Establish the causal direction between cascade rate and proton temperature

Establish the direction of causality between the compressible turbulent energy cascade rate and proton temperature in Alfvénic and non-Alfvénic solar-wind turbulence.

Background

The study finds a strong positive relationship between proton temperature and the compressible cascade rate across several solar-wind regimes. However, a statistical association alone cannot determine whether stronger turbulent transfer produces proton heating, whether hotter plasma enhances the compressible cascade measurement, or whether both arise from a third controlling factor. The authors therefore identify the causal direction as unresolved.