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

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 ($\tau_\mathrm{IS}$), the strange mode phase ($\tau_\mathrm{s}$), and their ratio $\mathcal{P}_\mathrm{s} = \tau_\mathrm{s} / \tau_\mathrm{IS}$. Toward higher masses, both $\tau_\mathrm{IS}$ and $\tau_\mathrm{s}$ 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 $\tau_\mathrm{s} \sim 10^{4.5}$-$10^{6}$ years, while $\tau_\mathrm{IS}$ 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.