Highest-Resolution Rotation Curve of the Inner Milky Way proving the Galactic Shock Wave

We present a rotation curve (RC) of the inner Galaxy of the 1st quadrant at $10\deg \le l \le 50\deg ~ (R=1.3-6.2~{\rm kpc})$ with the highest spatial (2 pc) and velocity (1.3 km/s) resolutions. We used the ${^{12}}$CO(J=1-0)-line survey data observed with the Nobeyama 45-m telescope at an effective angular resolution of $20"$ (originally $15")$, and applied the tangent-velocity method to the longitude-velocity diagrams by employing the Gaussian deconvolution of the individual CO-line profiles. A number of RC bumps, or local variation of rotation velocity, with velocity amplitudes $\pm \sim 9$ km/s and radial scale length $\sim 0.5-1$ kpc are superposed on the mean rotation velocity. The prominent velocity bump and corresponding density variation around $R\sim 4$ kpc in the tangential direction of the Scutum arm (4-kpc molecular arm) is naturally explained by an ordinary galactic shock wave in a spiral arm with small pitch angle, not necessarily requiring a bar-induced strong shock. Tables of RC are available at the PASJ supplementary data site and http://www.ioa.s.u-tokyo.ac.jp/~sofue/h-rot.htm.