Turbulent Proton Heating Rate in the Solar Wind from $5$ to $45~R_{\odot}$

Abstract: Various remote sensing observations have been used so far to probe the turbulent properties of the solar wind. Using the recently reported density modulation indices that are derived using angular broadening observations of Crab Nebula during 1952 - 2013, we measured the solar wind proton heating using the kinetic $\rm Alfv\acute{e}n$ wave dispersion equation. The estimated heating rates vary from $\approx 1.58 \times 10^{-14}$ to $1.01 \times 10^{-8} ~\rm erg~ cm^{-3}~ s^{-1}$ in the heliocentric distance range 5 - 45 $\rm R_{\odot}$. Further, we found that heating rates vary with the solar cycle in correlation with density modulation indices. The models derived using in-situ measurements (for example, electron/proton density, temperature, and magnetic field) that the recently launched Parker Solar Probe observes (planned closest perihelia $\rm 9.86~ R_{\odot}$ from the center of the Sun) are useful in the estimation of the turbulent heating rate precisely. Further, we compared our heating rate estimates with the one derived using previously reported remote sensing and in-situ observations.