Geometrical Expression for the Angular Resolution of a Network of
  Gravitational-Wave Detectors
  We report for the first time general geometrical expressions for the angular
resolution of an arbitrary network of interferometric gravitational-wave (GW)
detectors when the arrival-time of a GW is unknown. We show explicitly elements
that decide the angular resolution of a GW detector network. In particular, we
show the dependence of the angular resolution on areas formed by projections of
pairs of detectors and how they are weighted by sensitivities of individual
detectors. Numerical simulations are used to demonstrate the capabilities of
the current GW detector network. We confirm that the angular resolution is poor
along the plane formed by current LIGO-Virgo detectors. A factor of a few to
more than ten fold improvement of the angular resolution can be achieved if the
proposed new GW detectors LCGT or AIGO are added to the network. We also
discuss the implications of our results for the design of a GW detector
network, optimal localization methods for a given network, and electromagnetic
follow-up observations.
