THE INFLUENCE OF A CHROMOSPHERIC MAGNETIC-FIELD ON THE SOLAR P-MODES AND F-MODES .2. UNIFORM CHROMOSPHERIC FIELD

The influence of a chromospheric magnetic field on solar oscillations is investigated using a model in which the convection zone of the Sun is represented by a gravitationally stratified fluid having a linear temperature profile, above which is an isothermal chromosphere permeated by a uniform, horizontal magnetic field. We derive an exact dispersion relation which is solved asymptotically for small horizontal wavenumbers and numerically otherwise. We find that the frequency of p- and f-modes is raised by the presence of a magnetic field, the magnitude of the effect increasing with the degree l, radial order n, and chromospheric magnetic field strength B0. Also, in the absence of a magnetic field, an increase in chromospheric temperature results in a reduction of the frequency of a p-mode, while the f-mode is unaffected. Our calculations show that the effects of a chromospheric magnetic field are most noticeable in high-degree modes. On the basis of the model presented here, we expect frequencies to increase over the solar cycle with the approach of maximum activity by up to 50 μHzfor the highest values of l and n. In active regions, and for a given horizontal wavenumber, we would expect the frequencies to increase above quiet-Sun values by a similarly significant and observable amount. In particular, we suggest the f-mode cyclic frequency should be raised above its field-free value, (gk)1/2/2π, whatever the profile of the magnetic field in the chromosphere. Our model shows that the vertical velocity component in the chromosphere is reduced in amplitude by the presence of a canopy field. We offer an explanation of these results in simple physical terms. The f-mode is affected by magnetic tension and pressure which add extra restoring forces to the buoyancy from which it arises. This will increase the frequency of oscillation. The presence of the field makes the chromospheric density lower than in the field-free case, which reduces the inertia of the atmosphere. On the other hand, the magnetic field itself adds rigidity, tending to counteract the effect of diminished density. The magnetic field profile determines which of these two effects is dominant. The rigidity of the interface determines the way in which sound waves are reflected around the upper turning point of the p-mode cavity, and this in turn influences the frequency of oscillation.