Even a Precessing Clock Is Right Twice per Orbit—The Superperiods of eRO-QPE2 and Challenges for Quasiperiodic Eruption Orbital Models

We present O − C (“observed minus calculated”) timing analysis of the quasiperiodic eruption (QPE) source eRO-QPE2 with a multimission X-ray campaign including 32 observed eruptions spanning a month (i.e., 325 cycles). For disk instability models, the O − C is consistent with a damped random walk of the recurrence, albeit with highly uncertain parameters. For models with an underlying orbital clock, we infer a period of P ∼ 2.24 hr and two hierarchical superperiodic modulations with periods of ∼4.4 days (∼47 P) and ≈95 days (≈1000 P). We found no negative period derivative, with (Formula presented) ∣Ṗ∣≲2×10−6 s s−1 at 3σ. This limits gravitational-wave decay disfavoring high-eccentricity white dwarfs and high-mass/eccentricity intermediate-mass black holes. For disk-collision models, where the (Formula presented) Ṗ from gas drag and the QPE integrated energy bound the local disk density, a main-sequence star is disfavored as extreme mass-ratio inspiral (EMRI) secondary unless debris streams are present. The correlated odd/even O − C disfavors both disk crossings per orbit being observed. Interpreting the data with one observed event per orbit, the short modulation is consistent with apsidal precession for a ∼ 140 Rg, e ≈ 0.1, and MBH ≈ 1.5 × 105 M⊙. The longer modulation (much less constrained) is inconsistent with EMRI nodal precession, and disk precession is allowed in a limited parameter volume, while a hierarchical triple with an outer black hole at ∼0.4 mpc and mass ∼(0.1–1) × MBH is viable. However, more robust EMRI trajectory models yield no reliable solution, possibly due to narrow likelihood peaks in a high-dimensional space with sparse data.