Revealing mixed modes in compressible hydrodynamical simulations of red giant stars

Mixed modes are observed in many low-mass evolved stars. They provide information about core rotation rates of these stars, which are lower than predicted by stellar evolution models. The mixed modes themselves have been invoked as an angular momentum transport mechanism, but estimating their transport efficiency requires knowledge of their amplitudes. We constrain, for the first time, the mixed mode amplitudes in 2D hydrodynamical simulations of a $1.3M_\odot$ red giant using the code \textsc{music}. We perform two simulations with outer radial truncations at fractional radii $r_o/r_\star = 0.90$ and $r_o/r_\star = 0.98$. We compare the modes in the simulation with those found using both \textsc{gyre} and a \textsc{dedalus} eigenvalue solver. Excellent frequency agreement is found for all p-dominated modes, with minor discrepancies for g-dominated modes, especially in the frequency range $[60, \ 240]\ \mu\mathrm{Hz}$. We find excellent eigenfunction agreement for all modes except those in this frequency range. According to empirical predictions the largest kinetic energies are located around $\nu_{\mathrm{max}} = 312.8\ \mu\mathrm{Hz}$, but in both simulations the modes with frequencies $\nu <50\ \mu\mathrm{Hz}$ have the largest kinetic energies. In the simulation with $r/r_\star = 0.98$, the simulated modes have extrapolated surface velocities comparable to the empirical predictions, with highest surface velocities in a bell-shaped curve peaking around $\nu = 700 \ \mu\mathrm{Hz}$. The extrapolated surface velocities of the low frequency modes are small, and thus hard to observe, but their large kinetic energies deeper in the interior could significantly impact angular momentum transport, which has not yet been investigated.