Long Photometric Cycles in Double Periodic Variables from Nodal Precession of a Tilted Accretion Disk

Abstract

We investigate whether the long photometric cycles observed in double-periodic variables (DPVs) can arise from nodal precession of a tilted accretion disk driven by the tidal torque of the companion. Within a simple analytical framework, we derive testable relations linking the long-to-orbital period ratio to the binary mass ratio, the normalized disk size, and the disk tilt angle $\beta$, which itself can be inferred from the long-cycle amplitude, orbital inclination $i$, and disk luminosity fraction. The model naturally reproduces the two observed long-cycle light-curve morphologies -- sinusoidal and double-hump -- distinguished by the geometric criterion $i+\beta \le 90^\circ$ versus $i+\beta>90^\circ$. Applying these relations to a sample of DPVs, we find that the inferred disk sizes are physically reasonable and consistent with independent light-curve modeling for a non-negligible subset of systems. Our results show that tidal nodal precession represents a viable and potentially important contributor to the long-period variability of DPVs and provide a quantitative framework for future observational and theoretical studies.