Acceleration and Collimation of the Two-Sided Jets in the Nearby Low-luminosity Active Galactic Nucleus NGC 4261 (3C 270)

We study the acceleration and collimation of the two-sided jets in the nearby low-luminosity active galactic nucleus NGC 4261 (3C 270) using archival multifrequency, multi-epoch Very Long Baseline Array data. By applying multiple analysis methods and incorporating results from the literature, we robustly identify a parabolic-to-conical structural transition in both the jet and counterjet, with the transition occurring at $(1.23\pm0.24)\,$pc or $(8.1\pm1.6)\times10^3\,R_{\rm s}$ (Schwarzschild radii) for the jet and $(0.97\pm0.29)\,$pc or $(6.4\pm1.9)\times10^3\,R_{\rm s}$ for the counterjet. Assuming that the brightness asymmetry between the twin jets is primarily due to relativistic Doppler (de)boosting, we derive the jet velocity field at distances of $\sim (10^3-2\times10^4)\,R_{\rm s}$ based on the jet-to-counterjet brightness ratio and spectral index. Although local kinematic variations are present, the jet shows an overall acceleration to relativistic speeds from $\sim 10^3$ to $\sim8\times10^3\,R_{\rm s}$, with a maximum Lorentz factor of $\Gamma_{\rm max} \approx 2.6$. Beyond this region, the jet gradually decelerates to sub-relativistic speeds. These results support the existence of a (sub)parsec-scale ($\lesssim 1.5\,$pc) acceleration and collimation zone (ACZ) in NGC 4261, where the jet is accelerated via magnetic-to-kinetic energy conversion while being confined by external pressure. A brief comparison with M 87 suggests that the ACZ in NGC 4261 may represent a scaled-down analogue of that in M 87.