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We consider the optimal site selection of future generations of gravitational wave detectors. Previously, Raffai et al. optimized a 2-detector network with a combined figure of merit. This optimization was extended to networks with more than two detectors in a limited way by first fixing the parameters of all other component detectors. In this work we now present a more general optimization that allows the locations of all detectors to be simultaneously chosen. We follow the definition of Raffai et al. on the metric that defines the suitability of a certain detector network. Given the locations of the component detectors in the network, we compute a measure of the network's ability to distinguish the polarization, constrain the sky localization and reconstruct the parameters of a gravitational wave source. We further define the `flexibility index' for a possible site location, by counting the number of multi-detector networks with a sufficiently high Figure of Merit that include that site location. We confirm the conclusion of Raffai et al., that in terms of flexibility index as defined in this work, Australia hosts the best candidate site to build a future generation gravitational wave detector. This conclusion is valid for either a 3-detector network or a 5-detector network. For a 3-detector network site locations in Northern Europe display a comparable flexibility index to sites in Australia. However for a 5-detector network, Australia is found to be a clearly better candidate than any other location., Comment: 30 pages, 23 figures, 2 tables

We aim to find the optimal site locations for a hypothetical network of 1-3 triangular gravitational-wave telescopes. We define the following N-telescope figures of merit (FoMs) and construct three corresponding metrics: (a) capability of reconstructing the signal polarization; (b) accuracy in source localization; and (c) accuracy in reconstructing the parameters of a standard binary source. We also define a combined metric that takes into account the three FoMs with practically equal weight. After constructing a geomap of possible telescope sites, we give the optimal 2-telescope networks for the four FoMs separately in example cases where the location of the first telescope has been predetermined. We found that based on the combined metric, placing the first telescope to Australia provides the most options for optimal site selection when extending the network with a second instrument. We suggest geographical regions where a potential second and third telescope could be placed to get optimal network performance in terms of our FoMs. Additionally, we use a similar approach to find the optimal location and orientation for the proposed LIGO-India detector within a five-detector network with Advanced LIGO (Hanford), Advanced LIGO (Livingston), Advanced Virgo, and KAGRA. We found that the FoMs do not change greatly in sites within India, though the network can suffer a significant loss in reconstructing signal polarizations if the orientation angle of an L-shaped LIGO-India is not set to the optimal value of ~58.2deg(+k*90deg) (measured counterclockwise from East to the bisector of the arms)., Comment: 28 pages, 18 figures