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We constrain the orbital period ($P_{\rm orb}$) distribution of low-massdetached main-sequence eclipsing binaries (EBs) with light curves from theZwicky Transient Facility (ZTF), which provides a well-understood selectionfunction and sensitivity to faint stars. At short periods ($P_{\rm orb}\lesssim2$ days), binaries are predicted to evolve significantly due to magneticbraking (MB), which shrinks orbits and ultimately brings detached binaries intocontact. The period distribution is thus a sensitive probe of MB. We find thatthe intrinsic period distribution of low-mass ($0.1\lesssim M_1/M_{\odot} <0.9$) binaries is basically flat (${\rm d}N/{\rm d}P_{\rm orb} \propto P_{\rmorb}^0$), from $P_{\rm orb}=10$ days down to the contact limit. This isstrongly inconsistent with predictions of classical MB models based on theSkumanich relation, which are widely used in binary evolution calculations andpredict ${\rm d}N/{\rm d}P_{\rm orb} \propto P_{\rm orb}^{7/3}$ at shortperiods. The observed distributions are best reproduced by models in which themagnetic field saturates at short periods, with a MB torque that scales roughlyas $\dot{J}\propto P_{\rm orb}^{-1}$, as opposed to $\dot{J} \propto P_{\rmorb}^{-3}$ in the standard Skumanich law. We also find no significantdifference between the period distributions of binaries containing fully andpartially convective stars. Our results confirm that a saturated MB law, whichwas previously found to describe the spin-down of rapidly rotating isolated Mdwarfs, also operates in tidally locked binaries. We advocate using saturatedMB models in binary evolution calculations. Our work supports previoussuggestions that MB in cataclysmic variables (CVs) is much weaker than assumedin the standard evolutionary model, unless mass transfer leads to significantadditional angular momentum loss in CVs.

Magnetic braking saturates: evidence from the orbital period distribution of low-mass detached eclipsing binaries from ZTF