  Double-peaked line profiles are commonly considered a hallmark of rotating
disks, with the distance between the peaks a measure of the rotation velocity.
However, double-peaks can arise also from radiative transfer effects in
optically thick non-rotating sources. Utilizing exact solutions of the line
transfer problem we present a detailed study of line emission from
geometrically thin Keplerian disks. We derive the conditions for emergence of
kinematic double peaks in optically thin and thick disks, and find that it is
generally impossible to disentangle the effects of kinematics and line opacity
in observed double-peaked profiles. Unless supplemented by additional
information, a double-peaked profile alone is not a reliable indicator of a
rotating disk. In certain circumstances, triple and quadruple profiles might be
better indicators of rotation in optically thick disks.
