Physical interpretation of the oscillation spectrum on the RGB and AGB

TL;DR

The paper investigates how RGB and He-burning red giants differ in their HeII ionisation zone and how seismic diagnostics depend on stellar physics. By building a comprehensive MESA model grid and extracting p-mode frequencies with ADIPLS (while suppressing core g-modes), it links glitch signatures in the local large frequency separation to envelope structure, showing that glitch amplitudes and phases encode evolutionary state. The main findings are that stellar mass and metallicity dominate seismic parameters, RGB mass loss and rotational mixing drive phase differences between RGB and clump/AGB stars, and the HeII glitch is stronger in AGB/RC stars due to envelope density contrasts. The work highlights the limits of the asymptotic p-mode description at low $\Delta\nu$ and underscores the need for improved frequency expressions to classify highly evolved giants with strong glitches.

Abstract

The high-frequency resolution of the four-year $\textit{Kepler}$ time series allows detailed study of seismic modes in luminous giants. Seismic observables help infer interior structures via comparisons with stellar models. We aim to investigate differences between H-shell (Red-Giant Branch; RGB) and He-burning (red clump and Asymptotic-Giant Branch; AGB) stars in the He-II ionisation zone and the sensitivity of seismic parameters to input physics in stellar models. We used a grid of stellar models with masses $0.8-2.5M_\odot$ and metallicities $-1.0-0.25$dex, including mass loss, overshooting, thermohaline mixing, and rotation-induced mixing. P-mode frequencies were inferred by suppressing g-modes in the core. The main factors affecting seismic observables are stellar mass and metallicity. The He-II glitch amplitude in the local large frequency separation $Δν$ correlates with the He-II ionisation zone density, explaining observed differences between RGB and clump/AGB stars. That amplitude exceeds 10% of $Δν$ in high-luminosity giants, making the asymptotic expansion less accurate when $Δν\le 0.5\,μ$Hz. Mass loss on the RGB and rotation-induced mixing from the main sequence to the early-AGB produce phase differences in the He-II glitch modulation signature between RGB and clump/AGB stars. Efficient RGB mass loss (for $M \le 1.5\,M_\odot$) and mixing processes (for $M \ge 1.5\,M_\odot$) leave detectable signatures in p-mode frequencies, enabling classification of red giants.

Figures (12)

• Figure 1: Comparison of the mode frequencies computed with the method $N_{\mathrm{BV}}^{2} = 0$ to the frequencies of the mixed modes of lowest inertia in each $\Delta\nu$ interval, without modifying the outputs of MESA. a) Model frequencies of $\ell = 1$ modes in units of the large frequency separation $\Delta\nu$ for the 8 first radial orders and for a $1\,M_{\odot}$ track during the He-core burning and the early He-shell burning phase (input physics are summarised in Table \ref{['Table:reference_model']}). The dipole modes computed with the method $N_{\mathrm{BV}}^{2} = 0$ are shown in blue circles while the mixed dipole modes of lowest inertia are indicated by blue crosses. The grey dotted line shows the end of the clump phase, taken as when the central helium mass fraction goes below 0.01. b) histogram of the differences between the dipole mode frequencies $\nu_{1,\, \mathrm{p}}$ computed with the method $N_{\mathrm{BV}}^{2} = 0$ (blue circles) and the frequencies $\nu_{1,\, \mathrm{g}}$ of the dipole modes of lowest inertia (blue crosses). This histogram is computed for models in the whole He-burning phase and all radial orders up to $\nu/\Delta\nu = 9$. These differences are expressed as a percentile of $\Delta\nu$. The black solid line localises the median of the distribution, while the dotted lines show the $16^{\mathrm{th}}$ and $84^{\mathrm{th}}$ percentiles of the distribution. c) and d) same label as the upper panels, but for the $\ell = 2$ modes. Some modes could not be computed because they were missing or because they were inconsistent. This explains why some symbols are missing, especially the mixed non-radial modes of lowest inertia at $\nu/\Delta\nu \simeq 1$.
• Figure 2: a) The profile of the first adiabatic exponent $\Gamma_{1}$ as a function of the normalised acoustic radius in a $1\,M_{\odot}$ RGB model computed with MESA at $\Delta\nu = 1.65\, \mu$Hz. The parameters of the $\Gamma_{1}$ variations ($H_{\mathrm{HeII}}$, $t_{\mathrm{HeII}}$, and $b_{\mathrm{HeII}}$) are directly shown in the figure. The green solid line is the $\Gamma_{1}$ profile throughout the star. The thick orange dashed line indicates the baseline that connects the local maximum after the dip caused by the second He-ionisation with the $\Gamma_{1}$ profile before the dip. The thin red dashed line gives the fit of the $\Gamma_{1}$ profile with Eq. \ref{['eq:fit_Gamma_1_around_HeII']} around the dip. b) Glitch modulation induced by the second He-ionisation zone in the same model as in the left panel. The local large separation $\Delta\nu_{n,\ell}$ is shown in red circles, blue triangles and green squares for radial, dipole, and quadrupole modes, respectively. The green solid line is the damped oscillator model given by Eq. \ref{['eq:fit_glitch_signature_Dreau_2021']} fitted to the data points. We point out that the data points are plotted at the mean frequencies $(\nu_{n,\ell} + \nu_{n+1,\ell} )/ 2$. The upper x-axis indicates the radial order of $\ell = 0$ modes, and the blue dotted line locates the maximum oscillation power.
• Figure 3: Model frequencies from radial order $n = 1$ up to $n = 8$ computed with ADIPLS for a $1\,M_{\odot}$ track at solar metallicity. The MESA models are computed with the reference input physics listed in Table \ref{['Table:reference_model']}. Radial, dipole and quadrupole modes are shown in red circles, blue triangles and green squares, respectively. For the RGB (panel a) the grey frequencies are Clump+AGB models for comparison, and vice versa for the Clump+AGB (panel b). The non-radial modes ($\ell = 1,\, 2$) are computed by setting the squared Brunt-Väisälä frequency $N_{\mathrm{BV}}^{2} = 0$ in the core, but retaining the original $\Gamma_{1}$ profile, as described in Sect. \ref{['sec:method']}. Modes of the same degree $\ell$ and same radial order $n$ are connected by dotted lines, in red for $\ell = 0$, in blue for $\ell = 1$, and in green for $\ell = 2$. The radial orders are indicated at the lower edge of each branch, with the same colour code as the mode degree $\ell$. The presence of non-radial modes with frequencies below that of the fundamental radial mode are labelled by an "f". The magenta dashed lines delimit the typical frequency range [$\nu_{\mathrm{max}} - 0.25\, \nu_{\mathrm{max}}$, $\nu_{\mathrm{max}} + 0.25\, \nu_{\mathrm{max}}$] between which model frequencies are likely to be observed in the oscillation spectrum 2011ApJ...743..161W. In panel b), the grey dotted line shows the end of the clump phase, taken as when the central helium mass fraction goes below 0.01. We warn that the code could not find out the $\ell = 1$ modes during the clump phase and the early-AGB ($\nu_{\mathrm{max}} \in [10, 25]\,\mu$Hz) when setting $N_{\mathrm{BV}}^{2} = 0$ in the core. Because the code had troubles to return the non-radial modes for high-luminosity AGB models, we stopped the computation of non-radial modes of $\nu_{\mathrm{max}} \leq 0.5\,\mu$Hz after the He-core burning phase.
• Figure 4: Synthetic seismic parameters extracted from the p-mode frequencies computed with ADIPLS, as described in Sect. \ref{['subsec:method_seismic_param_asympt']}. The MESA models are computed with the reference input physics listed in Table \ref{['Table:reference_model']}, with $M = 1.0\, M_{\odot}$ and solar metallicity. a) Variation of the acoustic offset $\varepsilon$ as a function of $\Delta\nu$, with an emphasis on the evolutionary stage. Clump stars are shown by the orange "C" symbols while the RGB and AGB are colour-coded in blue and red, respectively. "C" symbols show the progress of the clump stage: small (large, respectively,) symbols correspond to the early (late, respectively,) clump phase. The arrows indicate the direction of evolution. b) and c) dimensionless small separations $d_{\mathrm{0\ell}}$ as a function of $\Delta\nu$. Mean error bars estimated for $\Delta\nu$ below or above $0.5\, \mu$Hz are represented on each panel.
• Figure 5: Synthetic glitch and structure parameters computed with MESA and ADIPLS. The MESA models are the same as those shown in Fig. \ref{['fig:seismic_parameters_asymptotic_pattern']}. The glitch amplitude $\mathcal{A}_{\mathrm{gl}}$ and period $\mathcal{G}_{\mathrm{gl}}$ are shown on the a) and b) panels, respectively, while the amplitude $H_{\mathrm{HeII}}$ and the width $b_{\mathrm{HeII}}$ of the HeII zone in the $\Gamma_{1}$ profile are exhibited on the c) and d) panels, respectively. The label matches that of Fig. \ref{['fig:seismic_parameters_asymptotic_pattern']}. In panel b), the additional light grey solid line is the modulation period expected from the location of the HeII ionisation zone $t_{\mathrm{HeII}}$, which is computed according to Eq. \ref{['eq:period_modulation_as_function_acoustic_depth']}.