Stranger Things: A Grid-based Survey of Strange Modes in Post-Main Sequence Models

Abstract

We present a systematic survey of strange mode pulsations in Cepheids using MESA and for the linear stability analysis, MESA RSP. Our model grid spans $2-15\,M_\odot$ in mass and [Fe/H] $= -0.95$-$0.17$ ($Z = 0.0015$-$0.0200$) in metallicity, with four convective overshoot prescriptions. Strange modes were identified in a relatively small fraction ($5-12.5$ %) of models, occurring at $n_\mathrm{pg} = 5-9$, with $n_\mathrm{pg} = 6$-$7$ as the most frequent radial modes. No unstable solutions were identified beyond $n_\mathrm{pg} = 9$, in contrast to earlier studies reporting strange modes at $n_\mathrm{pg} = 10-12$. We quantified the duration of the instability crossing phase ($τ_\mathrm{IS}$), the strange mode phase ($τ_\mathrm{s}$), and their ratio $\mathcal{P}_\mathrm{s} = τ_\mathrm{s} / τ_\mathrm{IS}$. Toward higher masses, both $τ_\mathrm{IS}$ and $τ_\mathrm{s}$ decrease, yet their ratio shows no systematic trend with mass in models that include convective core overshoot. The absolute timescales for strange modes remain short, typically $τ_\mathrm{s} \sim 10^{4.5}$-$10^{6}$ years, while $τ_\mathrm{IS}$ is often an order of magnitude shorter, implying that these stars may spend a larger fraction of their life in the strange mode phase than in the instability strip itself. The extended duration of the strange mode phase may enhance the detectability of strange mode pulsators, provided that observational precision is sufficient to capture their low-amplitude variability. The predicted periods ($0.6-6.3$ days) are well covered by a single $27-$day TESS sector, making strange mode pulsators potentially detectable with current space-based photometry, although blending with nearby sources may pose challenges.

Figures (13)

• Figure 1: Schematic view of the data processing and visualization of the mesalab pipeline.
• Figure 2: 3 cases of instability strip crossing over the blue loop phase. Case 1: the star enters from the red edge and turns back ($C_\mathrm{cross} = 1$, left panel). Case 2: the star passes through both red and blue edges and returns to the AGB phase ($C_\mathrm{cross} = 2$, middle panel). Case 3: the star crosses both edges of the instability strip, briefly shifts redward beyond the blue edge, then re-enters from the blue side before finally returning through both edges toward the AGB phase ($C_\mathrm{cross} = 3$, right panel).
• Figure 3: The number of blue loop crossings in each parameter set is shown on the mass–metallicity plane. Set 0 corresponds to the reference models without convective overshoot, while Sets 1–3 represent increasing overshoot efficiency. It can be clearly seen that higher overshoot suppresses blue loop excursions at the upper mass range. Moreover, in Set 0, the blue loop crossing regime fragments into two islands: at intermediate metallicities, blue loop crossings are almost absent across the entire mass range. Note that each crossing event corresponds to a single edge of the instability strip, traversed in both directions. For example, a crossing count of $C_\mathrm{cross} = 1$ indicates that the star entered and exited through the red edge only, without reaching the blue boundary (see more details in the text).
• Figure 4: Hertzsprung–Russell diagram showing all selected models that undergo a blue loop phase and cross the instability strip from the red edge for all the overshoot configurations (Sets 0-3) color-coded by the $Z$ metallicity. It is clearly visible that the extent of the loop increases with decreasing metallicity and also with increasing luminosity. Furthermore, a clear dependence on overshoot is also present. As the overshoot parameter increases, the number of models having a blue loop phase decreases significantly. These models were used as input for GYRE and MESA RSP asteroseismic simulations. The extension of the instability strip is adopted from canonical MESA tutorials.
• Figure 5: The bimodal nature of pulsational behaviour. All of the models fall into two groups: either dominated by low-order pulsations ($n_\mathrm{pg} = 0, 1,2$ or high-order pulsations $n_\mathrm{pg}\ge5$. The left-hand side panel presents the effect of metallicity on excited pulsation modes, while the right-hand side panel is color-coded by stellar mass for model Sets 0-3. Note that in both panels, curves are plotted in ascending order of metallicity or mass, respectively. This means that at higher radial orders, models with larger $Z$ or $M$ tend to visually obscure those with lower values. However, the overplot is less pronounced at lower radial orders, allowing the effect of low-metallicity or low-mass models to be visible more clearly - particularly in those models, where their growth rates are slightly higher. For a complementary view without overplot, see Figure \ref{['fig:eta_2d_heatmap']}, which shows 2D heatmaps of maximum growth rate across radial order and metallicity (left) or mass (right).