Mean density inversions for red giants and red clump stars

Since the CoRoT and Kepler missions, the availability of high-quality seismic spectra for red giants has made them the standard clocks and rulers for Galactic Archeology. With the expected excellent data from the TESS and PLATO missions, red giants will again play a key role in Galactic studies and stellar physics, thanks to the precise masses and radii determined by asteroseismology. The determination of these quantities is often based on so-called scaling laws, which have been used extensively for main-sequence stars. We show how the SOLA inversion technique can provide robust determinations of the mean density of red giants within 1 per cent of the real value, using only radial oscillations. Combined with radii determinations from Gaia of around 2 per cent precision, this approach provides robust, less model-dependent masses with an error lower than 10 per cent. It will improve age determinations, helping to accurately dissect the Galactic structure and history. We present results on artificial data of standard models, models including an extended atmosphere from averaged 3D simulations and non-adiabatic frequency calculations to test surface effects, and on eclipsing binaries. We show that the inversions provide very robust mean density estimates, using at best seismic information. However, we also show that a distinction between red-giant branch and red-clump stars is required to determine a reliable estimate of the mean density. The stability of the inversion enables an implementation in automated pipelines, making it suitable for large samples of stars.