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Most stars, binaries, and higher multiplicity systems are thought to form instellar clusters and associations, which later dissociate. Very wide binariescan be easily disrupted in clusters due to dynamical evaporation (softbinaries) and/or due to tidal disruption by the gravitational potential of thecluster. Nevertheless, wide binaries are quite frequent in the field, wherethey can sometimes play a key role in the formation of compact binaries, andserve as tools to study key physical processes. Here we use analytic tools tostudy the dynamical formation of soft binaries in clusters, and their survivalas field binaries following cluster dispersion. We derive the expectedproperties of very wide binaries both in clusters and in the field. Weanalytically derive their detailed distributions, including wide-binaryfraction as a function of mass in different cluster environments, binaries massfunctions and mass ratios, and the distribution of their orbital properties. Weshow that our calculations agree well on most aspects with the results ofN-body simulations, but show some different binary-fraction dependence on thecluster mass. We find that the overall fraction of wide binaries scales as$\propto N_\star^{-1}$ where $N_\star$ is the size of the cluster, even fornon-equal mass stars. More massive stars are more likely to capture widecompanions, with most stars above five solar mass likely to capture at leastone stellar companion, and triples formation is found to be frequent.

Born to be wide: the distribution of wide binaries in the field and soft binaries in clusters