The Potential of Asteroseismology to Resolve the Blue Supergiant Problem

Despite major progress in our understanding of massive stars, concerning discrepancies still remain between observations and theory. Most notable are the numerous stars observed beyond the theoretical main sequence, an evolutionary phase expected to be short-lived and hence sparsely populated. This is the "Blue Supergiant Problem." Stellar models with abnormal internal structures can provide long-lived solutions for this problem: core hydrogen-burning stars with oversized cores may explain the hotter ones, and core helium-burning stars with undersized cores may explain the cooler ones. Such stars may result from enhanced or suppressed mixing in single stars, or, more likely, as the products of binary interaction and stellar mergers. Here we investigate the potential of asteroseismology to uncover the nature of blue supergiants. We construct stellar models for the above scenarios and show that they predict $g$-mode period spacings that differ by an order of magnitude: $\sim$ 200~min versus $\sim$ 20~min for long-lived core H and He burning stars, respectively. For the classical scenario of H-shell-burning stars rapidly crossing the Hertzsprung gap, we furthermore predict changes of the order of $10^{-2}\,\mu\rm{Hz\,yr}^{-1}$ in high-frequency modes; this effect would be in principle observable from $\sim 5$~yr of asteroseismic monitoring if these modes can be identified. This raises the possibility of revealing the internal structure of blue supergiants, and thus determining whether these stars are indeed binary merger products. These asteroseismic diagnostics may be measurable through long time-series observations from the ongoing TESS mission and upcoming PLATO mission, thereby laying a path toward resolving the blue supergiant problem.