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Oscillation modes with a mixed character, as observed in evolved low-mass stars, are highly sensitive to the physical properties of the innermost regions. Measuring their properties is therefore extremely important to probe the core, but requires some care, due to the complexity of the mixed-mode pattern. This work aims at providing a consistent description of the mixed-mode pattern of low-mass stars, based on the asymptotic expansion. We also aim at studying the variation of the gravity offset $varepsilon_{g}$ with stellar evolution. We revisit previous work about mixed modes in red giants and empirically test how period spacings, rotational splittings, mixed-mode widths and heights can be estimated in a consistent view, based on the properties of the mode inertia ratios. From the asymptotic fit of the mixed-mode pattern of a large set of red giants at various evolutionary stages, we derive unbiased and precise asymptotic parameters. As the asymptotic expansion of gravity modes is verified with a precision close to the frequency resolution for stars on the red giant branch (10$^{-4}$ in relative values), we can derive accurate values of the asymptotic parameters. We decipher the complex pattern in a rapidly rotating star, and explain how asymmetrical splittings can be inferred, as well as the stellar inclinations. This allows us to revisit the stellar inclinations in two open clusters, NGC 6819 and NGC 6791: our results show that the stellar inclinations in these clusters do not have privileged orientation in the sky. The variation of the asymptotic gravity offset along with stellar evolution is investigated in detail. We also derive generic properties that explain under which conditions mixed modes can be observed.
The power of asteroseismology relies on the capability of global oscillations to infer the stellar structure. For evolved stars, we benefit from unique information directly carried out by mixed modes that probe their radiative cores. This third artic
Dipole mixed pulsation modes of consecutive radial order have been detected for thousands of low-mass red-giant stars with the NASA space telescope Kepler. Such modes have the potential to reveal information on the physics of the deep stellar interio
With recent advances in asteroseismology it is now possible to peer into the cores of red giants, potentially providing a way to study processes such as nuclear burning and mixing through their imprint as sharp structural variations -- glitches -- in
Asteroseismology allows us to probe the physical conditions inside the core of red giant stars. This relies on the properties of the global oscillations with a mixed character that are highly sensitive to the physical properties of the core. However,
When a star evolves into a red giant, the enhanced coupling between core-based gravity modes and envelope-based pressure modes forms mixed modes, allowing its deep interior to be probed by asteroseismology. The ability to obtain information about ste