Rotation at the Fully Convective Boundary: Insights from Wide WD + MS Binary Systems

Gyrochronology, a valuable tool for determining ages of low-mass stars where other techniques fail, relies on accurate calibration. We present a sample of 185 wide ($>$$100$ au) white dwarf + main sequence (WD + MS) binaries. Total ages of WDs are computed using all-sky survey photometry, Gaia parallaxes, and WD atmosphere models. Using a magnetic braking law calibrated against open clusters, along with assumptions about initial conditions and angular momentum transport, we construct gyrochrones to predict the rotation periods of MS stars. Both data and models show that, at the fully convective boundary (FCB), MS stars with WD ages up to 7.5 Gyr and within a $<50$ K effective temperature range experience up to a threefold increase in rotation period relative to stars slightly cooler than the FCB. We suggest that rapid braking at this boundary is driven by a sharp rise in the convective overturn timescale ($τ_{\mathrm{cz}}$) caused by structural changes between partially and fully convective stars and the $^3 \textrm{He}$ instability occurring at this boundary. While the specific location in mass (or temperature) of this feature varies with model physics, we argue that its existence remains consistent. Stars along this feature exhibit rotation periods that can be mapped, within 1$σ$, to a range of gyrochrones spanning $\approx 6$ Gyr. Due to current temperature errors ($\simeq$$50$ K), this implies that a measured rotation period cannot be uniquely associated to a single gyrochrone, implying that gyrochronology may not be feasible for M dwarfs very close to the FCB.