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 $R_{\rm{HK}}^{'}$ 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.