Localization of binary mergers with gravitational-wave detectors of second and third generation

The observation of gravitational wave signals from binary black hole mergers has established the field of gravitational wave astronomy. It is expected that future networks of gravitational wave detectors will possess great potential in probing various aspects of astronomy. An important consideration for successive improvement of current detectors or establishment on new sites is knowledge of the minimum number of detectors required to perform precision astronomy. We attempt to answer this question by assessing ability of future detector networks in detecting and localizing binary neutron stars mergers in the sky. This is an important aspect as a good localization ability is crucial for many of the scientific goals of gravitational wave astronomy, such as electromagnetic follow-up, measuring the properties of compact binaries throughout cosmic history, and cosmology. We find that although two detectors at improved sensitivity are sufficient to get a substantial increase in the number of observed signals, at least three detectors of comparable sensitivity are required to localize majority of the signals, typically to within around 10 deg$^{2}$ --- adequate for follow-up with most wide field of view optical telescopes.