The gravitational waves ( GW ) emitted during the coalescence of supermassive black holes ( SMBHs ) in the mass range \sim ( 10 ^ { 4 } – 10 ^ { 7 } ) { M _ { \odot } } / ( 1 + z ) will be detectable out to high redshifts with the future Laser Interferometric 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 \sim 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 \sim ( 4 \times 10 ^ { 5 } -10 ^ { 7 } ) { M _ { \odot } } SMBHs , the LISA error volume will typically contain a single near-Eddington quasar at z \sim 1 .
If SMBHs are spinning rapidly , the error volume is smaller and may contain a unique quasar out to redshift z \sim 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 } \sim ( 10 ^ { 10 } -10 ^ { 11 } ) { L _ { \odot } } .
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 .