Age uncertainties of red giants due to cumulative rotational mixing of progenitors calibrated by asteroseismology

Abstract

Galactic archaeology largely relies on precise ages of distant evolved stars in the Milky Way. Nowadays, asteroseismology can deliver ages for many red giants observed with high-cadence, high-precision photometric space missions. Our aim is to quantify age uncertainties of slowly-rotating red giants due to the cumulative effect of their fast rotation during core-hydrogen burning. Their rotation in earlier evolutionary phases caused mixing resulting in heavier helium cores and the prolongation of their main sequence. These rotational effects are usually ignored when age-dating red giants, despite our knowledge of fast rotation for stars with $M\ge1.3\,$M$_\odot$. We use a sample of 490 $γ$ Doradus pulsators with precise asteroseismic estimates of their internal rotation rate and with luminosity estimates from Gaia. For this sample, which includes stars rotating from nearly 0 to about 60% of the critical rate, we compute the cumulative effect on the age in their post-main sequence evolution caused by rotational mixing on the main sequence. We use stellar model grids with different physical prescriptions mimicking rotational mixing to assess systematic uncertainties on the age. With respect to non-rotating models, the sample of 490 stars, as red giant progenitors, reveals age differences up to 5% by the time they start hydrogen-shell burning when relying on the theory of rotationally induced diffusive mixing as included in the MIST isochrones. Using rotational mixing based on an advective-diffusive approach including meridional circulation leads to an age shift of 20% by the time of the TRGB. Age-dating of red giants is affected by the cumulative effect of rotational mixing during the main sequence. Such rotationally-induced age shifts should be taken into account in addition to other effects if the aim is to perform Galactic archaeological studies at the highest precision. (abridged)