Mergers of Supermassive Black Hole Binaries in Gas-rich Environments: Models of Event Rates and Electromagnetic Signatures

Supermassive black holes permeate the observable Universe, residing in the nuclei of all or nearly all nearby massive galaxies and powering luminous quasars as far as ten billion light years away. These monstrous objects must grow through a combination of gas accretion and mergers of less massive black holes. The direct detection of the mergers by future gravitational-wave detectors will be a momentous scientific achievement, providing tests of general relativity and revealing the cosmic evolution of supermassive black holes. An additional -- and arguably equally rewarding -- challenge is the concomitant observation of merging supermassive black holes with both gravitational and electromagnetic waves. Such synergistic, "multi-messenger" studies can probe the expansion history of the Universe and shed light on the details of accretion astrophysics. This thesis examines the mergers of supermassive black hole binaries and the observable signatures of these events. First, we consider the formation scenarios for the earliest supermassive black holes. This investigation is motivated by the Sloan Digital Sky Survey observation of a quasar that appears to be powered by a supermassive black hole with a mass of billions of solar masses, already in place one billion years after the Big Bang. Second, we develop semianalytic, time-dependent models for the thermal emission from circumbinary gas disks around merging black holes. Our calculations corroborate the qualitative conclusion of a previous study that for black hole mergers detectable by a space-based gravitational-wave observatory, a gas disk near the merger remnant may exhibit a dramatic brightening of soft X-rays on timescales of several years. Our results suggest that this "afterglow" may become detectable more quickly after the merger than previously estimated. Third, we investigate whether these afterglow episodes could be observed serendipitously by forthcoming wide-field, high-cadence electromagnetic surveys. Fourth, we introduce a new subset of time-dependent solutions for the standard equation describing thin, viscous Keplerian disks. Finally, we apply these solutions to model the electromagnetic emission of accretion disks around supermassive black hole binaries that may be detectable with precision pulsar timing