  In the present work we use a deep-exposure spectrum taken by the SUMER
spectrometer in a polar coronal hole in 1996 to measure the ion temperatures of
a large number of ions at many different heights above the limb between 0.03
and 0.17 solar radii. We find that the measured ion temperatures are almost
always larger than the electron temperatures and exhibit a non-monotonic
dependence on the charge-to-mass ratio. We use these measurements to provide
empirical constraints to a theoretical model of ion heating and acceleration
based on gradually replenished ion-cyclotron waves. We compare the wave power
required to heat the ions to the observed levels to a prediction based on a
model of anisotropic magnetohydrodynamic turbulence. We find that the empirical
heating model and the turbulent cascade model agree with one another, and
explain the measured ion temperatures, for charge-to-mass ratios smaller than
about 0.25. However, ions with charge-to-mass ratios exceeding 0.25 disagree
with the model; the wave power they require to be heated to the measured ion
temperatures shows an increase with charge-to-mass ratio (i.e., with increasing
frequency) that cannot be explained by a traditional cascade model. We discuss
possible additional processes that might be responsible for the inferred
surplus of wave power.
