Fig. 1.
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Geometry of a circular binary system. The system is comprised of a star, which is destined to experience complete collapse into a BH, and its companion. In this case, the object is represented as a BH. The reference frame is centred on the star at the moment of collapse, and its defined by the radial (r), tangential (t), and polar (p) orthogonal axes. In this frame, the orbital plane is defined as the r − t plane, with the orbital angular momentum vector (Jorb) along the p-axis. A natal kick on the collapsing star may have components in radial, tangential, and polar directions. The binary orbit is prograde (or retrograde) if the component spins of the star and black hole (BH) are aligned (or anti-aligned) with the orbital angular momentum vector.
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