Decoupling mixed modes: Stretched frequency recovers pure p modes

Non-radial oscillations in red giants exhibit mixed character due to the coupling of p and g modes. This results in uneven spacings in both periods and frequencies for these mixed modes, complicating the analysis of p- or g-mode cavities. An existing technique — the stretched period — aims to transform mixed-mode frequencies into the underlying true g-mode frequencies. This enables direct analysis of g-mode period spacings, buoyancy glitches, as well as rotational and magnetic splittings. In this work, we introduce a complementary approach — the stretched frequency — that reconstructs the true p-mode frequencies from mixed modes. We demonstrate its important applications, including (1) the mode identification of dipolar mixed modes, (2) the identification of acoustic glitches using non-radial modes, and (3) the accurate correction of surface effects for mixed modes, without order shifting as encountered in standard methods that rely solely on mode inertia. The newly introduced stretched frequency method, along with the stretched period, forms a new array of methods that fully decouple the information from mixed modes for the first time, providing insights into the oscillation properties of red giants and better tools for stellar modeling.