Lower bound for electron core beta in the solar wind

Solar wind electrons, especially under conditions of relatively low speed flow, often can be represented as two bi‐Maxwellian components, a cooler, more dense core (denoted by the subscript c) and a hotter, more tenuous halo. Solar wind observations from Ulysses between 1.5 and 2 AU further indicate that the β for electron core temperatures parallel to the background magnetic field, β‖c, has a distinct lower bound near 0.1. To seek the cause of this possible constraint, numerical solutions of the full Vlasov linear dispersion equation are used for four heat flux instabilities under a core/halo model with parameters representative of the solar wind near 1 AU. In this model the whistler heat flux instability is the growing mode of lowest threshold at most observed values of β‖c. As β‖c is decreased, however, the growth of this mode is reduced, so that at sufficiently small values of this parameter the Alfvén heat flux instability or the electron/ion acoustic instability becomes the fastest growing mode. The critical condition corresponding to this transition is calculated as a function of T‖c/Tp (where Tp is the proton temperature) and approximately corresponds to the observed constraint at β‖c ≃ 0.1. The Alfvén and ion acoustic instabilities both resonate with core electrons; the hypothesis is proposed that core heating by these two modes at the critical condition establishes a lower bound on β‖c.