The warped disk is modeled as a set of concentric circular rings with inclinations varying fairly smoothly from 72 degrees at the center to 76 degrees at the edge. The fitted circular velocity of each ring, plotted against its radius, defines the rotation curve. The rotation curve of NGC 3198 can be modeled by combining the gravitational forces of a thin exponential disk, and a dark halo with a core and power-law envelope. 1.5 kpc . Warps The same observations which allow us to establish the presence of dark halos also show that the outer regions of disk galaxies are often warped.
Warps are very common.
Their conclusion was that isolated disks with realistic surface-density profiles cannot support warped modes. Such a mode would have to be realized from a combination of ingoing and outgoing bending waves, and the surface-densities of real galaxies taper much too smoothly to efficiently reflect outgoing waves. At large radii the halo presumably dominates the gravitational field and the tenuous outer disk should settle into the principal plane of the halo, while at small radii the gravitational attraction of adjacent rings of disk material tends to enforce a coplanar geometry. This model does an impressive job of reproducing the warp of NGC 4013. The two major lines of evidence considered above both favor the impression that dark halos are many times more massive than the disks they contain, that the dark matter is much more extended than the luminous component, that the core radii of dark halos are relatively large, and that halos are somewhat but not extremely flattened.