Energy Supply by Low-frequency Break Sweeping for Heating the Fast Solar Wind from 0.3 to 4.8 au

Solar wind protons undergo significant heating during the expansion of the solar wind and turbulence plays an important role in this process. It is believed that the energy is injected from the energy-containing range into the inertial range and then transferred to dissipate into heat eventually. However, the energy injection process in the heliosphere remains unclear. Here we analyze this process. We utilize Helios 2 and Ulysses measurements of the fast solar wind at different radial distances from 0.29 to 4.8 au. We obtain the perpendicular heating rate based on the gradient of the magnetic moment. We estimate for the first time the energy supply rate due to the sweeping of low-frequency break based on the identification of low-frequency break and the corresponding power spectra density profile. We find that the energy supply rate is comparable to the perpendicular heating rate of protons, which support the idea that low-frequency range becomes part of the inertial range as the solar wind turbulence ages. These results help us understand the energy supply process from the energy-containing range and the heating process of solar wind protons.