We study the tidal disruption of binaries by a massive point mass (e.g., the black hole at the Galactic center), and we discuss how the ejection and capture preference between unequal-mass binary ...members depends on which orbit they approach the massive object. We show that the restricted three-body approximation provides a simple and clear description of the dynamics. The orbit of a binary with mass m around a massive object M should be almost parabolic with an eccentricity of |1 - e| <, ~ (m/M) super(1/3) << 1 for a member to be captured, while the other is ejected. Indeed, the energy change of the members obtained for a parabolic orbit can be used to describe non-parabolic cases. If a binary has an encounter velocity much larger than (M/m) super(1/3) times the binary rotation velocity, it would be abruptly disrupted, and the energy change at the encounter can be evaluated in a simple disruption model. We evaluate the probability distributions for the ejection and capture of circular binary members and for the final energies. In principle, for any hyperbolic (elliptic) orbit, the heavier member has more chance to be ejected (captured), because it carries a larger fraction of the orbital energy. However, if the orbital energy is close to zero, the difference between the two members becomes small, and there is practically no ejection and capture preferences. The preference becomes significant when the orbital energy is comparable to the typical energy change at the encounter. We discuss its implications to hypervelocity stars and irregular satellites around giant planets.
The observed size distribution of Kuiper belt objects (KBOs)—small icy and rocky Solar System bodies orbiting beyond Neptune—is well described by a power law at large KBO sizes. However, recent work ...by Bernstein et al. (2004, Astron. J. 128, 1364–1390) indicates that the size distribution breaks and becomes shallower for KBOs smaller than about 70 km in size. Here we show that we expect such a break at KBO radius
∼
40
km
since destructive collisions are frequent for smaller KBOs. Specifically, we assume that KBOs are gravity-dominated bodies with negligible material strength. This gives a power-law slope
q
≃
3
where the number
N
>
r
of KBOs larger than a size
r is given by
N
>
r
∝
r
1
−
q
; the break location follows from this slope through a self-consistent calculation. The existence of this break, the break's location, and the power-law slope we expect below the break are consistent with the findings of Bernstein et al. (2004, Astron. J. 128, 1364–1390). The agreement with observations indicates that KBOs as small as
∼
40
km
are effectively strengthless.
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