Possible coexistence of kinetic Alfv\'en and ion Bernstein modes in sub-ion scale compressive turbulence in the solar wind

We investigate compressive turbulence at sub-ion scales with measurements from the Magnetospheric MultiScale Mission. The tetrahedral configuration and high time resolution density data obtained by calibrating spacecraft potential allow an investigation of the turbulent density fluctuations in the solar wind and their three-dimensional structure in the sub-ion range. The wave-vector associated with the highest energy density at each spacecraft frequency is obtained by application of the Multi-point signal resonator technique to the four-point density data. The fluctuations show a strong wave-vector anisotropy $k_{\perp}\gg k_{\parallel}$ where the parallel and perpendicular symbols are with respect to the mean magnetic field direction. The plasma frame frequencies show two populations, one below the proton cyclotron frequency $\omega<\Omega_{ci}$ consistent with kinetic Alfv\'en wave (KAW) turbulence. The second component has higher frequencies $\omega > \Omega_{ci}$ consistent with ion Bernstein wave (IBW) turbulence. Alternatively, these fluctuations may constitute KAWs that have undergone multiple wave-wave interactions causing a broadening in the plasma frame frequencies. The scale-dependent kurtosis in this wave-vector region shows a reduction in intermittency at the small scales which can also be explained by the presence of wave activity. Our results suggest that small-scale turbulence exhibits linear-wave properties of kinetic Alfv\'en and possibly ion-Bernstein/magnetosonic waves. Based on our results, we speculate that these waves may play a role in describing the observed reduction in intermittency at sub ion scales.