The Velocity Distribution of Hypervelocity Stars

We consider the process of stellar binaries tidally disrupted by a supermassive black hole. For highly eccentric orbits, as one star is ejected from the three-body system, the companion remains bound to the black hole. Hypervelocity stars (HVSs) observed in the Galactic halo and S-stars observed orbiting the central black hole may originate from such mechanism. In this paper, we predict the velocity distribution of the ejected stars of a given mass, after they have travelled out of the Galactic potential. We use both analytical methods and Monte Carlo simulations. We find that each part of the velocity distribution encodes different information. At low velocities < 800 km/s, the Galactic Potential shapes universally the observed distribution, which rises towards a peak, related to the Galactic escape velocity. Beyond the peak, the velocity distribution depends on binary mass and separation distributions. Finally, the finite star life introduces a break related to their mass. A qualitative comparison of our models with current observations shows the great potential of HVSs to constrain bulge and Galactic properties. Standard choices for parameter distributions predict velocities below and above ~800 km/s with equal probability, while none are observed beyond ~700 km/s and the current detections are more clustered at low velocities 300-400 km/s. These features may indicate that the separation distribution of binaries that reach the tidal sphere is not flat in logarithmic space, as observed in more local massive binaries, but has more power towards larger separations, enhancing smaller velocities. In addition, the binary formation/evolution process or the injection mechanism might also induce a cut-off at ~ 10 solar radii in the separation distribution.

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