Two-fluid treatment of whistling behaviour and the warm Appleton-Hartree extension

Abstract: As an application of the completely general, ideal two-fluid analysis of waves in a warm ion-electron plasma, where six unique wave pair labels (S, A, F, M, O, and X) were identified, we here connect to the vast body of literature on whistler waves. We show that all six mode pairs can demonstrate whistling behaviour, when we allow for whistling of both descending and ascending frequency types, and when we study the more general case of oblique propagation to the background magnetic field. We show how the general theory recovers all known approximate group speed expressions for both classical whistlers and ion cyclotron whistlers, which we here extend to include ion contributions and deviations from parallel propagation. At oblique angles and at perpendicular propagation, whistlers are investigated using exact numerical evaluations of the two-fluid dispersion relation and their group speeds under Earth's magnetosphere conditions. This approach allows for a complete overview of all whistling behaviour and we quantify the typical frequency ranges where they must be observable. We use the generality of the theory to show that pair plasmas in pulsar magnetospheres also feature whistling behaviour, although not of the classical type at parallel propagation. Whistling of the high frequency modes is discussed as well, and we give the extension of the Appleton-Hartree relation for cold plasmas, to include the effect of a non-zero thermal electron velocity. We use it to quantify the Faraday rotation effect at all angles, and compare its predictions between the cold and warm Appleton-Hartree equation.