A positive period derivative in the quasi-periodic eruptions of ZTF19acnskyy

Abstract: We report the first direct measurement of the period derivative in a quasi-periodic eruption (QPE), finding a smoothly increasing period with $\dot{P}\approx (1.7\pm 0.02)\times10<sup>{-2}$ d d$<sup>{-1}$ in the source ZTF19acnskyy/"Ansky". Most models for QPEs invoke repeated interactions of a stellar-mass orbiting companion around the supermassive black hole (SMBH) in an extreme mass-ratio inspiral (EMRI). In these scenarios, a positive $\dot{P}$ is surprising, but not impossible to produce. We explore several possible explanations for the observed $\dot{P}$, including stable mass-transfer driven by impulsive mass loss events in an EMRI, velocity kicks at pericenter due to tidal interactions with the SMBH, apparent period changes due either to general relativistic precession effects in an EMRI or light travel-time delays in a hierarchical SMBH binary, and mass-transfer variations in a thermal/viscous disk instability model. We find that none of the considered models provides a complete explanation for the data, motivating further work on physical explanations for positive period derivatives in QPEs.