Encounters between Single and Binary Stars: The Effect of Intruder Mass on the Maximum Impact Velocity for Which the Mean Change in Binding Energy is Positive

A close encounter between a binary and an intruder will, on average, increase the orbital binding energy of the binary if the impact velocity V is below some critical value V_E. It will decrease it if V > V_E. The folklore that this crossover velocity V_E is the critical velocity V_HS separating hard binaries from soft binaries is false. (Hard binaries have enough binding energy for the total energy of the three-star system to be negative.) V_E is found to depend on the ratio of the mass of the intruder to the mass of the binary components. In the case of equally massive binary components, only if all three stars are equally massive does V_E ≈ V_HS. In close encounters with low-mass intruders, the binding energy decreases even when the impact velocity of the intruder is an order of magnitude less than V_HS. V_E increases to nearly 4 V_HS for intruders ten times as massive as the binary components. It then increases gradually to nearly 10 V_HS for intruders 10⁴ times as massive as the binary components. V_orbital, the initial orbital velocity in the pre-encounter binary, is: a better approximation to V_E than is V_HS. V_E is within a factor of 2 of V_orbital if the intruder is less than 100 times as massive as the binary components. V_E increases to about 5V_orbital for intruders l0⁴ times as massive as the binary components. These results suggest that it is much better to speak of the "slow-intruder" limit and the "fast-intruder" limit when gauging if an encounter will cause the binding energy of the binary orbit to increase or decrease rather than the customary "hard-binary" and "soft-binary" limits. A binary will increase its binding energy in en- counters in the slow-intruder limit and decrease it in the fast-intruder limit.