The Disruption of Binary Star Systems by Massive Black Holes and the Restricted 3-Body Problem
Hyper-velocity stars are stars that have been accelerated to speeds in excess of the escape velocity of the galaxy. The first hyper-velocity star observed was found in 2005 by Brown et. al. (2005) and to date we can confirm 25 stars as being hyper-velocity. The small number of these stars discovered is due to the relatively low rate of acceleration events as well as observational methods limiting observations to B type stars. The leading processes by which these stars may be accelerated are binary tidal disruption events in the center of our galaxy. A binary tidal disruption event occurs when a binary star system orbits close to a massive compact object, such as a massive black hole. When this occurs the binary members are separated and one of the binary members gains the orbital energy of its partner, ejecting it at high speeds leaving the partner bound to the black hole. These bound stars, known as S-stars, have been observed and can be used to calculate the mass of the central massive black hole in our galaxy. In this thesis, I present the result of a series of simulations of binary tidal disruption. These simulations provide insight into the required parameters to trigger a binary tidal disruption event as well as the properties of stars ejected via these events. My simulations utilize a restricted three body model to reduce the parameter space that I need to explore to simply the binary orientation, binary phase angle and the penetration depth D, that being the ratio of the closest distance the binary center of mass approaches to the black hole and the tidal radius. This approximation models binaries as having zero energy parabolic orbits but also allows me to model the binary orbit as radial for binaries that have orbits bringing them extremely close to the massive black hole. I will firstly show how the disruption rate behaves as a function of the individual initial conditions of the binary. As the penetration depth shrinks the majority of binaries will be disrupted, however as the penetration depth approaches zero there are still approximately 12\% of binaries that survive their orbit around the black hole. The magnitude of velocity gained by the ejected stars is relatively independent of penetration depth with ejected stars having energies of the order of $E \approx (Gm^2/a)(M/m)^{1/3}$ where $m$ is the mass of the binary, $M$ is the black hole mass and $a$ is the binary separation. Hyper-velocity stars seen in my simulations are only rarely ejected with energies greater or less than this order of magnitude. Because of this the distribution of binary properties (binary and black hole masses, and binary separation) is more important to the spectrum of hyper-velocity stars than the distribution of injection parameters (penetration depth, binary orientation binary phase, and eccentricity). While the average disruption rate can be well defined with penetration depth for a given orientation the disruption dependency is more complex with prograde orbits being favoured for disruption in shallow penetrations $D\approx 1\sim 2$, while binaries oriented with their angular momentum vector toward the black hole are favored in deep penetrations $D\ll 1$. Secondly I consider the disruption rate in terms of the binary phase at the periapsis of its orbit and attempt to constrain the critical criteria that determine the fate of the binary. By looking at binary disruption in terms of free solutions in the radial approximation I can approximate the range of binary phase angles that will survive their encounter with the black hole. Thirdly I explore the properties of the former partners of hyper-velocity stars that remain bound to the black hole in terms of their eccentricity. I find that post disruption bound stars have eccentricities close to unity. This is significantly higher than observed S-stars in our galaxy, suggesting stars in the center of our galaxy have undergone relaxation over time. Finally I discuss the implications of binary interactions for gravitational wave astronomy. Binaries that survive these orbits will have their own internal orbits shifted, gaining significant eccentricity and potentially having their semi-major axis changed. As surviving binaries have their orbits deformed, the inspiral time for binary compact objects can be decreased significantly.
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