M dwarf companions to white dwarfs I: relating magnetic activity, rotation and age

We make use of the largest and most homogeneous sample of white dwarf/M dwarf (WD/dM) binaries from the Sloan Digital Sky Survey (SDSS DR7) to investigate relations between magnetic activity, rotation, magnetic braking and age in M stars. These relations are studied separately for close WD/dM binaries that underwent a common envelope phase and thus contain tidally locked and hence rapidly rotating M dwarfs, and for wide WD/dM binaries that never interacted. For the wide WD/dM binary sample we find that the M dwarf activity fractions are significantly higher than those measured in single M stars of spectral type M0 to M5. We attribute this effect as a consequence of M dwarfs in wide SDSS WD/dM binaries being, on average, significantly younger and hence more active than the field M dwarf population. The measured M dwarf activity fractions in wide WD/dM binaries show as well a significant increase from spectral types M3 to M5, where these low-mass stars become fully convective. This provides additional observational evidence for magnetic braking being less efficient below the fully convective boundary, in agreement with the hypothesis of fully convective stars having considerably longer activity lifetimes than partially convective stars. The M dwarfs in all our close binaries are active, independently of the spectral type, giving robust observational evidence for magnetic activity being enhanced due to fast rotation. The rotational velocities of the M dwarfs in our close binary sample are significantly higher than seen among field M dwarfs, however the strength of magnetic activity remains saturated at log LHalpha/Lbol approximately -3.5. This unambiguously confirms the M dwarf saturation-type rotation-activity relation.