On the search of electromagnetic cosmological counterparts to coalescences of massive black hole binaries

We explore the nature of possible electromagnetic counterparts of coalescences of massive black hole binaries at cosmological distances detectable by the Laser Interferometer Space Antenna (LISA). An electromagnetic precursor, during the last year of gravitational wave (GW)-driven inspiral, or an afterglow within few years after coalescence, may highlight the position in the sky of galaxies hosting the LISA sources. We show that observations of precursors and afterglows are mutually exclusive, depending on the mass of the primary black hole. Precursors are expected to occur in binaries where the primary (more massive) black hole is heavier than similar to 10(7) M-circle dot. They may correspond to on-off states of accretion, that is, to a bright X-ray source decaying into quiescence before black hole coalescence, and are likely associated to disturbed galaxies showing signs of ongoing starbursts. Coalescences of lighter binaries, with masses less than or similar to 5 x 10(6) M-circle dot, lack of any precursor, as gas is expected to be consumed long before the GW-driven orbital decay. Such events would not be hosted by (massive) galaxies with an associated starburst, given the slow binary inspiral time compared to the typical time-scale of starbursts. In contrast, coalescence, for such light binaries, is followed by an electromagnetic afterglow, that is, an off-on accretion state rising in 20 yr. Using a cosmological merger tree algorithm, we show that future X-ray missions such as the XEUS will be able to identify, in 20-yr operation, almost all the massive BH binaries detectable by the LISA and, in only 5 yr, all the LISA sources at z > 6.