Localization of gravitational wave sources with networks of advanced detectors

Coincident observations with gravitational wave (GW) detectors and other astronomical instruments are among the main objectives of the experiments with the network of LIGO, Virgo, and GEO detectors. They will become a necessary part of the future GW astronomy as the next generation of advanced detectors comes online. The success of such joint observations directly depends on the source localization capabilities of the GW detectors. In this paper we present studies of the sky localization of transient GW sources with the future advanced detector networks and describe their fundamental properties. By reconstructing sky coordinates of ad hoc signals injected into simulated detector noise, we study the accuracy of the source localization and its dependence on the strength of injected signals, waveforms, and network configurations.

Figure 1

Amplitude spectral density of the design noise for the second-generation detectors.

Figure 2

The distributions of the network antenna factor $\mathcal{F}$ (left plots) and the network alignment factor $\alpha$ (right plots) at the frequency of 100 Hz as a function of latitude ($\theta$) and longitude ($\varphi$) for the networks $\mathrm{H}\tilde{\mathrm{H}}\mathrm{LV}$, ÃHLV, AHLV, HJLV, and AHJLV (from top to bottom).

Figure 3

Example of the likelihood sky map $L_{\mathrm{sky}}$ for an injected signal in the HLV network at $\theta =-30°$ and $\varphi =144°$: $L_{\mathrm{sky}}$ as a function of $\theta$ and $\varphi$ (top plot), and the $L_{\mathrm{sky}}$ distribution around the reconstructed location (bottom plot).

Figure 4

Median error angle vs average detector SNR obtained with the unmodeled algorithm for all types of injections and different network configurations: HLV, AHLV, HJLV, and AHJLV.

Figure 5

Median error angle for HLV, AHLV, HJLV, and AHJLV networks (from top to bottom) as a function of source coordinates ($\theta$—latitude, $\varphi$—longitude) for injections with the network $\mathrm{SNR}<30$.

Figure 6

Fraction of the sky (vertical axis) for three-site ($\mathrm{LH}\tilde{\mathrm{H}}\mathrm{V}$), four-site (AHLV and HJLV), and five-site (AHJLV) networks where sources (all waveform types with ${\rho }_{\mathrm{net}}<30$) are reconstructed with a given 50% (top panel) and 90% (bottom panel) error region (horizontal axis).

Figure 7

Median error angle vs SNR for the HLV network comparing different constraint searches. Top panel: SGQ9 LF waveform with unmodeled (black line) and linear (grey line) searches. Bottom panel: SGCQ9 LF with unmodeled (black line) and circular (grey line) searches.

Figure 8

Normalized residual energy $\Delta$ vs network SNR obtained with the unmodeled algorithm and the HLV network for all types of injections.

Figure 9

Dependence of $F_{+}$ (top plot, at $\theta =-30°$ and $\varphi =72°$) and the reconstruction accuracy on the polarization angle $\psi$ for two types of waveforms: linearly polarized SGQ9 LF waveforms (middle plot) and randomly polarized WNB LF waveforms (bottom plot).