X iv : a st ro - p h / 06 10 79 9 v 2 2 7 O ct 2 00 6 Origin of the Break and Mass - Dependence in the Wide - Binary Projected - Separation Distribution

The distribution of Galactic-disk wide binaries shows a clear break in slope at projected separations of about r ⊥ ∼ 2500 AU in two basically independent surveys by Chanamé & Gould and Lépine & Bongiorno. The latter also showed that the frequency of wide-binary companions to G-star primaries declines mono-tonically as a function of companion mass. We show that both effects can be explained by the operation of Heggie's law in the typical open-cluster environments where binaries form. One immediate conclusion is that most Galactic-disk stars formed in open clusters with internal dispersions of a few hundred meters per second and disruption times of a few hundred million years. Two separate studies demonstrate that there is break in the distribution of Galactic-disk wide-binary separations at about r ⊥ ∼ 2500 AU. For large separations, ∆θ 30 ′′ , Chanamé & Gould (2004) find a power-law distribution dN/d∆θ ∼ ∆θ −α , with α = 1.67 ± 0.07, while for 10 ′′ ∆θ 30 ′′ , they find a flat " Opik's (1924) Law " distribution, i.e., α ∼ 1. Because the characteristic distance of the Chanamé & Gould (2004) sample is about d ∼ 60 pc, this angular-scale break point corresponds to a physical scale of r ⊥ ∼ d∆θ ∼ 1800 AU. Lépine & Bongiorno (2006) studied wide-binaries with Hipparcos (ESA 1997) primaries. Because their targets have parallaxes, they present their results directly in terms of r ⊥ (rather than ∆θ). They find a break at about r ⊥ ∼ 3000 AU. Each estimate is uncertain at about the 20% level. Lépine & Bongiorno (2006) are hampered by small number statistics near the break because their bright-primary sample does not permit them to probe inward of ∆θ < 20 ′′. On the other hand, while Chanamé & Gould (2004) probe to smaller angular separations and have much better statistics, it is difficult to make precise the interpretation of their angular break in terms of physical scales because of the substantial uncertainties in the individual distances of their sample. Thus, the two studies are broadly consistent. Moreover, as we will