Late-type main sequence stars exhibit an x-ray to bolometric flux ratio that depends on { \tilde { R } o } , the ratio of rotation period to convective turnover time , as { \tilde { R } o } ^ { - \zeta } with 2 \leq \zeta \leq 3 for { \tilde { R } o } > 0.13 , but saturates with | \zeta| < 0.2 for { \tilde { R } o } < 0.13 .
Saturated stars are younger than unsaturated stars and show a broader spread of rotation rates and x-ray activity .
The unsaturated stars have magnetic fields and rotation speeds that scale roughly with the square root of their age , though possibly flattening for stars older than the sun .
The connection between faster rotators , stronger fields , and higher activity has been established observationally , but a theory for the unified time-evolution of x-ray luminosity , rotation , magnetic field and mass loss that captures the above trends has been lacking .
Here we derive a minimalist holistic framework for the time evolution of these quantities built from combining a Parker wind with new ingredients : ( 1 ) explicit sourcing of both the thermal energy launching the wind and the x-ray luminosity via dynamo produced magnetic fields ; ( 2 ) explicit coupling of x-ray activity and mass loss saturation to dynamo saturation ( via magnetic helicity build-up and convection eddy shredding ) ; ( 3 ) use of coronal equilibrium to determine how magnetic energy is divided into wind and x-ray contributions .
For solar-type stars younger than the sun , we infer conduction to be a subdominant power loss compared to x-rays and wind .
For older stars , conduction is more important , possibly quenching the wind and reducing angular momentum loss .
We focus on the time evolution for stars younger than the sun , highlighting what is possible for further generalizations .
Overall , the approach shows promise toward a unified explanation of all of the aforementioned observational trends .