http://arxiv.org/abs/1809.01727

Turbulent motions in the convective envelope of red giants excite a rich spectrum of solar-like oscillation-modes. Observations by CoRoT and Kepler have shown that the mode amplitudes increase dramatically as the stars ascend the red giant branch, i.e., as the frequency of maximum power $\nu_\mathrm{max}$ decreases. Most studies nonetheless assume that the modes are well-described by the linearized fluid equations. We investigate to what extent the linear approximation is justified as a function of stellar mass $M$ and $\nu_\mathrm{max}$, focusing on dipole mixed-modes with frequency near $\nu_\mathrm{max}$. A useful measure of a mode’s nonlinearity is the product of its radial wavenumber and its radial displacement $k_r \xi_r$ (i.e., its shear). We show that $k_r \xi_r \propto \nu_\mathrm{max}^{-9/2}$, implying that the nonlinearity of mixed-modes increases significantly as a star evolves. The modes are weakly nonlinear ($k_r \xi_r > 10^{-3}$) for $\nu_\mathrm{max} \lesssim 150 \, \mu\mathrm{Hz}$ and strongly nonlinear ($k_r \xi_r > 1$) for $\nu_\mathrm{max} \lesssim 30 \, \mu\mathrm{Hz}$, with only a mild dependence on $M$ over the range we consider ($1.2 – 2.0 M_\odot$). A weakly nonlinear mixed-mode can excite secondary waves in the stellar core through the parametric instability, resulting in enhanced, but partial, damping of the mode. We find that mixed-modes lie near the instability threshold when $\nu_\mathrm{max} \lesssim 80\, \mu \mathrm{Hz}$ ($200 \,\mu\mathrm{Hz}$) for $M\simeq 1.2 M_\odot$ ($2.0 M_\odot$). By contrast, a strongly nonlinear mode breaks as it propagates through the core and is fully damped there. We conclude with a brief discussion of potentially observable signatures of nonlinear effects and propose investigating whether they can explain why some red giants exhibit dipole modes with unusually small amplitudes, known as depressed modes.

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N. Weinberg and P. Arras
Fri, 7 Sep 18
37/65

Comments: 9 pages, 4 figures, submitted to ApJ