The advent of time-domain astronomy has made the discovery of transients, which are explosive and highly energetic astronomical phenomena that rise and fade on human timescales, commonplace, with tens of (e.g.) supernovae discovered on a nightly basis. The contemporaneous increase in the cadence and depth of astronomical surveys, which are telescopes (or arrays thereof) that pan hemispheres of the sky in search of new sources of light, has also provided insight into the evolution of transients on short timescales -- days to minutes following the initial explosion and detection. I will describe new self-similar solutions that characterize this early ``interaction phase'' of the explosions powering astrophysical transients, during which the explosion ejecta impinges upon the ambient medium surrounding the progenitor, creating a forward shock, reverse shock, and contact discontinuity ``shell'' that expands with time. These solutions describe the propagation of all three discontinuities, as well as the physical properties of the shocked ejecta and ambient gas, and temporally interpolate between the early ``coasting phase'' of the explosion and the eventual ``energy-conserving phase.'' These solutions are applicable to a wide array of transients, and I will briefly discuss their application to winds/outflows from tidal disruption events and high-energy stellar explosions that could power some fast-blue optical transients.
Eric Coughlin earned his B.Sc. in astrophysics from Lehigh University in 2011, and his PhD in astronomy and astrophysics from the University of Colorado at Boulder in 2016, where he worked on high-energy phenomena related to tidal disruption events. He was awarded the 2017 Dissertation Prize of the High-Energy Astrophysics Division of the American Astronomical Society, as well as an International Astronomical Union Thesis Prize, for the research comprising his doctoral work. After finishing his PhD he was an Einstein fellow at the University of California at Berkeley from 2016 to 2018, and at Columbia University from 2018 to 2019. He was subsequently a joint Hubble and Lyman Spitzer Junior fellow at Princeton University from 2019 to 2020, after which he joined the faculty in the physics department at Syracuse University in the Fall of 2020. Coughlin specializes in theoretical astrophysics, particularly in the fluid/gas dynamics of high-energy and explosive events.