Dynamical Stability of Earth‐like Planetary Orbits in Binary Systems

This paper explores the stability of an Earth-like planet orbiting a solarmass star in the presence of an outer-lying intermediate mass companion. Theoverall goal is to estimate the fraction of binary systems that allowEarth-like planets to remain stable over long time scales. We numericallydetermine the planet's ejection time $\tauej$ over a range of companion masses($M_C$ = 0.001 -- 0.5 $M_\odot$), orbital eccentricities $\epsilon$, andsemi-major axes $a$. This suite of $\sim40,000$ numerical experiments suggeststhat the most important variables are the companion's mass $M_C$ and periastrondistance $\rmin$ = $a(1-\epsilon)$ to the primary star. At fixed $M_C$, theejection time is a steeply increasing function of $\rmin$ over the range ofparameter space considered here (although the ejection time has a distributionof values for a given $\rmin$). Most of the integration times are limited to 10Myr, but a small set of integrations extend to 500 Myr. For each companionmass, we find fitting formulae that approximate the mean ejection time as afunction of $\rmin$. These functions can then be extrapolated to longer timescales. By combining the numerically determined ejection times with theobserved distributions of orbital parameters for binary systems, we estimatethat (at least) 50 percent of binaries allow an Earth-like planet to remainstable over the 4.6 Gyr age of our solar system.Comment: Accepted for publication to PASP, 26 pages including 9 figure