  Observations in the solar wind suggest that the compressive component of
inertial-range solar-wind turbulence is dominated by slow modes. The low
collisionality of the solar wind allows for non-thermal features to survive,
which suggests the requirement of a kinetic plasma description. The
least-damped kinetic slow mode is associated with the ion-acoustic (IA) wave
and a non-propagating (NP) mode. We derive analytical expressions for the
IA-wave dispersion relation in an anisotropic plasma in the framework of
gyrokinetics and then compare them to fully-kinetic numerical calculations,
results from two-fluid theory, and MHD. This comparison shows major
discrepancies in the predicted wave phase speeds from MHD and kinetic theory at
moderate to high $\beta$. MHD and kinetic theory also dictate that all plasma
normal modes exhibit a unique signature in terms of their polarization. We
quantify the relative amplitude of fluctuations in the three lowest particle
velocity moments associated with IA and NP modes in the gyrokinetic limit and
compare these predictions with MHD results and in-situ observations of the
solar-wind turbulence. The agreement between the observations of the wave
polarization and our MHD predictions is better than the kinetic predictions,
suggesting that the plasma behaves more like a fluid in the solar wind than
expected.
