Equipartition between Alfvénic turbulence and energetic ions as the origin of the -5 common spectrum in the heliosphere

Abstract

Suprathermal ion tails throughout the heliosphere follow a ``common spectrum,'' $f(v)\propto v^{-5}$. We show that scale-by-scale equipartition between strong Alfvénic turbulence and the ions it accelerates predicts both this exponent and the absolute amplitude, $F(v)=B^2/(16π^3 m_i v^5)$, with no free parameters. The prediction agrees within a factor of a few with ACE and Voyager 1 spectra across three decades in magnetic energy. We argue that this saturated level is reached where strong turbulence accelerates particles locally; quiet-time tails lie well below it, consistent with nonlocal acceleration.