Cleo (Shyeh Tjing) Loi
Stars are fluid bodies in which pressure, buoyancy, rotation and magnetism provide the restoring forces for wave propagation. Constructive interference of these waves generates global modes of oscillation, which can be detected through the periodic variations they induce in a star's brightness. Understanding the connection between the internal structure of a star and the properties of its normal modes is the focus of stellar oscillation theory, which generally regards rotation and magnetism to be weak perturbations compared to pressure and buoyancy. The discovery several years ago that a sizable fraction of red giant stars exhibit abnormally low dipole mode amplitudes relative to the rest of the population, suggesting the existence of a damping process localised to the deep interior, has presented a puzzle for theoreticians as it is not predicted in the standard framework. The restriction of this phenomenon to those stars with masses high enough to previously have hosted core dynamos points to the possible role of a hidden, relic magnetic field. However, the predictions of existing magnetic theories have difficulty accommodating several aspects, including the need to return a fraction of wave energy from the core to the envelope, and the persistent gravity-like character of affected modes. This poster presents the results of a Hamiltonian ray tracing study investigating the dynamics of magneto-gravity waves, using realistic stellar models and magnetic field configurations. We find that even in the presence of a strong field, there exist trajectories where waves remain predominantly gravity-like in character, and these are able to undergo reflection out of the core much like pure gravity waves. The remaining trajectories are ones where waves acquire significant Alfven character, becoming trapped and eventually dissipated. The allowance for partial energy return from the core offers a solution to the conundrum faced by the magnetic hypothesis.
The second slide presents results, in the form of a flow chart starting with the question 'Magnetic fields?'. This branches into two cases, 'No' and 'Yes'. The 'Yes' case branches into a further two cases, 'Trapping' and 'Reflection'. In each of the three cases there are plots, showing the 3D geometry of the ray trajectory and the time evolution of the wavevector components. These are labelled Figures 3, 4 and 5 for the case of no field, trapping and reflection, respectively. Figures 4 and 5 are each labelled with the value of the launch latitude and polarisation, and a note saying 'All other launch parameters identical'. In Figures 3 and 5 the ray periodically enters and exits the field region, with inner and outer turning points at finite radii. In Figure 4 the ray shows an inspiralling trajectory that does not exit the field region.
The third slide presents further results and some discussion. It contains two sections, with headings 'When will magnetic fields be important?' and 'Why are some rays trapped while others reflected?', and three figures, entitled 'Comparison of wave dispersion relations' (Figure 6), 'Gravity and Alfven frequencies' (Figure 7) and 'Distribution of trapped (blue) and reflected (red) rays' (Figure 8). Figure 6 contains two panels, one overplotting the dispersion relations of acoustic and Alfven waves, which are both straight lines through the origin. The other panel overplots the dispersion relations of gravity and Alfven waves, where one is a straight line through the origin and the other is a hyperbola. Figure 7 contains two panels, one for a trapped ray and one for a reflected ray. The gravity and Alfven curves are rapidly oscillating and their envelopes overlap for the trapped ray, but not the reflected ray. Figure 8 plots the 1200 launch points on a sphere, with red and blue patches indicating the outcome.
The fourth slide presents further discussion and a summary, as well as a list of references and details about the journal article the poster is based on (Loi 2020, MNRAS, 493, 5Cosmochemistry). There are two sections, headed by 'Comparison with observations' and 'What is happening?', and two figures, entitled 'Variation with frequency' (Figure 9) and 'Observed dichotomy' (Figure 10). There is also a cartoon of the structure of a red giant star, labelled with commentary on wave behaviour in different regions, and a table entitled 'Theoretical predictions' showing values predicted for various quantities such as damping rate. Figure 9 has two panels, showing how the trapping fraction varies with field strength, for different wave frequencies, and a plot of the power spectrum of a star with mode depression affecting only the lower part of the frequency range. Figure 10 shows observations of mode visibilities and compares them with the theoretical prediction.