Dynamics of passing-stars-perturbed binary star systems

In this work, we investigate the dynamical effects of a sequence of close encounters over 200 Myr varying in the interval of 10000 -- 100000 au between a binary star system and passing stars with masses ranging from 0.1$M_{\odot}$ to 10$M_{\odot}$. We focus on binaries consisting of two Sun-like stars with various orbital separations $a_{\scriptscriptstyle 0}$ from 50 au to 200 au initially on circular-planar orbits. We treat the problem statistically since each sequence is cloned 1000 times. Our study shows that orbits of binaries initially at $a_{\scriptscriptstyle 0}$ = 50 au will slightly be perturbed by each close encounter and exhibit a small deviation in eccentricity (+0.03) and in periapsis distance (+1 and -2 au) around the mean value. However increasing $a_{\scriptscriptstyle 0}$ will drastically increase these variances: up to +0.45 in eccentricity and between +63 au and -106 au in periapsis, leading to a higher rate of disrupted binaries up to 50% after the sequence of close encounters. Even though the secondary star can remain bound to the primary, $\sim$20% of the final orbits will have inclinations greater than 10$^{\circ}$. As planetary formation already takes place when stars are still members of their birth cluster, we show that the variances in eccentricity and periapsis distance of Jupiter- and Saturn-like planets will inversely decrease with $a_{\scriptscriptstyle 0}$ after successive fly-bys. This leads to higher ejection rate at $a_{\scriptscriptstyle 0}$ = 50 au but to a higher extent for Saturn-likes (60%) as those planets' apoapsis distances cross the critical stability distance for such binary separation.