A core-sensitive mixed $f$/$g$ mode of the Sun predicted by wave topology and hydrodynamical simulation

Helioseismology has revolutionized our understanding of the Sun by analyzing its global oscillation modes. However, the solar core remains elusive, limiting a full understanding of its evolution. In this work, we study a previously unnoticed global oscillation mode of the Sun using a fully compressible, hydrodynamical simulation of the solar interior, and assess that it is a mixed $f$/$g$ mode with a period of about one hour. This is the first global stellar hydrodynamics simulation that successfuly couple compressible and gravity modes. To understand this coupling, we invoke a recent theory on the nature of $f$-modes seen through the prism of wave topology, characterizing their ability to propagate deep into stellar interiors. We demonstrate that the mixed $f$/$g$ mode is highly sensitive to the core's rotation rate, providing a new promising pathway to explore the Sun's core.