Polarization test of gravitational waves from compact binary coalescences

Gravitational waves have only two polarization modes in general relativity. However, there are six possible modes of polarization in a generic metric theory of gravity. Thus, tests of gravitational-wave polarization can be tools for pursuing the nature of space-time structure. The observations of gravitational waves with a worldwide network of interferometric detectors such as Advanced LIGO, Advanced Virgo, and KAGRA will make it possible to obtain the information of gravitational-wave polarization from detector signals. We study the separability of the polarization modes for the inspiral gravitational waves from the compact binary coalescences systematically. Unlike some other waveforms such as burst, the binary parameters need to be properly considered. We show that three polarization modes of gravitational waves would be separable with the global network of three detectors to some extent, depending on the signal-to-noise ratio and the duration of the signal. We also show that with four detectors the three polarization modes would be more easily distinguished by breaking a degeneracy of the polarization modes and even the four polarization modes would be separable.

Figure 1

Parameter estimation errors in the waveform model T. The colors are $10M_{\odot }-10M_{\odot }$ with HLV (magenta), $10M_{\odot }-10M_{\odot }$ with HLVK (red), $1.4M_{\odot }-1.4M_{\odot }$ with HLV (cyan), and $1.4M_{\odot }-1.4M_{\odot }$ with HLVK (blue). The reason for the rapid change of $\mathrm{\Delta }{\psi }_p$ at around 3 is because we impose the priors for parameters having the range, angular parameters, and spin parameters of binary compact stars.

Figure 2

Parameter estimation errors in the waveform model TS1. The colors are $10M_{\odot }-10M_{\odot }$ with HLV (magenta), $10M_{\odot }-10M_{\odot }$ with HLVK (red), $1.4M_{\odot }-1.4M_{\odot }$ with HLV (cyan), and $1.4M_{\odot }-1.4M_{\odot }$ with HLVK (blue).

Figure 3

Parameter estimation errors of the additional polarization amplitudes assumed as 1 for all models. The colors are $10M_{\odot }-10M_{\odot }$ with HLV (magenta), $10M_{\odot }-10M_{\odot }$ with HLVK (red), $1.4M_{\odot }-1.4M_{\odot }$ with HLV (cyan), and $1.4M_{\odot }-1.4M_{\odot }$ with HLVK (blue).

Figure 4

The vertical axes are the estimation errors multiplied by the SNR and the correlation coefficients in the case of model TS1, and the horizontal one is the upper-frequency end used in evaluating the parameter estimation by Fisher analysis. The colors are $10M_{\odot }-10M_{\odot }$ with HLV (magenta), $10M_{\odot }-10M_{\odot }$ with HLVK (red), $1.4M_{\odot }-1.4M_{\odot }$ with HLV (cyan), and $1.4M_{\odot }-1.4M_{\odot }$ with HLVK (blue).

Figure 5

Scatter plots of the error of the nontensorial polarization amplitudes vs the estimation error of the inclination angle for BNSs in model TVxS2. The colors are $1.4M_{\odot }-1.4M_{\odot }$ with HLV (cyan) and $1.4M_{\odot }-1.4M_{\odot }$ with HLVK (blue).

Figure 6

Scatter plots of the error of the nontensorial polarization amplitude $A_{V_x}$ vs the estimation error of the inclination angle for BNSs in model TV. The colors are $1.4M_{\odot }-1.4M_{\odot }$ with HLV (cyan) and $1.4M_{\odot }-1.4M_{\odot }$ with HLVK (blue).

Figure 7

A scatter plot of the error of the nontensorial polarization amplitudes vs the estimation error of the inclination angle in model TS2. The colors are $10M_{\odot }-10M_{\odot }$ with HLV (magenta), $10M_{\odot }-10M_{\odot }$ with HLVK (red), $1.4M_{\odot }-1.4M_{\odot }$ with HLV (cyan), and $1.4M_{\odot }-1.4M_{\odot }$ with HLVK (blue).

Figure 8

The vertical axes are the estimation errors and the correlation coefficients in the case of model TS1, and the horizontal one is the fiducial values of the amplitude parameter $A_{S_1}$ used in evaluating the parameter estimation by Fisher analysis. The colors are $10M_{\odot }-10M_{\odot }$ with HLV (magenta), $10M_{\odot }-10M_{\odot }$ with HLVK (red), $1.4M_{\odot }-1.4M_{\odot }$ with HLV (cyan), and $1.4M_{\odot }-1.4M_{\odot }$ with HLVK (blue).