Wide-binary eccentricity distribution in young star clusters: dependence on the binary separation and mass

We study the wide-binary eccentricity ($e$) distribution in young star clusters and the role of turbulence in setting the form of the $e$ distribution using magnetohydrodynamical (MHD) simulations of star cluster formation. The simulations incorporate gravity, turbulence, magnetic fields, protostellar heating, and jets/outflows. We find that (1) simulations that employ purely compressive turbulence driving produce binaries with a superthermal $e$ distribution ($\alpha>1$ in $p(e) \propto e^\alpha$), while simulations with purely solenoidal driving or natural mixture of driving modes produce subthermal/thermal distributions ($\alpha \leq$ 1), (2) the $e$ distribution over the full range of binary separations in our simulations is set at the early stages of the star cluster formation process, (3) while binaries (separation of $r_{\mathrm{pair}} \leq 1000\, \mathrm{AU}$) have subthermal to thermal $e$ distributions ($\alpha \sim 0.8$), wide binaries ($r_{\mathrm{pair}} > 1000\, \mathrm{AU}$) have a superthermal distribution ($\alpha \sim 1.8$), and (4) low-mass binary systems (system masses of $M_{\mathrm{sys}} \leq 0.8\, \mathrm{M_\odot}$) have a highly superthermal distribution ($\alpha \sim 2.4$), whereas high-mass systems ($M_{\mathrm{sys}} > 0.8\, \mathrm{M_\odot}$) exhibit a subthermal/thermal distribution ($\alpha \sim 0.8$). The binary eccentricity distribution is often modelled as a thermal distribution. However, our results suggest that the $e$ distribution depends on the range of separation of the sampled binaries, which agrees with the findings from recent Gaia observations. We conclude that the dependence of the $e$ distribution on the binary separation and mass is linked to the binary formation mechanism governed by the turbulent properties of the parent cloud.