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 $\dot{P}\approx (1.7\pm 0.02)\times10^{-2}$ d d$^{-1}$ 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.

Figures (8)

• Figure 1: The soft X-ray light curve of Ansky from 2024-2026. Data were taken with the NICER (black), Swift (red), and XMM-Newton (blue) observatories. Gray shaded regions correspond to the $\pm1\sigma$ contours of $t_{\rm peak}$ measurements from our timing model (Table \ref{['tab:peak_times']}).
• Figure 2: Example burst profile from an XMM-observed burst (Epoch 15, $t_{\rm peak}=60869.51$). The dark gray band shows the model $t_{\rm peak}$ error estimated via MCMC. The light gray band shows our additional 0.1 day systematic uncertainty, which accounts for the scatter in XMM and Swift data near the peak.
• Figure 3: Left:$O-C$ diagram of the QPEs overplotted with models 1-4. The data are consistent with $P_0\approx 9.5$ d and $\dot{P}\approx 1.7\times10^{-2}$ d d$^{-1}$ at $T_0\approx 60710.1$. In principle, it is possible that the apparent period increase is due to a long-term period oscillation observed locally (models 2 and 4); the $>1$ yr data baseline over which $\dot{P}$ is constant constrains any such oscillation to have a period $\gtrsim 11$ yr and amplitude $\gtrsim 1000$ d. Right: data$-$model residuals. Models 1-2 show structured residuals, which models 3-4 interpret as a sine with period $\sim 155$ d and amplitude $\sim 0.8$ d (though see Appendix \ref{['app:oc_noise']}).
• Figure 4: We plot the period evolution for the four $O-C$ models. Shaded regions denote the 2025 data (Epochs -2-29) and the range of periods observed in 2024. The inset panel extrapolates over $\sim$few hundred epochs, showing the constant $\dot{P}$ and long-term oscillation models begin to diverge after $\gtrsim100$ epochs.
• Figure 5: Evolution of $P_{\rm orb}$, $e$, and $M_*$ for various choices of ($e_0$, $\zeta$), assuming impulsive mass-loss occurs at pericenter, from Eqns. \ref{['eq:delta_P']}-\ref{['eq:delta_e']}. Each trajectory on the top/middle panels has a random offset (up to 0.1/0.05 respectively) for visual clarity.