rotation curveA plot of the rotational velocity, V , as a function of radius, R , in a spiral galaxy (see illustration). Rotation curves are an important tool in mapping the distribution of mass in a galaxy. The velocity increases rapidly with distance from the center of the galaxy, and then remains approximately constant, even in the outermost parts of the visible galaxy. This implies that the mass is not centrally concentrated, as might be expected, but is distributed into a dark halo extending up to five times the radius of the optical disk. The rotation velocities are measured from the Doppler shift in stellar absorption lines or the emission line spectra of H II regions in the plane of the galaxy. Neutral hydrogen extends farther than the luminous matter of a galactic disk and radio observations can trace out the rotation curve to radii of tens of kiloparsecs.