Effects of Alfvénicity on the Compressible Energy Cascade in Magnetohydrodynamic Solar Wind Turbulence: Evidence from Parker Solar Probe, Solar Orbiter, and WIND observations

Abstract: The compressible MHD energy cascade in the solar wind is shaped by Alfvénicity, plasma fluctuations, and proton temperature, yet how these factors regulate the relative weight of compressible and incompressible energy transfer across heliocentric distances remains poorly understood. We apply compressible and incompressible exact relations to a large sample of 2-hour intervals from WIND (1~au), Parker Solar Probe ($<0.25$~au), and Solar Orbiter (0.3--1~au), classifying intervals as Alfvénic ($|σ_c|>0.75$) or non-Alfvénic ($|σ_c|<0.25$) and by wind speed, and examine the Yaglom-like and purely compressible components of the compressible cascade. Velocity fluctuation amplitude is the strongest predictor of the compressible cascade rate $\langle|\varepsilon_c|\rangle$, followed by density and magnetic field fluctuations. $\langle|\varepsilon_c|\rangle$ and $\langle|\varepsilon_i|\rangle$ are tightly correlated in all regimes, with their ratio organized by Alfvénicity and wind speed: non-Alfvénic and Alfvénic fast winds cluster along $$\langle|\varepsilon_c|\rangle=\langle|\varepsilon_i|\rangle$$, while Alfvénic slow wind shows a systematic excess consistent with internal energy contributions. The largest $\langle|\varepsilon_c|\rangle$ systematically occur in hotter intervals, with a two-decade increase from cool to hot events in Alfvénic slow and non-Alfvénic wind, a trend carried mainly by the purely compressible term, while the dominant Yaglom-like term controls the overall cascade magnitude. Alfvénicity and wind speed thus govern the efficiency of turbulent energy transfer across heliocentric distances, and the tight coupling between compressible and incompressible rates points to the need for compressible, multi-fluid descriptions of the solar wind dissipation budget.