  One proposed mechanism for heating the solar wind, from close to the sun to
beyond 10 AU, invokes low-frequency, oblique, Alfven-wave turbulence. Because
small-scale oblique Alfven waves (kinetic Alfven waves) are compressive, the
measured density fluctuations in the solar wind place an upper limit on the
amplitude of kinetic Alfven waves and hence an upper limit on the rate at which
the solar wind can be heated by low-frequency, Alfvenic turbulence. We evaluate
this upper limit for both coronal holes at 5 solar radii and in the near-Earth
solar wind. At both radii, the upper limit we find is consistent with models in
which the solar wind is heated by low-frequency Alfvenic turbulence. At 1 AU,
the upper limit on the turbulent heating rate derived from the measured density
fluctuations is within a factor of 2 of the measured solar wind heating rate.
Thus if low-frequency Alfvenic turbulence contributes to heating the near-Earth
solar wind, kinetic Alfven waves must be one of the dominant sources of solar
wind density fluctuations at frequencies of order 1 Hz. We also present a
simple argument for why density fluctuation measurements do appear to rule out
models in which the solar wind is heated by non-turbulent high-frequency waves
``sweeping'' through the ion-cyclotron resonance, but are compatible with
heating by low-frequency Alfvenic turbulence.
