Varying core-envelope coupling efficiency identified from stellar rotation--activity relation

Core-envelope coupling provides a reasonable explanation of the spin-down stalling of stars in open clusters, which was not predicted by classical gyrochronology. However, it remains an open question whether the coupling efficiency is constant or variable. M dwarfs, possessing thicker convective envelopes and thus longer coupling timescales than other late-type stars, are ideal objects for this investigation. In this work, based on the $R_{\mathrm{H}\mathrm{K}}^{{}^{\mathrm{\prime }}}$ measurements from LAMOST and DESI spectra, we construct new rotation–activity relations for M dwarfs. Unlike the traditional picture, we suggest that the new relation consists of three distinct regimes of fast, intermediate, and slow rotation, closely matching the three sequences of gyrochronology, namely the Convective'' sequence, Gap’‘, and Interface'' sequence. Our study reveals, for the first time, a variable activity decay rate in the intermediate-rotation regime (i.e., the Gap’’ region). This implies a varying core-envelope coupling efficiency, peaking towards the end of this region. It also coincides with the well-known stage of stalled stellar spin-down.