  HD 81809 has one of the highest quality activity cycles from the sample of
stars synoptically observed in the Mount Wilson Observatory HK Project.
However, this object is in fact a binary system, raising the question as to
which of the components is responsible for the observed cyclic activity and
what are the properties of that active component. The Hipparcos spacecraft
obtained resolved two-color photometry for this system that indicates that both
components are near the solar temperature. Combined with the precise Gaia
parallax and empirical bolometric corrections we derive component luminosities
of L_A = 5.8 +/- 0.3 Lsun and L_B = 1.025 +/- 0.055 Lsun, and radii R_A = 2.42
+/- 0.08 Rsun and R_B = 1.04 +/- 0.04 Rsun, confirming that the primary
component is a subgiant. We perform an independent estimate of the rotation
period of the A component based on vsini and find that it agrees with the 40.2
d period previously measured from the Ca HK time series. We explore plausible
scenarios for the deconvolved S-index and find that a cycling A component would
have an activity level within the bounds of ensemble activity-rotation trends,
while a cycling B component likely does not. Based on the available rotation
and activity evidence, we find the most likely characterization of the system
is a subgiant primary component responsible for the smooth cyclic behavior in
Ca HK with log(R'_HK) ~ -4.89, while the secondary component has relatively
flat activity at log(R'_HK) ~ -5.02.
