Plasma heating during the parametric excitation of acoustic waves in coronal magnetic loops

We examine plasma heating due to the dissipation of acoustic waves excited in coronal magnetic loops by parametric resonance with the five-minute oscillations in the velocity of the photospheric convection. The energy of acoustic waves excited in the coronal magnetic loop, rate of dissipation of acoustic waves, and rate of heating of the coronal plasma are determined. The maximum temperature predicted for the apex of the loop is calculated as a function of the velocity of photospheric oscillations, length of the loop, and electric current in the loop. It is shown that the mechanism proposed can explain the origin of quasi-stationary X-ray loops with temperatures of 3–6 MK. The lengths of these loops are resonant for acoustic waves excited by the five-minute photospheric oscillations. The use of the proposed mechanism to explain heating of the X-ray loops expected to be on stars of late spectral types is discussed.