  With MgH^+ ions as a test case, we investigate to what extent the rotational
motion of smaller polar molecular ions sympathetically cooled into Coulomb
crystals in linear Paul traps couples to the translational motions of the ion
ensemble. By comparing results obtained from rotational state-selective
resonance-enhanced photo-dissociation experiments with data from theoretical
simulations, we conclude that the effective rotational temperature exceeds the
translational temperature (< 100 mK) by more than two orders of magnitude,
indicating a very weak coupling. In fact, the experimental results are
consistent with the rotational temperature being in thermal equilibrium with
the surrounding environment at ~300 K.
