Constraints on the Alfv\'enicity of Switchbacks

Switchbacks (SBs) are localized structures in the solar wind containing deflections of the magnetic field direction relative to the background solar wind magnetic field. The amplitudes of the magnetic field deflection angles for different SBs vary from ~40 to ~160-170 degrees. Alignment of the perturbations of the magnetic field and the bulk solar wind velocity is observed inside SBs and causes spiky enhancements of the radial bulk velocity inside SBs. We have investigated the deviations of SB perturbations from Alfv\'enicity by evaluating the distribution of the parameter defined as the ratio of the parallel to $\Delta\vec{B}$ component of $\Delta\vec{V}$ to $\Delta\vec{V}_A = \Delta\vec{B}/4\pi n_i m_i$ inside SBs, i.e. $\alpha=V_{||}/|\Delta\vec{V}_A|$ ( $\alpha=\Delta\vec{V}/|\Delta\vec{V}_A|$ when $\Delta\vec{V}~\Delta\vec{B}$), which quantifies the deviation of the perturbation from an Alfv\'enic one. Based on Parker Solar Probe (PSP) observations, we show that $\alpha$ inside SBs has systematically lower values than it has in the pristine solar wind: $\alpha$ inside SBs observed during PSP Encounter 1 were distributed in a range of 0.2-0.9. The upper limit on $\alpha$ is constrained by the requirement that the jump in velocity across the switchback boundary be less than the local Alfv\'en speed. This prevents the onset of shear flow instabilities. The consequence is that the perturbation of the proton bulk velocity in SBs with deflection greater than 60 degrees cannot reach $\alpha=1$ (the Alfv\'enicity condition) and the highest possible $\alpha$ for a SB with the full reversal of B is 0.5. These results have consequences for the interpretation of switchbacks as large amplitude Alfv\'en waves.