The assembly of cosmic structure from baryons to black holes with joint gravitational-wave and X-ray observations

The evolution of structure, how the first black holes form and grow and the environments and baryonic content in which they reside remain largely outstanding questions in astrophysics and fundamental physics. They will be the focus of major observational programmes in the coming decade(s), using different probes to reconstruct a full picture of the physical processes at work. In particular, the X-ray Athena mission and the gravitational-wave Laser Interferometer Space Antenna (LISA) offer two independent and complementary angles to tackle these problems. Here we explore some of the science opportunities that would open up if observatories with capabilities comparable to Athena and LISA were to operate simultaneously, and not in different epochs as currently planned. We show that at least a handful of systems containing a massive black hole in the mass range ~ 10^5 - 10^8 Msun discovered by LISA at redshift ~ 1-to-5 could be monitored by Athena in an exposure time up to 1 Ms if prompt X-ray emission at the level of ~ 0.1% - 10% of the Eddington luminosity is present. We also show that Athena can plausibly detect diffuse X-ray emission from the hot gas of the environment hosting a ~ 10^8 Msun massive black hole binary at z <~ 1. The large uncertainties reflect the poor theoretical understanding of these complex physical processes, which in turn emphasises the vast discovery space that these joint observations would access, and therefore the potential for significant discoveries and surprises.