Matching seismic masses for RR Lyrae-type and oscillating red horizontal-branch stars in M4

Globular clusters offer a powerful way to test the properties of stellar populations and the late stages of low-mass stellar evolution. In this paper we study oscillating giant stars and overtone RR Lyrae-type pulsators in the nearest globular cluster, M4, with the help of high-precision, continuous light curves collected by the Kepler space telescope in the K2 mission. We determine the frequency composition of five RRc stars and model their physical parameters with a grid of linear pulsation models. We are able, for the first time, to compare seismic masses of RR Lyrae stars directly to the masses of the very similar red horizontal branch stars in the same stellar population, independently determined from asteroseismic scaling relations. We find a close match, with an average seismic mass of $0.651\pm0.028\,M_\odot$ for RR Lyrae stars and $0.657\pm0.034\,M_\odot$ for red horizontal-branch stars. While the validity of our RR Lyrae masses still relies on the similarity of neighboring horizontal branch subgroups, this result strongly indicates that RRc stars may indeed exhibit high-degree, $l = 8$ and 9 non-radial modes, and modeling these modes can provide realistic mass estimates. We also determine the He content of the cluster to be $Y = 0.266\pm 0.008$, and compare the seismic masses for our sample of RR Lyrae to theoretical mass relations and highlight the limitations of these relations.