tokens: of signal-to-noise ratio (S/N), and found it to be well described by a power-law function, . is about 0.01 mas in the innermost jet region where , and 0.1 mas downstream of the jet where , corresponding to 1/50 and 1/5 of the beam size, respectively. Therefore, we consider the upper limit of the imaging error to be because the jet radii are measured where the jet is detected when (see also Homan et al. 2002 , Appendix A for similar analysis). Note that we assume the time variability of the jet radius is negligible. 3.3. Radius Profile of the Jet Figure 2 shows the distribution of jet radius ( r ) as a function of the deprojected distance to the core ( z ), which we refer to as the radius profile of the jet. The jet viewing angle ( θ ) for deprojection is uncertain within an upper limit of 47° (Jones Wehrle 2002 ). We adopt θ = 19° derived from a detection of a sub-parsec scale counter-jet (Sudou et al. 2000 ). An independent model of the spectral energy distribution (SED) suggests a consistent result of θ ≃ 18° (Chiaberge et al. 2003 ). We use the deprojected length scale ( mas −1 ) along the jet throughout the rest of the paper. Note that the jet radius, as defined perpendicular to the jet axis, is not affected by projection effects. Figure 2. Top panel: the radius profile of the NGC 6251 jet in units of Schwarzschild radius ( r s ) and parsecs, using archival VLBA data at 15 and 5 GHz (green and blue triangles), and our EVN(-i, ii, iii) data at 1.6 GHz with three weighting schemes (violet square, cross, and circle). The single (orange solid line) and double (brown solid line) power-law models are fitted to the profile, where we show the case of the sharpness parameter n = 100 here. Statistics ( f -test) shows that the data are better fitted by double power-law models (with all n ) than by a single power law (see also Section 3 ). Furthermore, the double power-law model is also supported by the VLA data (gray plus signs) and VLBI cores (gray triangles and squares), as discussed in Section 4.1 . Note that the VLA data and VLBI cores are not included in the regression analysis. Middle and bottom panels: the relative residuals of the jet radii for the single () and double () power-law models. The single power law shows a systematic deviation at the two ends of the distance scale, while the double power laws (i.e., for all n ) show uniformly distributed relative residuals on all distance scales. We conclude that the jet structure is described by a parabolic shape upstream () and a conical shape downstream () with a transition located at a characteristic distance z 0 = (1–2) × 10 5 r s (brown dashed line), which is fairly close to the sphere of gravitational influence (SGI) of the SMBH (, black dashed line) in order of magnitude. 3.4. Collimation Profile by Power-law Models Collimation profiles are generally described by power-law functions with some local features, as a manifestation of the global evolution of jet structure. We perform
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