A Helical Trajectory Interpretation of a Multi-wavelength Event in a Blazar S5 0716+714

Abstract: Relativistic jets in blazars exhibit strong variability across multiple timescales, but the connection between temporal variability and the evolution of jet structures remains poorly understood. In this work, we investigate the $γ$-ray variability of the BL Lac object S5 0716+714 from July 2014 to June 2015 and explore its possible connection with the parsec-scale jet evolution. We identify an escalating periodic oscillation (EPO) in the $γ$-ray light curve, characterized by a sequence of successive flux enhancements with progressively increasing temporal separations. Combining \textit{Fermi}-LAT data with contemporaneous 43 GHz Very Long Baseline Array (VLBA) observations, we find a temporal association between the EPO and the downstream propagation of a superluminal knot. A helical trajectory model simultaneously fitting the $γ$-ray variability and the two-dimensional VLBA component positions reproduces the observed flux modulation and component motion. These results suggest that geometric Doppler modulation caused by the changing viewing angle of a moving jet component provides a possible explanation for the observed EPO. This work provides a framework of connecting blazar variability to the knot evolution of relativistic jets.