We report multi-frequency VLBI studies of the sub-parsec scale structure of
the two-sided jet in the nearby radio galaxy NGC 4261. Our analyses include new
observations using the Source Frequency Phase Referencing technique with the
Very Long Baseline Array at 44 and 88 GHz, as well as archival data at 15 and
43 GHz. Our results show an extended double-sided structure at 43/44 GHz and
provide a clear image of the nuclear region at 88 GHz, showing a core size of
∼0.09 mas and a brightness temperature of ∼1.3×109 K. Proper
motions are measured for the first time in the two-sided jet, with apparent
speeds ranging from 0.31±0.14c to 0.59±0.40c in the approaching jet
and 0.32±0.14c in the receding jet. The jet-to-counter-jet brightness
ratio allows us to constrain the viewing angle to between ∼54∘ and
84∘ and the intrinsic speed to between ∼0.30c and 0.55c. We
confirm the parabolic shape of the upstream jet on both sides of the central
engine, with a power-law index of 0.56±0.07. Notably, the jet collimation
is found to be already completed at sub-parsec scales, with a transition
location of about 0.61 pc, which is significantly smaller than the Bondi radius
of 99.2 pc. This behavior can be interpreted as the initial confinement of the
jet by external pressure from either the geometrically thick, optically thin
advection-dominated accretion flows (ADAF) or the disk wind launched from it.
Alternatively, the shape transition may also be explained by the internal flow
transition from a magnetically dominated to a particle-dominated regime.Comment: 9 pages, 5 figures, 2 table