Acoustic oscillations in the field-free, gravitationally stratified cavities under solar bipolar magnetic canopies

Aims. The main goal is to study the dynamics of the gravitationally stratified, field-free cavities in the solar atmosphere, located under small-scale, cylindrical magnetic canopies, in response to explosive events in the lower-lying regions (due to granulation, small-scale magnetic reconnection, etc.). Methods. We derive the two-dimensional Klein-Gordon equation for isothermal density perturbations in cylindrical coordinates. The equation is first solved by a standard normal mode analysis in order to obtain the free oscillation spectrum of the cavity. Then, the equation is solved in the case of impulsive forcing associated to a pressure pulse specified in the lower-lying regions. Results. The normal mode analysis shows that the entire cylindrical cavity of granular dimensions tends to oscillate with frequencies of 5-8 mHz and also with the atmospheric cut-off frequency. Furthermore, the passage of a pressure pulse, excited in the convection zone, sets up a wake in the cavity oscillating with the same cut-off frequency. The wake oscillations can resonate with the free oscillation modes, which leads to an enhanced observed oscillation power. Conclusions. The resonant oscillations of these cavities explain the observed power halos near magnetic network cores and active regions.