  Two mechanisms of two-color (\omega + 2\omega) laser-induced field-free
molecular orientation, based on the hyperpolarizability and ionization
depletion, are explored and compared. The CO molecule is used as a
computational example. While the hyperpolarizability mechanism generates small
amounts of orientation at intensities below the ionization threshold,
ionization depletion quickly becomes the dominant mechanism as soon as ionizing
intensities are reached. Only the ionization mechanism leads to substantial
orientation (e.g. on the order of |<cos\theta>| > 0.1). For intensities typical
of laser-induced molecular alignment and orientation experiments, the two
mechanism lead to robust, characteristic timings of the field-free orientation
wave-packet revivals relative to the the alignment revivals and the revival
time. The revival timings can be used to detect the active orientation
mechanism experimentally.
