  Radio-mode AGN feedback plays a key role in the evolution of galaxy groups
and clusters. Its physical origin lies in the kpc-scale interaction of AGN jets
with the intracluster medium. Large-scale jet simulations often initiate light
internally-supersonic jets with density contrast $0.01<\eta<1$. Here we argue
for the first time for the importance of very-light ($\eta<0.01$)
internally-subsonic jets. We investigated the shapes of young X-ray cavities
produced in a suite of hydrodynamic simulations, and found that bottom-wide
cavities are always produced by internally-subsonic jets, while
internally-supersonic jets inflate cylindrical, center-wide, or top-wide
cavities. We found examples of real cavities with shapes analogous to those
inflated in our simulations by internally-subsonic and internally-supersonic
jets, suggesting a dichotomy of AGN jets according to their internal Mach
numbers. We further studied the long-term cavity evolution, and found that old
cavities resulted from light jets spread along the jet direction, while those
produced by very light jets are significantly elongated along the perpendicular
direction. The northwestern ghost cavity in Perseus is pancake-shaped,
providing tentative evidence for the existence of very light jets. Our
simulations show that very-light internally-subsonic jets decelerate faster and
rise much slower in the ICM than light internally-supersonic jets, possibly
depositing a larger fraction of jet energy to cluster cores and alleviating the
problem of low coupling efficiencies found previously. The internal Mach number
points to the jet's energy content, and internally-subsonic jets are
energetically dominated by non-kinetic energy, such as thermal energy, cosmic
rays, or magnetic fields.
