Unveiling the Emission Mechanisms of Blazar PKS 1510−089. III. Relationship between the γ -Ray Variability and the Parsec-scale Jet

Over a 17 yr period, we analyze the multiwavelength relationship in the blazar PKS 1510-089, utilizing γ -ray, multifrequency radio (15, 43, and 230 GHz), optical spectra, and photometric data. Spearman rank correlations suggest that γ -ray production is cospatial with the 43 GHz quasi-stationary core (Q0), while the remaining decoupled from the 15 GHz core ( K 0) due to frequency-dependent opacity. A kinematic analysis identified nine superluminal components (Q2 − Q10) and a stationary feature (Q1) at ∼2.0 pc that we interpret as a downstream accelerator. To investigate the long-term evolution of jet opacity and flaring dynamics, we performed a time-resolved cross correlation analysis by dividing the dataset into four temporal epochs characterized by distinct quiescent γ -ray states. These results reveal that the kinematic transitivity of the jet is state dependent: while plasma disturbances propagate through successive τ ∼ 1 surfaces with clear, resolvable delays during quiescent and discrete flaring epochs, massive energy injections act as a low-pass filter, where extreme optical depth and spatial blending temporarily disrupt this kinematic coherence. Finally, the emergence of component Q10 in 2024 as a γ -ray dark event suggests a fundamental restructuring of the radiative environment of the jet following the 2021 high-energy quenching, likely driven by a depletion of external seed photons or enhanced internal γ -ray opacity.