The polytropic behavior of Solar Wind protons as observed by Ulysses spacecraft during Solar minimum

We analyze proton bulk parameters derived from Ulysses observations and investigate the polytropic behavior of solar wind protons over a wide range of heliocentric distances and latitudes. The large-scale variations of the proton density and temperature over heliocentric distance, indicate that plasma protons are governed by sub-adiabatic processes (polytropic index $γ$ < 5/3), if we assume protons with three effective kinetic degrees of freedom. From the correlation between the small-scale variations of the plasma density and temperature in selected sub-intervals, we derive a polytropic index $γ$ ~ 1.4 on average. Further examination shows that the polytropic index does not depend on the solar wind speed. This agrees with the results of previous analyses of solar wind protons at ~ 1 au. We find that the polytropic index varies slightly over the range of the heliocentric distances and heliographic latitudes explored by Ulysses. We also show that the homogeneity of the plasma and the accuracy of the polytropic model applied to the data-points vary over Ulysses orbit. We compare our results with the results of previous studies which derive the polytropic index of solar wind ions within the heliosphere using observations from various spacecraft. We finally discuss the implications of our findings in terms of heating mechanisms and the effective degrees of freedom of the plasma protons.