Multiwavelength quasi-periodic variability of the blazar Ton 599

During the last 40-50 years, the TeV blazar Ton 599 has systematically experienced major outbursts detected in a wide wavelength range from radio to $γ$-rays. In this work, we present an analysis of Ton 599 quasi-periodic variability across multiple wavelengths using an observing baseline from 1983 to 2025. The $γ$-ray, optical, and radio emissions are found to be highly correlated with time lags $\sim0$-$360$ days, which indicates that they are triggered by the same population of particles. Using the Lomb-Scargle periodogram and the Weighted Wavelet Z-transform, we revealed several periodic components with characteristic periods of 1.4, 1.7, 2.3, 6.5, and 7.5 yrs. The result is consistent with the detection of periodic components in the 1997-2011 light curves, which means that we observe the same mechanism causing long-term periodic variability. A model of a binary supermassive black hole (SMBH) with a precessing jet, applied to the radio light curves of Ton 599, yields frequency-dependent best-fitting parameters with orbital periods ranging from $\sim$1.2 to 1.7 yrs and precession periods from $\sim$5.8 to 7.7 yrs. This result implies the existence of an SMBH system modulating emission through both the orbiting and jet precession effects, with differing observed periods possibly reflecting frequency-dependent emission regions along a structured, stratified jet. Nonetheless, the short-term periodicity and exceptionally strong flares likely arise from internal jet shocks, which aligns with typical blazar behavior. We suggest that the multiband quasi-periodicity of Ton 599 is reasonably described by a combination of geometric effects (orbital motion and precession) and stochastic processes.