Multiwavelength variability of the high-energy neutrino candidate PKS 0735+178 over three decades
We present the multiwavelength variability of the BL Lac object PKS 0735+178, associated with the high-energy neutrino event IC211208A. The light curves cover the radio (1-230 GHz), optical, and Fermi-LAT $\gamma$-ray bands over a $\sim$30 years time-scale. The light curves are correlated, with delays from 0 to 1200 days increasing towards lower frequencies, consistent with emission from an opacity-stratified jet. The bright flare after the IC211208A event indicates emission from a compact, optically thick region with enhanced activity and more efficient particle acceleration. Short optical and $\gamma$-ray bursts have been detected very close to the neutrino event, within a few days. The $\sim$12-day lag between the $\gamma$-ray and optical emissions is detected for the first time, suggesting that the emission regions are not co-spatial. A characteristic variability time-scale of $\sim$10-11 yr is robustly detected in the radio-mm bands ($\geq3\sigma$), while the optical and $\gamma$-ray data show weaker, shorter-period signals. The independent constraints from the VLBI core-shift measurements and radio time delays yield consistent estimates of the jet geometry and disturbance propagation, supporting variability governed by jet propagation effects. The long-term modulation is consistent with a slow variation in energy release at the jet base, while individual flares arise from shocks propagating downstream. Jet precession may contribute to the long-term modulation; however, the required viewing angles are inconsistent with the VLBI constraints, indicating that precession alone cannot explain the observed variability.