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 L _ { \mathrm { H \alpha } } /L _ { \mathrm { bol } } \sim - 3.5 .
This unambiguously confirms the M dwarf saturation-type rotation-activity relation .