Popcorn in the sky: Identifying primordial black holes in the gravitational-wave background

Primordial black holes (PBHs) are possible sources of a gravitational-wave background (GWB), detectable with the next observing runs of LIGO--Virgo--KAGRA. In case of a detection, it will be crucial to distinguish the possible sources of this GWB. One under-explored possibility is to exploit the duty cycle that quantifies the number of sources present in the time domain signal, which can be very different depending on the nature and population of the sources. We compute the duty cycle for a realistic population of PBH binaries, isolating the shot-noise, popcorn and continuous contributions to the GWB. We identify the dependence of the duty cycle on the signal frequency, duration and amplitude as a crucial metric for distinguishing PBHs from other sources in the GWB and constraining PBH models. Our work motivates the development of specific analysis tools to extract these observables, in order to unlock new cosmological insights with upcoming GW data.