Magnetic helicity signature and its role in regulating magnetic energy spectra and proton temperatures in the solar wind

In a previous paper, we found that proton temperatures are clearly associated with the proton-scale turbulence in the solar wind, and magnetic helicity signature appears to be an important indicator in the association. Based on 15 years of in situ measurements, the present paper further investigates the magnetic helicity of solar wind turbulence and its role in regulating magnetic energy spectra and proton temperatures. Results show that the presence of the helicity signature is very common in solar wind turbulence at scales $0.3 \lesssim k\rho_p \lesssim 1$, with $k$ being the wavenumber and $\rho_p$ the proton gyroradius. The sign of the helicity is mostly positive, indicating the dominance of right-handed polarization of the turbulence. The helicity magnitude usually increases with $k$ and $\beta_{{\parallel}p}$ (the proton parallel beta) when $k\rho_p$ and $\beta_{{\parallel}p}$ are less than unity. As helicity magnitude increases, the power index of the energy spectrum becomes more negative, and the proton temperatures $T_{{\perp}p}$ and $T_{{\parallel}p}$ rise significantly, where $T_{{\perp}p}$ and $T_{{\parallel}p}$ are the perpendicular and parallel temperatures with respect to the background magnetic field. In particular, the rise of $T_{{\perp}p}$ is faster than $T_{{\parallel}p}$ when $\beta_{{\parallel}p} < 1$ is satisfied. The faster rise of $T_{{\perp}p}$ with the helicity magnitude may be interpreted as the result of the preferentially perpendicular heating of solar wind protons by kinetic Alfv\'en wave (KAW) turbulence.