational-wave polarization modes for separation of polarizations. However, a single detector having great sensitivity at lower frequency could be effectively regarded as a virtual detector network including a set of detectors along its trajectory due to a long gravitational-wave signal from a compact binary and the Earth’s rotation. Thus, time-varying antenna pattern functions can help test the polarizations of gravitational waves. We study the effects of the Earth’s rotation on the polarization test and show a possibility to test the nontensorial polarization modes from future observations of compact binary mergers with ground-based gravitational detectors such as Einstein telescope and Cosmic Explorer.

Figure 1

Sensitivity curves for the third-generation gravitational-wave detectors such as Einstein telescope and Cosmic Explorer. The Einstein telescope has two sensitivity estimates, ET-B and ET-D. The sensitivity curve for the ideal detector that has better low-frequency constant sensitivity than ET-D below 400 Hz is also shown.

Figure 2

Time to merger as a function of frequency for $1.4-1.4M_{\odot }$ (green), $10-10M_{\odot }$ (red), and $30-30M_{\odot }$ (blue).

Figure 3

Cumulative histograms for parameter estimation errors for $1.4-1.4M_{\odot }$ BNS at $z=0.1$ in the model TS1 with a single 3G detector. The colors are with ET-B (green), ET-D (red), CE (magenta), and ideal (blue).

Figure 4

Medians of parameter estimation errors for $1.4-1.4M_{\odot }$ BNS at $z=0.1$ when changing the lower cutoff frequency $f_{\min }$ in the case of ET-D. The range below 5 Hz is important for the polarization test.

Figure 5

Medians of parameter estimation errors for $1.4-1.4M_{\odot }$ BNS at $z=0.1$ when changing the fiducial value of $A_{S1}$ in the case of an ET-D. The error of $A_{S1}$ is hardly changed when the fiducial values are less than $1/10$, giving the detection limit.

Figure 6

Compact binary merger rate distribution based on the Madau plot with the flat-in-log delay-time distribution. The overall factors of the star formation rate density are based on the BNS merger rate $1540{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$ [7] and the BBH merger rate $53.2{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$ [78].