Premerger localization of gravitational-wave standard sirens with LISA: Harmonic mode decomposition

The continuous improvement in localization errors (sky position and distance) in real time as LISA observes the gradual inspiral of a supermassive black hole (SMBH) binary can be of great help in identifying any prompt electromagnetic counterpart associated with the merger. We develop a new method, based on a Fourier decomposition of the time-dependent, LISA-modulated gravitational-wave signal, to study this intricate problem. The method is faster than standard Monte Carlo simulations by orders of magnitude. By surveying the parameter space of potential LISA sources, we find that counterparts to SMBH binary mergers with total mass M~10^5-10^7 M_Sun and redshifts z<~3 can be localized to within the field of view of astronomical instruments (~deg^2) typically hours to weeks prior to coalescence. This will allow targeted searches for variable electromagnetic counterparts as the merger proceeds, as well as monitoring of the most energetic coalescence phase. A rich set of astrophysical and cosmological applications would emerge from the identification of electromagnetic counterparts to these gravitational-wave standard sirens.