Rotation Curve Anomaly and Galactic Warp in M 51

We revisit the anomaly of rotation curve in the nearly face-on galaxy M 51 that shows an apparently faster decrease of rotation velocity than the Keplerian law in the outer disk, further showing apparent counter rotation in the outermost H i disk. We interpreted this anomaly as being due to warping of the galactic disk, and determined the warping structure of M 51's disk using the tilted-ring method, while assuming that the intrinsic rotation curve is normal. It has been shown that the disk is nearly flat in the inner disk at a constant inclination angle, but the disk suddenly bends at radius 7.5 kpc by about 27°. The inclination angle, then, decreases monotonically outward, reaching a perfect face-on ring at 18 kpc, beyond which the disk is warped in the opposite sense to the inner disk, resulting in apparent counter rotation.