  The Advanced Laser Interferometer Gravitational-wave Observatory (LIGO)
discovered gravitational waves (GWs) from a binary black hole merger in 2015
September and may soon observe signals from neutron star mergers. There is
considerable interest in searching for their faint and rapidly fading
electromagnetic (EM) counterparts, though GW position uncertainties are as
coarse as hundreds of square degrees. Because LIGO's sensitivity to binary
neutron stars is limited to the local universe, the area on the sky that must
be searched could be reduced by weighting positions by mass, luminosity, or
star formation in nearby galaxies. Since GW observations provide information
about luminosity distance, combining the reconstructed volume with positions
and redshifts of galaxies could reduce the area even more dramatically. A key
missing ingredient has been a rapid GW parameter estimation algorithm that
reconstructs the full distribution of sky location and distance. We demonstrate
the first such algorithm, which takes under a minute, fast enough to enable
immediate EM follow-up. By combining the three-dimensional posterior with a
galaxy catalog, we can reduce the number of galaxies that could conceivably
host the event by a factor of 1.4, the total exposure time for the Swift X-ray
Telescope by a factor of 2, the total exposure time for a synoptic optical
survey by a factor of 2, and the total exposure time for a narrow-field optical
telescope by a factor of 3. This encourages us to suggest a new role for small
field of view optical instruments in performing targeted searches of the most
massive galaxies within the reconstructed volumes.
