Using the most recent kinematic and radial velocity data in the literature, we calculate the binding energy of Proxima Centauri relative to the center of mass of the α Centauri system. When we adopt the centroids of the observed data, we find that the three stars constitute a bound system, albeit with a semimajor axis that is of order the same size as α Cen AB's Hill radius in the Galactic potential. We carry out a Monte Carlo simulation under the assumption that the errors in the observed quantities are uncorrelated. In this simulation, 44% of the trial systems are bound, and systems on the 1-3 σ tail of the radial velocity distribution can have Proxima currently located near the apastron position of its orbit. Our analysis shows that a further, very significant improvement in the characterization of the system can be gained by obtaining a more accurate measurement of the radial velocity of Proxima Cen.
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