# Features of Structure and Absorption in the Jet-Launching Region of M87
## 3 Results
### Transverse Jet Structure
The ridgeline is presented in the left panels of Figure 3 as red curves superimposed on the contour plots. As our result shows, both limbs are tortuous within \(d\) = 1.30 mas; as going outward, the northern limb is still tortuous, while its southern counterpart becomes smooth. We present PAs of the intensity peak of both limbs as a function of \(d\) in Figure 4. The general trend is both limbs approach to the jet axis gradually as going outward, but there are some local structures seen on both limbs. We also notice that, if the structure measured at higher frequency is moved outward for 0.1 or 0.2 mas, then it looks quite consistent with that measured at the adjacent lower frequency. This apparent shift could possibly be attributed to a resolution effects which occur if there are gradients in the intensity for a jet. This is a combination of gradients in intensity, coupled with angular resolution depending on frequency. Within \(d\) = 1.30 mas, at 86 GHz, the northern limb is deflected northward at \(d\) = 1.05 mas, while at 43 GHz, the corresponding deflection is seen at \(d\) = 1.30 mas; at 86 GHz, the southern limb veers southward at \(d\) = 0.62 and 1.18 mas respectively, while at 43 GHz the corresponding changes are seen at \(d\) = 0.75 and 1.30 mas respectively. Beyond \(d\) = 1.30 mas, the northern limb becomes fragmentized, and its orientation changes abruptly at least at three locations (\(d\) = 1.45, 2.55 and 4.55 mas), a wiggle is seen between \(d\) = 1.70 and 2.30 mas, and an interruption is seen around \(d\) = 6.00 mas; on the contrary, the southern limb evolves smoothly as going outward, only a mild wiggle is seen between \(d\) = 3.00 and 4.00 mas, and its PA tends to be stable at \(\sim-10^{\circ}\) since \(d\) = 4.00 mas. In the following analysis, we move the jet structure measured at 86 GHz outward for 0.15 mas, and the structure measured at 22 GHz inward for 0.25 mas to eliminate the effect brought by different angular resolutions. We define the apparent jet opening angle \(\psi_{app}\) as the difference of PAs of two limbs. The panel (a) of Figure 5 shows \(\psi_{app}\) as a function of \(d\). The parabolic collimation profile, \(\psi_{app}\propto r^{0.58}\), determined  
Figure 4: (**a**) Position angles of the northern limb in M87 as functions of core distance \(d\). (**b**) Position angles of the southern limb in M87 as functions of core distance \(d\). The colors represent the measured frequencies, magenta for 86 GHz, blue for 43 GHz and green for 22 GHz. The uncertainty of PA is estimated as \(\frac{20^{\circ}}{\mathrm{SNR}}\), in which \(20^{\circ}\) is a typical width of the jet limb, and \(\mathrm{SNR}\) is the ratio between the intensity peak and the \(\sigma\) of images. only peaks with intensity above \(5\sigma\) are presented to make sure the result is reliable. by [11; 12], is also presented for reference. The overall jet generally evolves around the parabolic profile, but some local structural features are clearly seen. So we divide the jet into six segments, and each segment includes an expansion and a following recollimation: segment 1 includes an quick expansion between \(d=0.75\) and 0.90 mas, followed by a gradual recollimation between \(d=0.90\) and 1.30 mas; segment 2 includes an expansion between \(d=1.30\) and 1.45 mas, followed by a quick recollimation between \(d=1.45\) and 1.50 mas; segment 3 includes an gradual expansion between \(d=1.50\) and 2.00 mas, followed by a gradual recollimation between \(d=2.00\) and 2.55 mas; segment 4 includes a quick expansion between \(d=2.55\) and 2.60 mas, followed by a slow recollimation between \(d=2.60\) and 3.35 mas; segment 5 includes an expansion between \(d=3.35\) and 3.65 mas, followed by a gradual recollimation between \(d=3.65\) and 4.25 mas; segment 6 includes an expansion between \(d=4.25\) and 4.60 mas, followed by a recollimation beyond \(d=4.60\) mas. We define the apparent offset of jet center \(\delta_{app}\) as the arithmetic average of the PAs of two jet limbs as well.