By applying the theory of slowly rotating stars to the Sun, the solar quadrupole and octopole moments J2 and J4 were computed using a solar model obtained from CESAM stellar evolution code (Morel (1997)) combined with a recent model of solar differential rotation deduced from helioseismology ). This model takes into account a near-surface radial gradient of rotation which was inferred and quantified from MDI f-modes observations by Corbard and Thompson (2002). The effect of this observational near-surface gradient on the theoretical values of the surface parameters J2, J4 is investigated. The results show that the octopole moment J4 is much more sensitive than the quadrupole moment J2 to the subsurface radial gradient of rotation.

Context. Recent observations have revealed that the solar atmosphere is highly structured in density, temperature, and magnetic field. The presence of these gradients may lead to the appearance of currents in the plasma, which in the weakly collisional corona can constitute sources of free energy for driving micro-instabilities. Such instabilities are very important since they represent a possible source of ion-cyclotron waves that have been conjectured as playing a prominent role in coronal heating, but whose solar origin remains unclear. Aims. Considering a density stratification transverse to the magnetic field, this paper aims at studying the possible occurrence of gradient-induced plasma micro-instabilities under the conditions typical of coronal holes. Methods. Taking the WKB (Wentzel-Kramers-Brillouin) approximation into account, we performed the Fourier plane wave analysis using the collisionless multi-fluid model. By neglecting the electron inertia, this model allowed us to take into account ion-cyclotron wave effects that are absent from the one-fluid model of magnetohydrodynamics (MHD). Realistic models of density and temperature, as well as a 2D analytical magnetic-field model, have been used to define the background plasma in the open-field funnel in a polar coronal hole. The ray-tracing theory has been used to compute the ray path of the unstable waves, as well as the evolution of their growth rates during the propagation. Results. We demonstrate that in typical coronal hole conditions, and when assuming typical transverse density length scales taken from radio observations, the current generated by a relative electron-ion drift provides enough free energy for driving the mode unstable. This instability results from coupling between slow-mode waves propagating in opposite directions. However, the ray-tracing computation shows that the unstable waves propagate upward to only a short distance but then are reflected backward. The corresponding growth rate increases and decreases intermittently in the upward propagating phase, and the instability ceases while the wave is propagating downward. Conclusions. Drift currents caused by fine structures in the density distribution in the magnetically-open coronal funnels can provide enough energy to drive plasma micro-instabilities, which constitute a possible source of the ion-cyclotron waves that have been invoked for coronal heating.

Context. Spectroscopic observations and theoretical models suggest resonant wave-particle interactions, involving high-frequency ion-cyclotron waves, as the principal mechanism for heating and accelerating ions in the open coronal holes. However, the mechanism responsible for the generation of the ion-cyclotron waves remains unclear. One possible scenario is that ion beams originating from small-scale reconnection events can drive micro-instabilities that constitute a possible source for the excitation of ion-cyclotron waves. Aims. We use the multi-fluid model in the low-β coronal plasma to study ion beam-driven electromagnetic instabilities. By neglecting the electron inertia this model allows one to take into account ion-cyclotron wave effects that are absent from the one-fluid magnetohydrodynamics (MHD) model. Realistic models of density and temperature as well as a 2-D analytical magnetic field model are used to define the background plasma in the open-field funnel region of a polar coronal hole. Methods. Taking into account the WKB (Wentzel-Kramers-Brillouin) approximation, a Fourier plane-wave linear mode analysis is employed to derive the dispersion relation. The ray-tracing theory is used to compute the ray path of the unstable wave as well as the evolution of the growth rate of the wave while propagating in the coronal funnel. Results. We demonstrate that in typical coronal hole conditions and assuming realistic values of the beam velocity, the free energy provided by the ion beam propagating parallel to the ambient field can drive micro-instabilities through resonant ion-cyclotron excitation.

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