Rogue echoes from exotic compact objects

Binary systems containing exotic, ultracompact stars may emit repeated bursts of gravitational waves (GWs) following inspiral and merger. The detection of such GW ``echoes'' would be a smoking-gun-signature of new physics, but searches for them have not yielded a convincing detection. In this talk I will show that the delay time between a the initial GW event and its echoes is generically much greater than expectations. I will describe a general argument and provide several specific examples where the time delays can be billions of years, resulting in rogue echoes that are not correlated with GW events and evade tailored searches. However, such echoes may be detectable by unmodeled searches for transient GW events.