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 $β$, 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 $i+β\le 90^\circ$ versus $i+β>90^\circ$. 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.

Figures (3)

• Figure 1: Schematic illustration (not to scale) of a tilted accretion disk undergoing nodal precession around the accretor. The accretor is located at the origin, and the binary orbital plane is defined as the $x$--$y$ plane. The observer's line of sight lies in the $x$--$z$ plane and is denoted by the unit vector $\hat{\boldsymbol{o}}$, while the unit vector along the disk angular momentum is denoted by $\hat{\boldsymbol{l}}$. This geometry defines the angles used in the derivation of the photometric modulation.
• Figure 2: Model-predicted disk radius normalized by the orbital separation, $(R_{\rm d}/a)_{\rm mod}$, as a function of the mass ratio $q$, for DPVs listed in Table \ref{['tab1']}. The dashed line shows the theoretical relation for a representative period ratio $P_{\rm long}/P_{\rm orb}=33$ with $\cos\beta=1$. The dotted line indicates the tidal radius $R_{\rm t}/a$. For some systems, error bars are absent or very small because uncertainties in the relevant input parameters are not reported or are negligible in the original references.
• Figure 3: Comparison between the disk radius inferred from the tilted-disk precession model, $(R_{\rm d}/a)_{\rm mod}$, and the observationally inferred values $(R_{\rm d}/a)_{\rm obs}$. Each point represents one of the 11 DPVs with available observational disk-radius estimates. The dashed line indicates equality. Uncertainty ellipses denote the $1\sigma$ uncertainties of individual systems.