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We simulate the coupled stellar and tidal evolution of short-period binarystars (orbital period $P_{orb} \lsim$8 days) to investigate the orbitaloscillations, instellation cycles, and orbital stability of circumbinaryplanets (CBPs). We consider two tidal models and show that both predict anoutward-then-inward evolution of the binary's semi-major axis $a_{bin}$ andeccentricity $e_{bin}$. This orbital evolution drives a similar evolution ofthe minimum CBP semi-major axis for orbital stability. By expanding on previousmodels to include the evolution of the mass concentration, we show that themaximum in the CBP orbital stability limit tends to occur 100 Myr after theplanets form, a factor of 100 longer than previous investigations. This resultprovides further support for the hypothesis that the early stellar-tidalevolution of binary stars has removed CBPs from short-period binaries. We thenapply the models to Kepler-47 b, a CBP orbiting close to its host stars'stability limit, to show that if the binary's initial $e_{bin} \gsim$0.24, theplanet would have been orbiting within the instability zone in the past andprobably wouldn't have survived. For stable, hypothetical cases in which thestability limit does not reach a planet's orbit, we find that the amplitudes of$a_{bin}$ and $e_{bin}$ oscillations can damp by up to 10\% and 50\%,respectively. Finally, we consider equal-mass stars with $P_{orb} =$ 7.5 daysand compare the HZ to the stability limit. We find that for stellar masses$\lsim0.12M_{\odot}$, the HZ is completely unstable, even if the binary orbitis circular. For $e_{bin} \lsim$0.5, that limit increases to $0.17M_{\odot}$,and the HZ is partially destabilized for stellar masses up to $0.45M_{\odot}$.These results may help guide searches for potentially habitable CBPs, as wellas characterize their evolution and likelihood to support life after they arefound.

Orbital evolution of potentially habitable planets of tidally interacting binary stars