Finding the electromagnetic counterparts of cosmological standard sirens

The gravitational waves (GWs) emitted during the coalescence of supermassive black holes (SMBHs) in the mass range similar to 10(4) - 10(7) M-circle dot/(1 + z) will be detectable out to high redshifts with the future Laser Interferometer Space Antenna (LISA). The distance and direction to these standard sirens'' can be inferred directly from the GW signal, with a precision that depends on the masses, spins, and geometry of the merging system. In a given cosmology, the LISA-measured luminosity distance translates into a redshift shell. We calculate the size and shape of the corresponding three-dimensional error volume in which an electromagnetic counterpart to a LISA event could be found, taking into account errors in the background cosmology ( as expected by the time LISA flies), weak gravitational lensing (de) magnification due to inhomogeneities along the line of sight, and potential source-peculiar velocities. Weak-lensing errors largely exceed other sources of uncertainties (by a factor of similar to 7 for typical sources at z = 1). Under the plausible assumption that SMBH-SMBH 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 three-dimensional LISA error volume, as a function of BH mass and event redshift. Low redshifts offer the best opportunities to identify quasar counterparts to cosmological standard sirens. For mergers of similar to 4; (10(5)-10(7)) M-circle dot SMBHs, the LISA error volume will typically contain a single near-Eddington quasar at z similar to 1. If SMBHs are spinning rapidly, the error volume is smaller and may contain a unique quasar out to redshift z similar to 3. This will allow a straightforward test of the hypothesis that GW events are accompanied by bright quasar activity and, if the hypothesis proves correct, will guarantee the identification of a unique quasar counterpart to a LISA event, with a B-band luminosity of L-B similar to (10(10)-10(11)) L-circle dot. Robust counterpart identifications would allow unprecedented tests of the physics of SMBH accretion, such as precision measurements of the Eddington ratio. They would clarify the role of gas as a catalyst in SMBH coalescences and would also offer an alternative method to constrain cosmological parameters.