Unlike partially convective stars such as the Sun, fully convective stars do not possess a radiative core. Whether a star needs this core to generate a solar-like magnetic dynamo is still unclear. Recent studies suggest fully and partially convective stars exhibit very similar period-activity relationships, hinting that dynamos generated by stars with and without radiative cores hold similar properties. Here, using kinematic ages, we discover an abrupt change in the stellar spin-down law across the fully convective boundary. We found that fully convective stars exhibit a higher angular momentum loss rate, corresponding to a torque that is ~1.51 times higher for a given angular velocity than partially convective stars around the fully convective boundary. Because stellar-wind torques depend primarily on large-scale magnetic fields and mass-loss rates, both of which are suggested to be similar for partially and fully convective stars, the observed abrupt change in spin-down law suggests that the dynamos of partially and fully convective stars may be fundamentally different.

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