Asymptotic power spectra and visibilities of damped mixed modes

TL;DR

This work develops a progressive-wave formalism to derive an analytic resonance pattern for solar-like oscillations in red giants, connecting damping in the p- and g-mode cavities to observable mixed-mode visibilities and multiplet signatures. By formulating one- and two-cavity systems with explicit damping/phase terms, the authors quantify how core damping governs the detectability of mixed modes and predict visibilities that transition from unity to the infinite-damping limit as core damping strengthens. A parameter study reveals that observed red-giant populations with low dipole visibilities can be explained by finite core damping, with visibilities and peak structures sensitively tied to coupling, period spacing, and viewing inclination. The method is validated by applying it to Mosser et al. (2017), enabling estimates of core damping rates from visibilities and offering a coherent framework to interpret the presence or absence of mixed-mode signatures in red giants, with implications for probing internal magnetic fields and evolutionary changes in damping.

Abstract

Recent observational studies of red giant stars have estimated the visibility of their mixed oscillation modes, which is a proxy of the average energy of these modes. Among other things, they demonstrated that although the damping rate of the oscillations in the core of many red giants appears to be negligible, other red giants exhibit high core damping rates that are sometimes consistent with the infinite value limit. Up until now, it has not been possible to link the mixed mode visibilities to core damping rates in a quantitative way. In this study, we use the progressive wave picture to derive an analytical function expressing the approximate resonance pattern of red giants up to a proportionality factor. This function can model the influence of the damping on the oscillations, as well as take into account other effects such as mode asymmetries. In particular, this expression can be used to obtain a quantitative estimate for the visibility of mixed modes and to predict the detectability of mixed mode and multiplet signatures under different core damping rates. Here, we conduct a parameter study to investigate how the damping processes affect these aspects. We find that the visibility approaches the value expected for an infinite core damping rate already at finite values. Furthermore, we find that both the mixed mode and the multiplet signatures disappear at finite core damping rates. This implies that the observational characteristics of red giants with finite core damping rates can appear as if their core damping rate were infinite, providing an explanation for the observed populations. Moreover, we have used our method to quantitatively estimate the core damping rates of red giants with unusually low mixed mode amplitudes from their observed visibilities.

Figures (22)

• Figure 1: Sketch of the single-cavity system. The curly bracket indicates interference.
• Figure 2: Sketch of the two-cavity system. Curly brackets indicate interference.
• Figure 3: Normalized power spectrum as a function of frequency for the set of stellar parameters A (see Table \ref{['tab: sets of stellar parameters']}) with $|R_{\rm t}|=0.95$ for different values of $|R_{\rm b}|$ in a single-cavity system. Colored solid lines show $p$ calculated using Eq. \ref{['eq: normalized power spectrum 1 cavity']}. Cyan dotted lines show the normalized power spectrum a sum of Lorentzians whose positions and widths were calculated using the resonance condition. The frequency resolution is selected so that all peaks are resolved. In the bottom row, we show the residual of each $p$ and its corresponding sum of the Lorentzian functions.
• Figure 4: Same as Fig. \ref{['fig: IRE_Lorentz_1cavity']} calculated with Eq. \ref{['eq: normalized power spectrum 2 cavities']} for different values of $|R_{\rm g}|$ in a two-cavity system. Lorentzians are only shown for $|R_{\rm g}|=1$ (i.e., no damping in the g-mode cavity) and 0 (i.e., complete loss of energy in the g-mode cavity), since the peak height is unconstrained otherwise (see main text). The case $|R_{\rm g}|=0$ is identical to the case $|R_{\rm b}|=0.778$ in Fig. \ref{['fig: IRE_Lorentz_1cavity']}.
• Figure 5: Relative power spectrum as a function of frequency for the set of stellar parameters B with $|R_{\rm p}|=0.95$ and different values of $|R_{\rm g}|$. Gray vertical lines indicate the location of the local minima, green circles (red crosses) indicate the location of the resolved (unresolved) modes. The resolution criterion is described in Sect. \ref{['sect: a resolution criterion']}. When the unresolved modes no longer corresponded to local maxima on the selected frequency grid, we used the resonance condition to determine their position.