Study of the temperature-speed relationship from 0.1 to 1 AU and estimation of the expected temperature radial profiles

Many spacecraft observations made near Earth revealed a clear correlation between the solar wind temperature, T and the bulk speed, V. This relationship is also used to estimate the expected proton temperature at a given solar wind speed. However, the mechanisms leading to this correlation are not yet fully understood.  We use measurements made by the Solar Probe Cup (SPC) instrument onboard Parker Solar Probe and show that the proton temperature follows a power-law dependence on the proton bulk speed even at small radial distances from the Sun around 0.1 AU. The median T-V relationship becomes steeper with increasing heliocentric distance, and the exponent of the T-V dependence is significantly smaller closer to the Sun than near Earth. We derive the radial dependence of this exponent and compare it with predictions from the spherically symmetric 1D time-stationary solar wind expansion models (Shi et al., 2022). We identify a model that includes an external force as the most successful in reproducing the observed radial dependence. Due to the limited number of SPC observations near the Sun capturing high-speed solar winds, the radial profile of the measured proton temperature for fast solar winds has a high uncertainty.  Thus, we use the observed radial dependence of the T-V relationship to compute the radial profiles of the expected solar wind temperature for different solar wind speeds. Our findings suggest that slow solar wind streams cool significantly faster with heliocentric distance than the high-speed streams.