Do There Exist Energy Closures to the Observed Mirror Waves?

Low-frequency mirror waves are frequently observed in the planetary magnetosheaths for the plasma conditions of (Formula presented.) and (Formula presented.). This study first shows that the thermodynamic conditions of the observed mirror events may well be described by a set of double-polytropic (DP) laws first proposed by Hau and Sonnerup (1993, https://doi.org/10.1029/93gl01706), (Formula presented.) and (Formula presented.), with the polytropic values being in the ranges of (Formula presented.) and (Formula presented.). The physical basis of the empirical thermodynamic relations is then examined based on the mixed Vlasov-MHD formulation for low-frequency linear mirror instability (Ferrière & Andre, 2002, https://doi.org/10.1029/2002JA009273) which shows that the theoretical energy equations possess the DP forms with (Formula presented.) and (Formula presented.) being functions of (Formula presented.); in particular, for mirror unstable cases (Formula presented.) and (Formula presented.). The theoretical predictions are found to be in high agreements with the empirical polytropic values with the average errors of ∼6.5%.