  We derive a set of self-consistent marginally stable states for a system of
ion-cyclotron waves propagating parallel to the large-scale magnetic field
through a homogeneous proton-electron plasma. The proton distributions and the
wave dispersions are related through the condition that no further
ion-cyclotron resonant particle scattering or wave growth/damping may take
place. The thermal anisotropy of the protons in these states therefore defines
the threshold value for triggering the proton-cyclotron anisotropy instability.
A number of recent papers have noted that the anisotropy of solar wind protons
at 1 AU does not seem to be limited by the proton-cyclotron anisotropy
threshold, even at low plasma beta. However, this puzzle seems to be due solely
to the estimation of this anisotropy threshold under the assumption that the
protons have a bi-Maxwellian distribution. We note that bi-Maxwellian
distributions are never marginally stable to the resonant cyclotron
interaction, so these estimates do not represent physically valid thresholds.
The threshold anisotropies obtained from our marginally stable states are much
larger, as a function of proton parallel beta, than the bi-Maxwellian
estimates, and we show that the measured data remains below these more rigorous
thresholds. Thus, the results of this paper resolve the apparent contradiction
presented by the solar wind anisotropy observations at 1 AU: The bi-Maxwellian
anisotropies are not rigorous thresholds, and so do not limit the proton
distributions in the solar wind.
