Revisiting orbital recurrence in the dimmings of Boyajian's star (KIC~8462852)

Abstract

KIC~8462852 (Boyajian's star) shows deep, asymmetric, and highly irregular dimming events with no simple repetition pattern. A symmetric 1.1\% transit detected by \emph{TESS} in 2019 has been interpreted as a possible giant planet or brown dwarf, while the irregular dips are generally attributed to transiting dust from exocomets or planetesimal fragments. We test whether the broader dip families may nevertheless recur orbitally. Our scenario assumes a major disruption that produced fragments with slightly different periods, causing successive returns to spread progressively in orbital phase. We compare this recurrent model with a null hypothesis of chronologically independent family centers, accounting for the observing window, and marginalize over the recurrence period $P$ and dispersion scale $σ_P$. We obtain $B_{10}=44.9$ in favor of recurrence, corresponding to ``very strong'' evidence on the Jeffreys scale. The maximum-likelihood solution is $P_{\rm ML}=781.6$~d and $σ_{P,\rm ML}=80.0$~d, close to the 776.1-d timescale obtained if D800 and the 2019 \emph{TESS} event are separated by four revolutions. Independently of the timing fit, this period predicts a transit duration of about 20.5~h for the published stellar and transit parameters, in close agreement with the observed $\sim21$~h. The result is conditional on the adopted topology, priors, family definition, and observing selection function, and does not prove orbital recurrence. Nevertheless, the family timings strongly favor this specific recurrent-fragment model over independent occurrence, making progressive orbital phase dispersion a viable and physically motivated interpretation.