Wide binary stars formed in the turbulent interstellar medium

The ubiquitous interstellar turbulence regulates star formation and the scaling relations between the initial velocity differences and the initial separations of stars. We propose that the formation of wide binaries with initial separations $r$ in the range $\sim 10^3~\text{AU} \lesssim r \lesssim 10^5$ AU is a natural consequence of star formation in the turbulent interstellar medium. With the decrease of $r$, the mean turbulent relative velocity $v_\text{tur}$ between a pair of stars decreases, while the largest velocity $v_\text{bon}$ at which they still may be gravitationally bound increases. When $v_\text{tur} < v_\text{bon}$, a wide binary can form. In this formation scenario, we derive the eccentricity distribution $p(e)$ of wide binaries for an arbitrary relative velocity distribution. By adopting a turbulent velocity distribution, we find that wide binaries at a given initial separation generally exhibit a superthermal $p(e)$. This provides a natural explanation for the observed superthermal $p(e)$ of the wide binaries in the Solar neighborhood.