Proton heating estimates from near-Earth observations of coronal mass ejections in solar cycle 24

As solar coronal mass ejections (CMEs) propagate through the heliosphere, they expend energy in heating protons to compensate for the cooling that occurs due to expansion. CME propagation models usually treat energy dissipation implicitly via a polytropic index ($\delta$). Here we calculate the power dissipation implied by a given $\delta$ and compare it with the power available in the turbulent velocity fluctuations. We make this comparison using near-Earth {\em in-situ} observations of 27 of the most geoeffective CMEs ($D_{\mathrm{s}\mathrm{t}}<-75$ nT) in solar cycle 24. For $\delta =5\mathrm{/}3$, the power in the turbulent velocity fluctuations is $\approx 54$% smaller than what would be required to maintain the proton temperature at the observed values. If the power in the turbulent cascade is assumed to be fully expended in local proton heating, the most probable value for $\delta$ is 1.35. Our results contribute to a better understanding of CME energetics, and thereby to improved CME propagation models and estimates of Earth arrival times.