Exponent in the empirical relationship between magnetosheath heat flux and solar wind parameters

Determine the exponent a in the empirical relationship linking magnetosheath ion field-aligned heat flux toward the upstream direction to n_sw · V_sw^a, thereby characterizing the dependence of the heat flux on solar wind dynamic pressure or energy flux.

Background

In assessing which upstream parameters control the magnetosheath field-aligned heat flux, the authors find positive correlations with solar wind speed and density but note these parameters are anti-correlated. They hypothesize the heat flux may depend on a combined quantity of the form n_sw * V_sw^a.

They test several candidate exponents a (1, 2, 3) and observe stronger correlations for a = 2 or 3, consistent with dependencies on dynamic pressure or energy flux. Nonetheless, they explicitly state the exponent a is unknown, leaving a precise formulation unresolved.