The Red-Giant Branch Bump Revisited: Constraints on Envelope Overshooting in a Wide Range of Masses and Metallicities

The red-giant branch bump provides valuable information for the investigation of the internal structure of low-mass stars. Because current models are unable to accurately predict the occurrence and efficiency of mixing processes beyond convective boundaries, one can use the luminosity of the bump --- a diagnostic of the maximum extension of the convective envelope during the first-dredge up --- as a calibrator for such processes. By combining asteroseismic and spectroscopic constraints, we expand the analysis of the bump to masses and metallicities beyond those previously accessible using globular clusters. Our dataset comprises nearly 3000 red-giant stars observed by {\it Kepler} and with APOGEE spectra. Using statistical mixture models, we are able to detect the bump in the average seismic parameters $\nu_{\rm max}$ and $\langle \Delta \nu \rangle$, and show that its observed position reveals general trends with mass and metallicity in line with expectations from models. Moreover, our analysis indicates that standard stellar models underestimate the depth of efficiently mixed envelopes. The inclusion of significant overshooting from the base of the convective envelope, with an efficiency that increases with decreasing metallicity, allows to reproduce the observed location of the bump. Interestingly, this trend was also reported in previous studies of globular clusters.