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tokens: we adopt the relation M star = M core /2, to ensure that the total mass of stars in our Class 0 binaries does not exceed that of their host cores. We may then rewrite equation ( 5 ) as After dividing equation ( 6 ) by equation ( 3 ), we find The numerical value for this ratio is actually an upper bound. First, Class 0 stars may have masses that are less than M core /2. Second, we have ignored the fact that the density distribution in the core is centrally peaked (see e.g. Jørgensen et al. 2007 ). Both corrections act to lower the ratio, but not by a lot. For example, if M star / M core is correct, but the interior density is 10 times the mean (an extreme assumption), then r star / r 0 falls to just 0.23. The lesson, in any case, is that the widest Class 0 binaries, which are presumably the youngest, are bound to their host core and not to each other. Nevertheless, the net force pulling on each star is inwards 4 towards the companion star, causing the two stars to drift together even as they are gathering mass from the core. The stars initially share the rotational motion of the core, but their transverse speed subsequently increases by conservation of angular momentum. Once their separation falls below the critical value, the stars attract each other and enter a true binary orbit. Inward drift continues and accelerates as angular momentum is transferred to the background gas via dynamical friction. Stahler ( 2010 ) has provided an analytic treatment for this orbital decay. Simulations of orbital shrinking indicate the process primarily occurs at early times. Offner et al. ( 2016 ) explored binary formation and evolution in magnetohydrodynamical simulations, and found that binaries with separations of few 10 3 au could shrink to separations of 100 au in only 0.1 Myr. Similarly, Bate, Bonnell Bromm ( 2002 ) found that wide binaries could produce very close binaries through accretion processes or via dynamical interactions while the stars are embedded in a gas-rich core. The optimal w_sb model gives a shrinking time-scale of t s / t 0 = 1.39, which becomes t s ≈ 0.28 Myr for t 0 = 0.2 Myr. (Note that the ejection models explored in Appendix A yield a similar shrinking rate for the optimal w_sb* model.) This shrinking rate is about three times longer than what was obtained by Offner et al. ( 2016 ) for a 4 M ⊙ core. Most of the cores in Perseus have masses of ∼1 M ⊙ (Sadavoy et al. 2010 ), so an average t s ≈ 0.3 Myr may still be in rough agreement with the simulations. Both the w_sb and w_sb* models predict that binary shrinking occurs primarily during the embedded phase, as is also found by simulations. Thus, our simple evolutionary models broadly agree with the theoretical studies currently available. Finally, our observations show that relatively tight binaries have random orientations with respect to their host cores, a situation that does not hold for the predominantly aligned wide binaries (recall Fig. 5 ). Thus, the processes