Finding the electromagnetic counterparts of cosmological standard sirens

The gravitational waves (GW) emitted during the coalescence of supermassive black holes (SMBHs) in the mass range 10^4-10^7 M_sun will be detectable out to high redshifts with LISA. We calculate the size and orientation of the three-dimensional error ellipse in solid angle and redshift within which the LISA event could be localized using the GW signatures alone. We take into account uncertainties in LISA's measurements of the luminosity distance and direction to the source, in the background cosmology, in weak gravitational lensing magnification due to inhomogeneities along the line of sight, and potential source peculiar velocities. We find that weak lensing errors exceed other sources of uncertainties by nearly an order of magnitude. Under the plausible assumption that BH mergers are accompanied by gas accretion leading to Eddington-limited quasar activity, we then compute the number of quasars that would be found in a typical LISA error volume, as a function of BH mass and redshift. We find that low redshifts offer the best opportunities to identify quasar counterparts to cosmological standard sirens, and that the LISA error volume will typically contain a single near-Eddington quasar at z=1. This will allow a straightforward test of the hypothesis that BH mergers are accompanied by bright quasar activity and, if the hypothesis proves correct, will guarantee the identification of a unique quasar counterpart. This would yield unprecedented tests of the physics of SMBH accretion, and offer an alternative method to precisely constrain cosmological parameters.